idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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52,201 | Test to compare user interfaces | The main thing is study design and perhaps less statistics.
Hypothesis
Your data will probably result try to answer the following questions:
Is interface A easier to understand than interface B
Does experience with a previous interface improve the second run
Does it matter if you tried system A first and then went on ... | Test to compare user interfaces | The main thing is study design and perhaps less statistics.
Hypothesis
Your data will probably result try to answer the following questions:
Is interface A easier to understand than interface B
Does | Test to compare user interfaces
The main thing is study design and perhaps less statistics.
Hypothesis
Your data will probably result try to answer the following questions:
Is interface A easier to understand than interface B
Does experience with a previous interface improve the second run
Does it matter if you tried ... | Test to compare user interfaces
The main thing is study design and perhaps less statistics.
Hypothesis
Your data will probably result try to answer the following questions:
Is interface A easier to understand than interface B
Does |
52,202 | Test to compare user interfaces | My take on this, which is admittedly biased by techniques I'm familiar with.
Study design: In your case, I think you can get away with a simple randomized design. I hesitate to have each subject try both GUI setups for two reasons: It complicates analysis, and its possible that greater familiarity with the "problem set... | Test to compare user interfaces | My take on this, which is admittedly biased by techniques I'm familiar with.
Study design: In your case, I think you can get away with a simple randomized design. I hesitate to have each subject try b | Test to compare user interfaces
My take on this, which is admittedly biased by techniques I'm familiar with.
Study design: In your case, I think you can get away with a simple randomized design. I hesitate to have each subject try both GUI setups for two reasons: It complicates analysis, and its possible that greater f... | Test to compare user interfaces
My take on this, which is admittedly biased by techniques I'm familiar with.
Study design: In your case, I think you can get away with a simple randomized design. I hesitate to have each subject try b |
52,203 | Test to compare user interfaces | Which test you have to use depends on the variables you intend to measure. A Likert type questionnaire needs a different test than time measurements. So first you need to know what the criteria are for the experimental interface to be better. Then you have to find out how to measure these and what measure constitutes a... | Test to compare user interfaces | Which test you have to use depends on the variables you intend to measure. A Likert type questionnaire needs a different test than time measurements. So first you need to know what the criteria are fo | Test to compare user interfaces
Which test you have to use depends on the variables you intend to measure. A Likert type questionnaire needs a different test than time measurements. So first you need to know what the criteria are for the experimental interface to be better. Then you have to find out how to measure thes... | Test to compare user interfaces
Which test you have to use depends on the variables you intend to measure. A Likert type questionnaire needs a different test than time measurements. So first you need to know what the criteria are fo |
52,204 | What methods can be used to specify priors from data? | If you have all this data, I think the best answer is to actually fit a single large model, using Hierarchical Modeling rather than do it in two steps (generating a prior then fitting a model). This is basically the answer I gave to this question. I explain this a little bit more there.
In a hierarchical model you mod... | What methods can be used to specify priors from data? | If you have all this data, I think the best answer is to actually fit a single large model, using Hierarchical Modeling rather than do it in two steps (generating a prior then fitting a model). This i | What methods can be used to specify priors from data?
If you have all this data, I think the best answer is to actually fit a single large model, using Hierarchical Modeling rather than do it in two steps (generating a prior then fitting a model). This is basically the answer I gave to this question. I explain this a l... | What methods can be used to specify priors from data?
If you have all this data, I think the best answer is to actually fit a single large model, using Hierarchical Modeling rather than do it in two steps (generating a prior then fitting a model). This i |
52,205 | What methods can be used to specify priors from data? | A useful way to incorporate data into a prior distribution is the principle of maximum entropy. You basically provide constraints that the prior distribution is to satisfy (e.g. mean, variance, etc.,etc.) and then choose the distribution which is most "spread out" that satisfies these constraints.
The distribution gen... | What methods can be used to specify priors from data? | A useful way to incorporate data into a prior distribution is the principle of maximum entropy. You basically provide constraints that the prior distribution is to satisfy (e.g. mean, variance, etc., | What methods can be used to specify priors from data?
A useful way to incorporate data into a prior distribution is the principle of maximum entropy. You basically provide constraints that the prior distribution is to satisfy (e.g. mean, variance, etc.,etc.) and then choose the distribution which is most "spread out" ... | What methods can be used to specify priors from data?
A useful way to incorporate data into a prior distribution is the principle of maximum entropy. You basically provide constraints that the prior distribution is to satisfy (e.g. mean, variance, etc., |
52,206 | What methods can be used to specify priors from data? | I propose the following solution to 2), and would appreciate feedback:
Data include mean, $Y$, sample size $n$, and standard error $\sigma$; calculate precision ($\tau=\frac{1}{\sigma\sqrt{n}}$) because it is required for logN parameterization by BUGS
data $Y\sim \text{N}(\beta_0,\tau)$
precision $\tau\sim\text{Gamma}... | What methods can be used to specify priors from data? | I propose the following solution to 2), and would appreciate feedback:
Data include mean, $Y$, sample size $n$, and standard error $\sigma$; calculate precision ($\tau=\frac{1}{\sigma\sqrt{n}}$) beca | What methods can be used to specify priors from data?
I propose the following solution to 2), and would appreciate feedback:
Data include mean, $Y$, sample size $n$, and standard error $\sigma$; calculate precision ($\tau=\frac{1}{\sigma\sqrt{n}}$) because it is required for logN parameterization by BUGS
data $Y\sim \... | What methods can be used to specify priors from data?
I propose the following solution to 2), and would appreciate feedback:
Data include mean, $Y$, sample size $n$, and standard error $\sigma$; calculate precision ($\tau=\frac{1}{\sigma\sqrt{n}}$) beca |
52,207 | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated? | Well, it depends if the interaction was your main hypothesis or not. If this the case, then you are encouraged to report the negative result, otherwise you can simply refit your model (without the B and A:B terms) to get a better estimate of A.
Now, the part of your conclusion that you emphasized doesn't sound correct ... | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated? | Well, it depends if the interaction was your main hypothesis or not. If this the case, then you are encouraged to report the negative result, otherwise you can simply refit your model (without the B a | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated?
Well, it depends if the interaction was your main hypothesis or not. If this the case, then you are encouraged to report the negative result, otherwise you can simply refit your model (without the B and A:B terms) to get ... | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated?
Well, it depends if the interaction was your main hypothesis or not. If this the case, then you are encouraged to report the negative result, otherwise you can simply refit your model (without the B a |
52,208 | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated? | Please let me know if you have replicates in your experiment. As you mention using Tukey HSD, I am guessing you don't have any replicates. If you experiment analyzes test of additivity in a two-way factorial Analysis of Variance (ANOVA) with one observation per cell, then please read ahead or otherwise ignore my soluti... | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated? | Please let me know if you have replicates in your experiment. As you mention using Tukey HSD, I am guessing you don't have any replicates. If you experiment analyzes test of additivity in a two-way fa | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated?
Please let me know if you have replicates in your experiment. As you mention using Tukey HSD, I am guessing you don't have any replicates. If you experiment analyzes test of additivity in a two-way factorial Analysis of V... | If an ANOVA indicates no main effect and no interaction, should the lack of interaction be stated?
Please let me know if you have replicates in your experiment. As you mention using Tukey HSD, I am guessing you don't have any replicates. If you experiment analyzes test of additivity in a two-way fa |
52,209 | R command for stcox in Stata | In package survival, it's coxph. John Fox has a nice introduction to using coxph in R:
Cox Proportional-Hazards Regression for Survival Data | R command for stcox in Stata | In package survival, it's coxph. John Fox has a nice introduction to using coxph in R:
Cox Proportional-Hazards Regression for Survival Data | R command for stcox in Stata
In package survival, it's coxph. John Fox has a nice introduction to using coxph in R:
Cox Proportional-Hazards Regression for Survival Data | R command for stcox in Stata
In package survival, it's coxph. John Fox has a nice introduction to using coxph in R:
Cox Proportional-Hazards Regression for Survival Data |
52,210 | R command for stcox in Stata | In case you're looking for a quick code translation.
Assuming your Stata and R variables are the same...
stset time, failure(fail)
stcox var1 var2
in Stata translates to
library(survival)
coxph(Surv(time, fail) ~ var1 + var2)
in R assuming your dataframe is attached.
Note: if you're comparing results in R and Stata,... | R command for stcox in Stata | In case you're looking for a quick code translation.
Assuming your Stata and R variables are the same...
stset time, failure(fail)
stcox var1 var2
in Stata translates to
library(survival)
coxph(Surv( | R command for stcox in Stata
In case you're looking for a quick code translation.
Assuming your Stata and R variables are the same...
stset time, failure(fail)
stcox var1 var2
in Stata translates to
library(survival)
coxph(Surv(time, fail) ~ var1 + var2)
in R assuming your dataframe is attached.
Note: if you're comp... | R command for stcox in Stata
In case you're looking for a quick code translation.
Assuming your Stata and R variables are the same...
stset time, failure(fail)
stcox var1 var2
in Stata translates to
library(survival)
coxph(Surv( |
52,211 | Which Deep Learning Method to use for the classification of precious stones (diamonds, sapphire, ruby etc) based on digital photo images and data set? | Convolutional neural networks (CNNs) and/or vision transformers (both neural networks) with transfer learning would have been my first thought, too. However, there are situations, where that might not work so well. Note that in the work you cite, it seems like they had "2042 training images and 284 unseen (test) images... | Which Deep Learning Method to use for the classification of precious stones (diamonds, sapphire, rub | Convolutional neural networks (CNNs) and/or vision transformers (both neural networks) with transfer learning would have been my first thought, too. However, there are situations, where that might not | Which Deep Learning Method to use for the classification of precious stones (diamonds, sapphire, ruby etc) based on digital photo images and data set?
Convolutional neural networks (CNNs) and/or vision transformers (both neural networks) with transfer learning would have been my first thought, too. However, there are s... | Which Deep Learning Method to use for the classification of precious stones (diamonds, sapphire, rub
Convolutional neural networks (CNNs) and/or vision transformers (both neural networks) with transfer learning would have been my first thought, too. However, there are situations, where that might not |
52,212 | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease (such as in a CNN?) | From the documentation of np.convolve: "mode{‘full’, ‘valid’, ‘same’}, optional By default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen."
By contrast... | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease | From the documentation of np.convolve: "mode{‘full’, ‘valid’, ‘same’}, optional By default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease (such as in a CNN?)
From the documentation of np.convolve: "mode{‘full’, ‘valid’, ‘same’}, optional By default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At ... | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease
From the documentation of np.convolve: "mode{‘full’, ‘valid’, ‘same’}, optional By default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At |
52,213 | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease (such as in a CNN?) | The short answer is: this is how convolution works. As you can see e.g. in the examples at https://en.wikipedia.org/wiki/Convolution the support of the convolution is larger than that of the convoluted functions:
As Sycorax mentions, sometimes the tails are omitted for practical reasons. Note that in some application ... | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease | The short answer is: this is how convolution works. As you can see e.g. in the examples at https://en.wikipedia.org/wiki/Convolution the support of the convolution is larger than that of the convolute | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease (such as in a CNN?)
The short answer is: this is how convolution works. As you can see e.g. in the examples at https://en.wikipedia.org/wiki/Convolution the support of the convolution is larger than that of the convolute... | Why does a 1D convolution increase the size of the output, while a 2D convolution tends to decrease
The short answer is: this is how convolution works. As you can see e.g. in the examples at https://en.wikipedia.org/wiki/Convolution the support of the convolution is larger than that of the convolute |
52,214 | Validity of regression diagnostics for deterministic computer experiments | This question reminds me a bit of the question Could a mismatch between loss functions used for fitting vs. tuning parameter selection be justified? , where I answered that it can be useful to use a different loss function than the loss function which needs to be optimized. The reason is that statistical fluctuations m... | Validity of regression diagnostics for deterministic computer experiments | This question reminds me a bit of the question Could a mismatch between loss functions used for fitting vs. tuning parameter selection be justified? , where I answered that it can be useful to use a d | Validity of regression diagnostics for deterministic computer experiments
This question reminds me a bit of the question Could a mismatch between loss functions used for fitting vs. tuning parameter selection be justified? , where I answered that it can be useful to use a different loss function than the loss function ... | Validity of regression diagnostics for deterministic computer experiments
This question reminds me a bit of the question Could a mismatch between loss functions used for fitting vs. tuning parameter selection be justified? , where I answered that it can be useful to use a d |
52,215 | Validity of regression diagnostics for deterministic computer experiments | Statistical methods applied to deterministic phenomena: Statistical methods like regression analysis can be quite useful in situations where one is dealing with deterministic values, particularly in cases where the deterministic behaviour is complex enough that it is not helpful to express this behaviour in determinist... | Validity of regression diagnostics for deterministic computer experiments | Statistical methods applied to deterministic phenomena: Statistical methods like regression analysis can be quite useful in situations where one is dealing with deterministic values, particularly in c | Validity of regression diagnostics for deterministic computer experiments
Statistical methods applied to deterministic phenomena: Statistical methods like regression analysis can be quite useful in situations where one is dealing with deterministic values, particularly in cases where the deterministic behaviour is comp... | Validity of regression diagnostics for deterministic computer experiments
Statistical methods applied to deterministic phenomena: Statistical methods like regression analysis can be quite useful in situations where one is dealing with deterministic values, particularly in c |
52,216 | Validity of regression diagnostics for deterministic computer experiments | It sounds like your deterministic experiments are effectively evaluating an unknown function $f$ at many different input values $x$. If evaluating $f$ at new $x$ values is cheap, then you can easily get arbitrarily large samples; so hypothesis tests (which are partly a measure of sample size) aren't going to be a very ... | Validity of regression diagnostics for deterministic computer experiments | It sounds like your deterministic experiments are effectively evaluating an unknown function $f$ at many different input values $x$. If evaluating $f$ at new $x$ values is cheap, then you can easily g | Validity of regression diagnostics for deterministic computer experiments
It sounds like your deterministic experiments are effectively evaluating an unknown function $f$ at many different input values $x$. If evaluating $f$ at new $x$ values is cheap, then you can easily get arbitrarily large samples; so hypothesis te... | Validity of regression diagnostics for deterministic computer experiments
It sounds like your deterministic experiments are effectively evaluating an unknown function $f$ at many different input values $x$. If evaluating $f$ at new $x$ values is cheap, then you can easily g |
52,217 | Validity of regression diagnostics for deterministic computer experiments | In other words: Can stepwise regression or variable selection using AIC (or similar statistics based on the likelihood or distributional assumptions of the regression model) be justified also in the case of deterministic computer experiments?
Here's an argument for likelihood-based statistics. Let $Y = f(X)$, where $f... | Validity of regression diagnostics for deterministic computer experiments | In other words: Can stepwise regression or variable selection using AIC (or similar statistics based on the likelihood or distributional assumptions of the regression model) be justified also in the c | Validity of regression diagnostics for deterministic computer experiments
In other words: Can stepwise regression or variable selection using AIC (or similar statistics based on the likelihood or distributional assumptions of the regression model) be justified also in the case of deterministic computer experiments?
He... | Validity of regression diagnostics for deterministic computer experiments
In other words: Can stepwise regression or variable selection using AIC (or similar statistics based on the likelihood or distributional assumptions of the regression model) be justified also in the c |
52,218 | $\sin(x)$ is a counterexample to the universal approximation theorem | A ReLU network is ultimately a piecewise-linear continuous function. Each neuron in the first hidden layer is just a shifted and scaled ReLU. Taking a linear combination of those produces a piecewise linear function, with (at most) as many hingepoints as there are neurons. Applying ReLU to that can create new hingep... | $\sin(x)$ is a counterexample to the universal approximation theorem | A ReLU network is ultimately a piecewise-linear continuous function. Each neuron in the first hidden layer is just a shifted and scaled ReLU. Taking a linear combination of those produces a piecewis | $\sin(x)$ is a counterexample to the universal approximation theorem
A ReLU network is ultimately a piecewise-linear continuous function. Each neuron in the first hidden layer is just a shifted and scaled ReLU. Taking a linear combination of those produces a piecewise linear function, with (at most) as many hingepoin... | $\sin(x)$ is a counterexample to the universal approximation theorem
A ReLU network is ultimately a piecewise-linear continuous function. Each neuron in the first hidden layer is just a shifted and scaled ReLU. Taking a linear combination of those produces a piecewis |
52,219 | $\sin(x)$ is a counterexample to the universal approximation theorem | The classical (Cybenko) universal approximation theorem has a condition about the function being approximated on a compact space.
On the real line, the Heine-Borel theorem says that compacts sets are the closed and bounded sets.
Therefore, the Cybenko universal approximation theorem does not apply to a function over th... | $\sin(x)$ is a counterexample to the universal approximation theorem | The classical (Cybenko) universal approximation theorem has a condition about the function being approximated on a compact space.
On the real line, the Heine-Borel theorem says that compacts sets are | $\sin(x)$ is a counterexample to the universal approximation theorem
The classical (Cybenko) universal approximation theorem has a condition about the function being approximated on a compact space.
On the real line, the Heine-Borel theorem says that compacts sets are the closed and bounded sets.
Therefore, the Cybenko... | $\sin(x)$ is a counterexample to the universal approximation theorem
The classical (Cybenko) universal approximation theorem has a condition about the function being approximated on a compact space.
On the real line, the Heine-Borel theorem says that compacts sets are |
52,220 | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use? | If you stick really close to the data generating process, these are repeated binary decisions. I.e. each participants makes three decisions of choosing the local product or not (each time a 1/0 outcome).
It's not count data, because the counts cannot reach any arbitrary number. Arguably, it could be truncated (at 3) co... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to | If you stick really close to the data generating process, these are repeated binary decisions. I.e. each participants makes three decisions of choosing the local product or not (each time a 1/0 outcom | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use?
If you stick really close to the data generating process, these are repeated binary decisions. I.e. each participants makes three decisions of choosing the local product or not (each time a 1/0 outcome).
It's not c... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to
If you stick really close to the data generating process, these are repeated binary decisions. I.e. each participants makes three decisions of choosing the local product or not (each time a 1/0 outcom |
52,221 | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use? | Although ordinal regression is a generally useful choice for ordered outcomes, in this particular case a binary regression could also be considered.
In each of the 3 trials per individual there is a binary choice: local versus non-local. In R you can model this situation with binary regression, coding the outcomes in a... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to | Although ordinal regression is a generally useful choice for ordered outcomes, in this particular case a binary regression could also be considered.
In each of the 3 trials per individual there is a b | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use?
Although ordinal regression is a generally useful choice for ordered outcomes, in this particular case a binary regression could also be considered.
In each of the 3 trials per individual there is a binary choice: ... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to
Although ordinal regression is a generally useful choice for ordered outcomes, in this particular case a binary regression could also be considered.
In each of the 3 trials per individual there is a b |
52,222 | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use? | Yes, ordinal logistic regression (also referred to as the proportional odds model) is your best choice. If your outcome were to have 7+ ordered categories, linear regression may also be used, though because you have few ordered categories (i.e., 4) I would use ordinal logistic regression as suggested in the comments by... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to | Yes, ordinal logistic regression (also referred to as the proportional odds model) is your best choice. If your outcome were to have 7+ ordered categories, linear regression may also be used, though b | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use?
Yes, ordinal logistic regression (also referred to as the proportional odds model) is your best choice. If your outcome were to have 7+ ordered categories, linear regression may also be used, though because you hav... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to
Yes, ordinal logistic regression (also referred to as the proportional odds model) is your best choice. If your outcome were to have 7+ ordered categories, linear regression may also be used, though b |
52,223 | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use? | Beware of adding difficult-to-compare indicators
Treating your variable as an ordinal assumes both that each decision has equal weight (local apple is equivalent to local grape even if the latter is 4 times the price and the former has 2 times the reduction in environmental impact by purchasing locally) and yet that th... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to | Beware of adding difficult-to-compare indicators
Treating your variable as an ordinal assumes both that each decision has equal weight (local apple is equivalent to local grape even if the latter is 4 | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to use?
Beware of adding difficult-to-compare indicators
Treating your variable as an ordinal assumes both that each decision has equal weight (local apple is equivalent to local grape even if the latter is 4 times the pri... | Dependent Variable takes on the values 0, 1, 2, 3 - What is the right (logistic) regression model to
Beware of adding difficult-to-compare indicators
Treating your variable as an ordinal assumes both that each decision has equal weight (local apple is equivalent to local grape even if the latter is 4 |
52,224 | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed] | The parabola going through $(a,f(a))$, $(b,f(b))$, $(c,f(c))$ has a minimum at
$$G(a,b,c):=\frac{1}{2}\left( \frac{f(a)(b^2-c^2)+f(b)(c^2-a^2)+f(c)(a^2-b^2)}{f(a)(b-c)+f(b)(c-a)+f(c)(a-b)}\right)$$
So if you start with three reasonable guesses $x_0$, $x_1$ and $x_2$, you can iterate with $x_{n+1}=G(x_{n-2}, x_{n-1}, x_... | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed] | The parabola going through $(a,f(a))$, $(b,f(b))$, $(c,f(c))$ has a minimum at
$$G(a,b,c):=\frac{1}{2}\left( \frac{f(a)(b^2-c^2)+f(b)(c^2-a^2)+f(c)(a^2-b^2)}{f(a)(b-c)+f(b)(c-a)+f(c)(a-b)}\right)$$
So | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed]
The parabola going through $(a,f(a))$, $(b,f(b))$, $(c,f(c))$ has a minimum at
$$G(a,b,c):=\frac{1}{2}\left( \frac{f(a)(b^2-c^2)+f(b)(c^2-a^2)+f(c)(a^2-b^2)}{f(a)(b-c)+f(b)(c-a)+f(c)(a-b)}\right)$$
So if you start with three ... | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed]
The parabola going through $(a,f(a))$, $(b,f(b))$, $(c,f(c))$ has a minimum at
$$G(a,b,c):=\frac{1}{2}\left( \frac{f(a)(b^2-c^2)+f(b)(c^2-a^2)+f(c)(a^2-b^2)}{f(a)(b-c)+f(b)(c-a)+f(c)(a-b)}\right)$$
So |
52,225 | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed] | Ternary search is a simple algorithm to find the minimum (or maximum) of a unimodal function without using any derivative information. It proceeds by starting with some interval, and then recursively discards one-third of the interval until some tolerance is reached. | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed] | Ternary search is a simple algorithm to find the minimum (or maximum) of a unimodal function without using any derivative information. It proceeds by starting with some interval, and then recursively | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed]
Ternary search is a simple algorithm to find the minimum (or maximum) of a unimodal function without using any derivative information. It proceeds by starting with some interval, and then recursively discards one-third of the... | What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed]
Ternary search is a simple algorithm to find the minimum (or maximum) of a unimodal function without using any derivative information. It proceeds by starting with some interval, and then recursively |
52,226 | How to test if two events with unknown probabilities are different or not | It turns out the counts of the other outcomes don't matter: a suitable chi-squared test works just fine here.
Let the chance of outcome $A$ be $p.$ Under your null hypothesis, the chance of $B$ is the same and (therefore) the chance of seeing something other than $A$ and $B$ is $1-2p.$ Because your rolls are independe... | How to test if two events with unknown probabilities are different or not | It turns out the counts of the other outcomes don't matter: a suitable chi-squared test works just fine here.
Let the chance of outcome $A$ be $p.$ Under your null hypothesis, the chance of $B$ is the | How to test if two events with unknown probabilities are different or not
It turns out the counts of the other outcomes don't matter: a suitable chi-squared test works just fine here.
Let the chance of outcome $A$ be $p.$ Under your null hypothesis, the chance of $B$ is the same and (therefore) the chance of seeing som... | How to test if two events with unknown probabilities are different or not
It turns out the counts of the other outcomes don't matter: a suitable chi-squared test works just fine here.
Let the chance of outcome $A$ be $p.$ Under your null hypothesis, the chance of $B$ is the |
52,227 | How to test if two events with unknown probabilities are different or not | A Bayesian approach to the problem works out neatly. The reference posterior (see equation 6) of $\phi\equiv{p_A/p_B}$ is
$\phi^{ref}\sim{}B'(\phi;x_A+1/2,x_B+1/2)$,
where $B'$ is the beta prime distribution and $x_A$ and $x_B$ are the number of observations of $A$ and $B$ from the independent trials. Notice that the p... | How to test if two events with unknown probabilities are different or not | A Bayesian approach to the problem works out neatly. The reference posterior (see equation 6) of $\phi\equiv{p_A/p_B}$ is
$\phi^{ref}\sim{}B'(\phi;x_A+1/2,x_B+1/2)$,
where $B'$ is the beta prime distr | How to test if two events with unknown probabilities are different or not
A Bayesian approach to the problem works out neatly. The reference posterior (see equation 6) of $\phi\equiv{p_A/p_B}$ is
$\phi^{ref}\sim{}B'(\phi;x_A+1/2,x_B+1/2)$,
where $B'$ is the beta prime distribution and $x_A$ and $x_B$ are the number of ... | How to test if two events with unknown probabilities are different or not
A Bayesian approach to the problem works out neatly. The reference posterior (see equation 6) of $\phi\equiv{p_A/p_B}$ is
$\phi^{ref}\sim{}B'(\phi;x_A+1/2,x_B+1/2)$,
where $B'$ is the beta prime distr |
52,228 | "Dumb" log-loss for a binary classifier | You are correct, your if your "dumb" classifier knows the frequency of successes in the test set, it in fact works as an oracle, and is not that dumb. You're leaking the data from test set. It is easy to imagine an extreme case with big discrepancy between train and test set where such "dumb" classifier would in fact o... | "Dumb" log-loss for a binary classifier | You are correct, your if your "dumb" classifier knows the frequency of successes in the test set, it in fact works as an oracle, and is not that dumb. You're leaking the data from test set. It is easy | "Dumb" log-loss for a binary classifier
You are correct, your if your "dumb" classifier knows the frequency of successes in the test set, it in fact works as an oracle, and is not that dumb. You're leaking the data from test set. It is easy to imagine an extreme case with big discrepancy between train and test set wher... | "Dumb" log-loss for a binary classifier
You are correct, your if your "dumb" classifier knows the frequency of successes in the test set, it in fact works as an oracle, and is not that dumb. You're leaking the data from test set. It is easy |
52,229 | "Dumb" log-loss for a binary classifier | I like my explanation of $R^2$ here and how it relates to a naïve model. You would be looking for the McFadden’s $R^2$ that I mention, as that compares the log loss of your model to that of one that naively predicts the prior probability every time, much as linear regression $R^2$ naively guesses the pooled/marginal me... | "Dumb" log-loss for a binary classifier | I like my explanation of $R^2$ here and how it relates to a naïve model. You would be looking for the McFadden’s $R^2$ that I mention, as that compares the log loss of your model to that of one that n | "Dumb" log-loss for a binary classifier
I like my explanation of $R^2$ here and how it relates to a naïve model. You would be looking for the McFadden’s $R^2$ that I mention, as that compares the log loss of your model to that of one that naively predicts the prior probability every time, much as linear regression $R^2... | "Dumb" log-loss for a binary classifier
I like my explanation of $R^2$ here and how it relates to a naïve model. You would be looking for the McFadden’s $R^2$ that I mention, as that compares the log loss of your model to that of one that n |
52,230 | Peak of Poisson distribution | The mode of the Poisson distribution occurs at the value $\text{Mode}(\lambda) = \lceil \lambda \rceil - 1$, whereas your proposed approximation is:
$$\widehat{\text{Mode}}(\lambda) \equiv \lambda - \tfrac{1}{2}.$$
Letting $u(\lambda) \equiv \lceil \lambda \rceil - \lambda$ denote the "upper remainder" of the number $\... | Peak of Poisson distribution | The mode of the Poisson distribution occurs at the value $\text{Mode}(\lambda) = \lceil \lambda \rceil - 1$, whereas your proposed approximation is:
$$\widehat{\text{Mode}}(\lambda) \equiv \lambda - \ | Peak of Poisson distribution
The mode of the Poisson distribution occurs at the value $\text{Mode}(\lambda) = \lceil \lambda \rceil - 1$, whereas your proposed approximation is:
$$\widehat{\text{Mode}}(\lambda) \equiv \lambda - \tfrac{1}{2}.$$
Letting $u(\lambda) \equiv \lceil \lambda \rceil - \lambda$ denote the "uppe... | Peak of Poisson distribution
The mode of the Poisson distribution occurs at the value $\text{Mode}(\lambda) = \lceil \lambda \rceil - 1$, whereas your proposed approximation is:
$$\widehat{\text{Mode}}(\lambda) \equiv \lambda - \ |
52,231 | Peak of Poisson distribution | The analysis at https://stats.stackexchange.com/a/211612/919 shows the mode of any Poisson$(\lambda)$ distribution is near $\lambda$ itself. Although that question concerns only integral $\lambda,$ its results answer the present question, too.
Let $p_\lambda(k)$ be the Poisson$(\lambda)$ probability for $k\in\{0,1,2,\... | Peak of Poisson distribution | The analysis at https://stats.stackexchange.com/a/211612/919 shows the mode of any Poisson$(\lambda)$ distribution is near $\lambda$ itself. Although that question concerns only integral $\lambda,$ i | Peak of Poisson distribution
The analysis at https://stats.stackexchange.com/a/211612/919 shows the mode of any Poisson$(\lambda)$ distribution is near $\lambda$ itself. Although that question concerns only integral $\lambda,$ its results answer the present question, too.
Let $p_\lambda(k)$ be the Poisson$(\lambda)$ p... | Peak of Poisson distribution
The analysis at https://stats.stackexchange.com/a/211612/919 shows the mode of any Poisson$(\lambda)$ distribution is near $\lambda$ itself. Although that question concerns only integral $\lambda,$ i |
52,232 | $N \sim \text{Po}(\lambda)$ and $X_1,X_2,....,X_N$ are iid and independent of $N$, what is distribution of $Z_N = \max \{X_i\}_{i=1}^{N}$ | I assume that you take $Z$ to be the supremum of the set $\{X_1,X_2,\dots,X_N\}$ since this is also reasonably defined (as negative infinity) when the set is empty (in the event that $N=0$).
Conditional on $N$, $Z$ has cdf
\begin{align}
F_{Z|N}(z)&=P(\sup\{X_i\}_{i=1}^N\le z|N)
\\&=P(X_1\le z \cap \dots \cap X_N\le z|N... | $N \sim \text{Po}(\lambda)$ and $X_1,X_2,....,X_N$ are iid and independent of $N$, what is distribut | I assume that you take $Z$ to be the supremum of the set $\{X_1,X_2,\dots,X_N\}$ since this is also reasonably defined (as negative infinity) when the set is empty (in the event that $N=0$).
Condition | $N \sim \text{Po}(\lambda)$ and $X_1,X_2,....,X_N$ are iid and independent of $N$, what is distribution of $Z_N = \max \{X_i\}_{i=1}^{N}$
I assume that you take $Z$ to be the supremum of the set $\{X_1,X_2,\dots,X_N\}$ since this is also reasonably defined (as negative infinity) when the set is empty (in the event that... | $N \sim \text{Po}(\lambda)$ and $X_1,X_2,....,X_N$ are iid and independent of $N$, what is distribut
I assume that you take $Z$ to be the supremum of the set $\{X_1,X_2,\dots,X_N\}$ since this is also reasonably defined (as negative infinity) when the set is empty (in the event that $N=0$).
Condition |
52,233 | How well do power calculations actually work in reality? | You don't know when $H_0$ is false, so you can't compute the correct empirical rejection rate for power from looking at the results of tests. You shouldn't include the cases where the null was true in that calculation. (If you could say when $H_0$ was false, you wouldn't need tests in the first place.)
Further, even i... | How well do power calculations actually work in reality? | You don't know when $H_0$ is false, so you can't compute the correct empirical rejection rate for power from looking at the results of tests. You shouldn't include the cases where the null was true in | How well do power calculations actually work in reality?
You don't know when $H_0$ is false, so you can't compute the correct empirical rejection rate for power from looking at the results of tests. You shouldn't include the cases where the null was true in that calculation. (If you could say when $H_0$ was false, you... | How well do power calculations actually work in reality?
You don't know when $H_0$ is false, so you can't compute the correct empirical rejection rate for power from looking at the results of tests. You shouldn't include the cases where the null was true in |
52,234 | How well do power calculations actually work in reality? | You can view a typical power calculation not as guess work, but as an estimate of the unknown fixed true power. This means you can also perform inference on power by constructing a confidence interval for it using parameter estimates and standard error estimates from historical studies. In the example below the point... | How well do power calculations actually work in reality? | You can view a typical power calculation not as guess work, but as an estimate of the unknown fixed true power. This means you can also perform inference on power by constructing a confidence interva | How well do power calculations actually work in reality?
You can view a typical power calculation not as guess work, but as an estimate of the unknown fixed true power. This means you can also perform inference on power by constructing a confidence interval for it using parameter estimates and standard error estimates... | How well do power calculations actually work in reality?
You can view a typical power calculation not as guess work, but as an estimate of the unknown fixed true power. This means you can also perform inference on power by constructing a confidence interva |
52,235 | How well do power calculations actually work in reality? | To answer this question, it is useful to first separate the power function itself from sample-size calculations that try to achieve a stipulated level of power against an alternative hypothesis. The power function arises whenever we have a proposed method of hypothesis testing and it measures the probability of reject... | How well do power calculations actually work in reality? | To answer this question, it is useful to first separate the power function itself from sample-size calculations that try to achieve a stipulated level of power against an alternative hypothesis. The | How well do power calculations actually work in reality?
To answer this question, it is useful to first separate the power function itself from sample-size calculations that try to achieve a stipulated level of power against an alternative hypothesis. The power function arises whenever we have a proposed method of hyp... | How well do power calculations actually work in reality?
To answer this question, it is useful to first separate the power function itself from sample-size calculations that try to achieve a stipulated level of power against an alternative hypothesis. The |
52,236 | What are the skewness and kurtosis of the sample mean? | $$\begin{align}
\boxed{
\quad \quad \ \ \ \mathbb{E}(\bar{X}_n) = \mu
\quad \quad \quad \quad \quad \quad \quad \ \
\mathbb{V}(\bar{X}_n) = \frac{\sigma^2}{n}, \\[12pt]
\quad \mathbb{Skew}(\bar{X}_n) = \frac{\gamma}{\sqrt{n}}
\quad \quad \quad \quad \quad
\mathbb{Kurt}(\bar{X}_n) = 3 + \frac{\kappa - 3}{n}. \quad \\}
... | What are the skewness and kurtosis of the sample mean? | $$\begin{align}
\boxed{
\quad \quad \ \ \ \mathbb{E}(\bar{X}_n) = \mu
\quad \quad \quad \quad \quad \quad \quad \ \
\mathbb{V}(\bar{X}_n) = \frac{\sigma^2}{n}, \\[12pt]
\quad \mathbb{Skew}(\bar{X}_n) | What are the skewness and kurtosis of the sample mean?
$$\begin{align}
\boxed{
\quad \quad \ \ \ \mathbb{E}(\bar{X}_n) = \mu
\quad \quad \quad \quad \quad \quad \quad \ \
\mathbb{V}(\bar{X}_n) = \frac{\sigma^2}{n}, \\[12pt]
\quad \mathbb{Skew}(\bar{X}_n) = \frac{\gamma}{\sqrt{n}}
\quad \quad \quad \quad \quad
\mathbb{... | What are the skewness and kurtosis of the sample mean?
$$\begin{align}
\boxed{
\quad \quad \ \ \ \mathbb{E}(\bar{X}_n) = \mu
\quad \quad \quad \quad \quad \quad \quad \ \
\mathbb{V}(\bar{X}_n) = \frac{\sigma^2}{n}, \\[12pt]
\quad \mathbb{Skew}(\bar{X}_n) |
52,237 | What are the skewness and kurtosis of the sample mean? | Solution
The calculation amounts to removing the linear term in the cumulant generating function (log characteristic function) of the distribution and simply replacing its argument $t$ by the factor $t\sqrt{n}/\sigma$ needed to standardize the sum, afterwards multiplying everything by $n$ to account for the $n$ iid var... | What are the skewness and kurtosis of the sample mean? | Solution
The calculation amounts to removing the linear term in the cumulant generating function (log characteristic function) of the distribution and simply replacing its argument $t$ by the factor $ | What are the skewness and kurtosis of the sample mean?
Solution
The calculation amounts to removing the linear term in the cumulant generating function (log characteristic function) of the distribution and simply replacing its argument $t$ by the factor $t\sqrt{n}/\sigma$ needed to standardize the sum, afterwards multi... | What are the skewness and kurtosis of the sample mean?
Solution
The calculation amounts to removing the linear term in the cumulant generating function (log characteristic function) of the distribution and simply replacing its argument $t$ by the factor $ |
52,238 | What are the skewness and kurtosis of the sample mean? | What are the first four central moments of the sample mean?
Computer algebra systems are particularly adept at this sort of algebra munching. Here I am using the mathStatica package for Mathematica where $s_r = \sum _{i=1}^n X^r$. The first say 7 central moments of the sample mean $\frac{s_1}{n}$ are:
where:
$\mu_r$ ... | What are the skewness and kurtosis of the sample mean? | What are the first four central moments of the sample mean?
Computer algebra systems are particularly adept at this sort of algebra munching. Here I am using the mathStatica package for Mathematica w | What are the skewness and kurtosis of the sample mean?
What are the first four central moments of the sample mean?
Computer algebra systems are particularly adept at this sort of algebra munching. Here I am using the mathStatica package for Mathematica where $s_r = \sum _{i=1}^n X^r$. The first say 7 central moments o... | What are the skewness and kurtosis of the sample mean?
What are the first four central moments of the sample mean?
Computer algebra systems are particularly adept at this sort of algebra munching. Here I am using the mathStatica package for Mathematica w |
52,239 | Facebook prophet gives a very high MAPE, how can I improve it? | You have suspiciously regular massive spikes sometime about halfway through the third quarter of every year. You don't tell us where your data come from, but if they are US, this is presumably a Black Friday effect. Have you told your model about this very specific predictor?
In general, How to know that your machine l... | Facebook prophet gives a very high MAPE, how can I improve it? | You have suspiciously regular massive spikes sometime about halfway through the third quarter of every year. You don't tell us where your data come from, but if they are US, this is presumably a Black | Facebook prophet gives a very high MAPE, how can I improve it?
You have suspiciously regular massive spikes sometime about halfway through the third quarter of every year. You don't tell us where your data come from, but if they are US, this is presumably a Black Friday effect. Have you told your model about this very ... | Facebook prophet gives a very high MAPE, how can I improve it?
You have suspiciously regular massive spikes sometime about halfway through the third quarter of every year. You don't tell us where your data come from, but if they are US, this is presumably a Black |
52,240 | Does offset always have to be on log scale with NB GLMM? | Normally, an offset is used when we are modelling some sort of rate data (e.g. deaths per 100,000, crashes per 100,000 etc).
This is naturally modelled as some sort of ratio so have data in the form of $E(y_i)/n_i$
In GLM, we model the expectation through some sort of link function, so
$$ g^{-1}(E(y_i)/n_i) = \mathbf{x... | Does offset always have to be on log scale with NB GLMM? | Normally, an offset is used when we are modelling some sort of rate data (e.g. deaths per 100,000, crashes per 100,000 etc).
This is naturally modelled as some sort of ratio so have data in the form o | Does offset always have to be on log scale with NB GLMM?
Normally, an offset is used when we are modelling some sort of rate data (e.g. deaths per 100,000, crashes per 100,000 etc).
This is naturally modelled as some sort of ratio so have data in the form of $E(y_i)/n_i$
In GLM, we model the expectation through some so... | Does offset always have to be on log scale with NB GLMM?
Normally, an offset is used when we are modelling some sort of rate data (e.g. deaths per 100,000, crashes per 100,000 etc).
This is naturally modelled as some sort of ratio so have data in the form o |
52,241 | Does offset always have to be on log scale with NB GLMM? | This question is related to the choice of link function for your generalized linear model. McCullagh and Nelder say (page 31):
The link function relates the linear predictor $\eta$ to the expected value $\mu$ of a datum [outcome value] $y$.
The link function is what makes this a generalized linear model. Hidden in yo... | Does offset always have to be on log scale with NB GLMM? | This question is related to the choice of link function for your generalized linear model. McCullagh and Nelder say (page 31):
The link function relates the linear predictor $\eta$ to the expected va | Does offset always have to be on log scale with NB GLMM?
This question is related to the choice of link function for your generalized linear model. McCullagh and Nelder say (page 31):
The link function relates the linear predictor $\eta$ to the expected value $\mu$ of a datum [outcome value] $y$.
The link function is... | Does offset always have to be on log scale with NB GLMM?
This question is related to the choice of link function for your generalized linear model. McCullagh and Nelder say (page 31):
The link function relates the linear predictor $\eta$ to the expected va |
52,242 | Standard deviation for a half-normal distribution | The half normal distribution is usually parametrised so that the $\sigma$ from the corresponding normal distribution is its scale parameter. However, this is not the standard deviation of it, which is $\sigma\sqrt{1-\frac{2}{\pi}}$, see https://en.wikipedia.org/wiki/Half-normal_distribution. It should be intuitive that... | Standard deviation for a half-normal distribution | The half normal distribution is usually parametrised so that the $\sigma$ from the corresponding normal distribution is its scale parameter. However, this is not the standard deviation of it, which is | Standard deviation for a half-normal distribution
The half normal distribution is usually parametrised so that the $\sigma$ from the corresponding normal distribution is its scale parameter. However, this is not the standard deviation of it, which is $\sigma\sqrt{1-\frac{2}{\pi}}$, see https://en.wikipedia.org/wiki/Hal... | Standard deviation for a half-normal distribution
The half normal distribution is usually parametrised so that the $\sigma$ from the corresponding normal distribution is its scale parameter. However, this is not the standard deviation of it, which is |
52,243 | Standard deviation for a half-normal distribution | If you randomly assign a sign (+ or -) to each member of the sample generated from a half-normal distribution, the result will be indistinguishable from a sample generated from the corresponding unfolded normal distribution.
Your method wouldn't work - for example, if your sample size is 2, it would be very surprising ... | Standard deviation for a half-normal distribution | If you randomly assign a sign (+ or -) to each member of the sample generated from a half-normal distribution, the result will be indistinguishable from a sample generated from the corresponding unfol | Standard deviation for a half-normal distribution
If you randomly assign a sign (+ or -) to each member of the sample generated from a half-normal distribution, the result will be indistinguishable from a sample generated from the corresponding unfolded normal distribution.
Your method wouldn't work - for example, if y... | Standard deviation for a half-normal distribution
If you randomly assign a sign (+ or -) to each member of the sample generated from a half-normal distribution, the result will be indistinguishable from a sample generated from the corresponding unfol |
52,244 | Standard deviation for a half-normal distribution | With data $x_1, x_2, \ldots, x_n,$ you propose synthesizing a dataset of $2n$ values $|x_1|, -|x_1|, |x_2|, -|x_2|, \ldots, |x_n|, -|x_n|.$ Because each absolute value $|x_i|$ balances its negative $-|x_i|,$ the mean is zero. The usual standard deviation estimator therefore reduces to the square root of
$$\frac{1}{2n-... | Standard deviation for a half-normal distribution | With data $x_1, x_2, \ldots, x_n,$ you propose synthesizing a dataset of $2n$ values $|x_1|, -|x_1|, |x_2|, -|x_2|, \ldots, |x_n|, -|x_n|.$ Because each absolute value $|x_i|$ balances its negative $ | Standard deviation for a half-normal distribution
With data $x_1, x_2, \ldots, x_n,$ you propose synthesizing a dataset of $2n$ values $|x_1|, -|x_1|, |x_2|, -|x_2|, \ldots, |x_n|, -|x_n|.$ Because each absolute value $|x_i|$ balances its negative $-|x_i|,$ the mean is zero. The usual standard deviation estimator ther... | Standard deviation for a half-normal distribution
With data $x_1, x_2, \ldots, x_n,$ you propose synthesizing a dataset of $2n$ values $|x_1|, -|x_1|, |x_2|, -|x_2|, \ldots, |x_n|, -|x_n|.$ Because each absolute value $|x_i|$ balances its negative $ |
52,245 | What does "even if the evidence remains correlational" mean? | Both the cited finding that, "People who trust the media more are more knowledgeable about politics and the news" and the cited finding that, "The more people trust science, the more scientifically literate they are", are results found in observational data. It is well established that it is difficult to infer causali... | What does "even if the evidence remains correlational" mean? | Both the cited finding that, "People who trust the media more are more knowledgeable about politics and the news" and the cited finding that, "The more people trust science, the more scientifically li | What does "even if the evidence remains correlational" mean?
Both the cited finding that, "People who trust the media more are more knowledgeable about politics and the news" and the cited finding that, "The more people trust science, the more scientifically literate they are", are results found in observational data. ... | What does "even if the evidence remains correlational" mean?
Both the cited finding that, "People who trust the media more are more knowledgeable about politics and the news" and the cited finding that, "The more people trust science, the more scientifically li |
52,246 | What does "even if the evidence remains correlational" mean? | It means, that changing one of those variables may, as well as may not, lead to changing the other. We can not apriori say which is how much likely.
Imagine, that you can force somebody to increase the knowledge about science. If evidence is correlational it may or may not result in changing the trust. If there existed... | What does "even if the evidence remains correlational" mean? | It means, that changing one of those variables may, as well as may not, lead to changing the other. We can not apriori say which is how much likely.
Imagine, that you can force somebody to increase th | What does "even if the evidence remains correlational" mean?
It means, that changing one of those variables may, as well as may not, lead to changing the other. We can not apriori say which is how much likely.
Imagine, that you can force somebody to increase the knowledge about science. If evidence is correlational it ... | What does "even if the evidence remains correlational" mean?
It means, that changing one of those variables may, as well as may not, lead to changing the other. We can not apriori say which is how much likely.
Imagine, that you can force somebody to increase th |
52,247 | What does "even if the evidence remains correlational" mean? | Evidence being "correlational" (more often called "observational") means that this was passive observational evidence of a statistical association between things, without any controlled experimentation. For example, consider the claim that "[t]he more people trust science, the more scientifically literate they are." ... | What does "even if the evidence remains correlational" mean? | Evidence being "correlational" (more often called "observational") means that this was passive observational evidence of a statistical association between things, without any controlled experimentatio | What does "even if the evidence remains correlational" mean?
Evidence being "correlational" (more often called "observational") means that this was passive observational evidence of a statistical association between things, without any controlled experimentation. For example, consider the claim that "[t]he more people... | What does "even if the evidence remains correlational" mean?
Evidence being "correlational" (more often called "observational") means that this was passive observational evidence of a statistical association between things, without any controlled experimentatio |
52,248 | What does "even if the evidence remains correlational" mean? | Trust in Science -> Scientific Literacy is observationally equivalent with Scientific Literacy -> Trust in Science. Similarly, Education -> Trust in Science & Education -> Scientific Literacy is also observationally equivalent with Trust in Science -> Scientific Literacy. So when they say "even if this evidence remain... | What does "even if the evidence remains correlational" mean? | Trust in Science -> Scientific Literacy is observationally equivalent with Scientific Literacy -> Trust in Science. Similarly, Education -> Trust in Science & Education -> Scientific Literacy is also | What does "even if the evidence remains correlational" mean?
Trust in Science -> Scientific Literacy is observationally equivalent with Scientific Literacy -> Trust in Science. Similarly, Education -> Trust in Science & Education -> Scientific Literacy is also observationally equivalent with Trust in Science -> Scienti... | What does "even if the evidence remains correlational" mean?
Trust in Science -> Scientific Literacy is observationally equivalent with Scientific Literacy -> Trust in Science. Similarly, Education -> Trust in Science & Education -> Scientific Literacy is also |
52,249 | What does "even if the evidence remains correlational" mean? | What does the bolded phrase mean?
I agree with you that it means the evidence isn't causal. In other words, no causal inference was tested so they only note the correlation in the survey data.
Does it mean that even if the evidence isn't causal, the next phrase still makes sense?
Yes. Even if the relationship isn'... | What does "even if the evidence remains correlational" mean? | What does the bolded phrase mean?
I agree with you that it means the evidence isn't causal. In other words, no causal inference was tested so they only note the correlation in the survey data.
Does | What does "even if the evidence remains correlational" mean?
What does the bolded phrase mean?
I agree with you that it means the evidence isn't causal. In other words, no causal inference was tested so they only note the correlation in the survey data.
Does it mean that even if the evidence isn't causal, the next p... | What does "even if the evidence remains correlational" mean?
What does the bolded phrase mean?
I agree with you that it means the evidence isn't causal. In other words, no causal inference was tested so they only note the correlation in the survey data.
Does |
52,250 | Is it possible to use generated non-normal errors with a linear regression model | Not sure what is the question here. First of all, yes, you can simulate data using any data generating process. However, if what you want is to compare the scenario to data simulated from a normal distribution, you just need to make sure that in both cases, the theoretical variance and means are the same.
For example, ... | Is it possible to use generated non-normal errors with a linear regression model | Not sure what is the question here. First of all, yes, you can simulate data using any data generating process. However, if what you want is to compare the scenario to data simulated from a normal dis | Is it possible to use generated non-normal errors with a linear regression model
Not sure what is the question here. First of all, yes, you can simulate data using any data generating process. However, if what you want is to compare the scenario to data simulated from a normal distribution, you just need to make sure t... | Is it possible to use generated non-normal errors with a linear regression model
Not sure what is the question here. First of all, yes, you can simulate data using any data generating process. However, if what you want is to compare the scenario to data simulated from a normal dis |
52,251 | Is it possible to use generated non-normal errors with a linear regression model | is it ok to generate data from latter distributions to build Linear Regression Models?
You can simulate whatever you want. What matters more perhaps is the type of conclusions you want to draw from the results: I can imagine people using linear regression when the true error distribution is $t$-distributed, and it is ... | Is it possible to use generated non-normal errors with a linear regression model | is it ok to generate data from latter distributions to build Linear Regression Models?
You can simulate whatever you want. What matters more perhaps is the type of conclusions you want to draw from t | Is it possible to use generated non-normal errors with a linear regression model
is it ok to generate data from latter distributions to build Linear Regression Models?
You can simulate whatever you want. What matters more perhaps is the type of conclusions you want to draw from the results: I can imagine people using ... | Is it possible to use generated non-normal errors with a linear regression model
is it ok to generate data from latter distributions to build Linear Regression Models?
You can simulate whatever you want. What matters more perhaps is the type of conclusions you want to draw from t |
52,252 | Is it possible to use generated non-normal errors with a linear regression model | I think you'll want to revisit how regression simulation in supposed to work. The idea is to code the Data Generating Process
(DGP) and as a result you will know what is true in the population. Then you build a sample using this DGP and run a regression on this sample (can be linear regression or Huber or any other typ... | Is it possible to use generated non-normal errors with a linear regression model | I think you'll want to revisit how regression simulation in supposed to work. The idea is to code the Data Generating Process
(DGP) and as a result you will know what is true in the population. Then y | Is it possible to use generated non-normal errors with a linear regression model
I think you'll want to revisit how regression simulation in supposed to work. The idea is to code the Data Generating Process
(DGP) and as a result you will know what is true in the population. Then you build a sample using this DGP and ru... | Is it possible to use generated non-normal errors with a linear regression model
I think you'll want to revisit how regression simulation in supposed to work. The idea is to code the Data Generating Process
(DGP) and as a result you will know what is true in the population. Then y |
52,253 | Is it possible to use generated non-normal errors with a linear regression model | It is certainly possible to generate random variables from distributions other than the normal distribution in R. You can find a large list of probability distributions here. If you are interested in conducting simulation analysis looking at the effects of outliers, a natural thing to do would be to use a T-distribut... | Is it possible to use generated non-normal errors with a linear regression model | It is certainly possible to generate random variables from distributions other than the normal distribution in R. You can find a large list of probability distributions here. If you are interested i | Is it possible to use generated non-normal errors with a linear regression model
It is certainly possible to generate random variables from distributions other than the normal distribution in R. You can find a large list of probability distributions here. If you are interested in conducting simulation analysis lookin... | Is it possible to use generated non-normal errors with a linear regression model
It is certainly possible to generate random variables from distributions other than the normal distribution in R. You can find a large list of probability distributions here. If you are interested i |
52,254 | Confused about rejection region and P-value | I think this will be best understood with an example. Let us solve a hypothesis test for the mean height of people in a country. We have the information about the heights of a sample of people in that country. First, we define our null and alternative hypthesis:
$H_0: \mu \geq a$
$H_1: \mu < a$
And (let me change you... | Confused about rejection region and P-value | I think this will be best understood with an example. Let us solve a hypothesis test for the mean height of people in a country. We have the information about the heights of a sample of people in that | Confused about rejection region and P-value
I think this will be best understood with an example. Let us solve a hypothesis test for the mean height of people in a country. We have the information about the heights of a sample of people in that country. First, we define our null and alternative hypthesis:
$H_0: \mu \g... | Confused about rejection region and P-value
I think this will be best understood with an example. Let us solve a hypothesis test for the mean height of people in a country. We have the information about the heights of a sample of people in that |
52,255 | Confused about rejection region and P-value | The rejection region is fixed beforehand. If the null hypothesis is true then some $\alpha \%$ of the observations will be in the region.
The p-value is not the same as this $\alpha \%$.
The p-value is computed for each separate observation, and can be different for two observations that both fall inside the rejection ... | Confused about rejection region and P-value | The rejection region is fixed beforehand. If the null hypothesis is true then some $\alpha \%$ of the observations will be in the region.
The p-value is not the same as this $\alpha \%$.
The p-value i | Confused about rejection region and P-value
The rejection region is fixed beforehand. If the null hypothesis is true then some $\alpha \%$ of the observations will be in the region.
The p-value is not the same as this $\alpha \%$.
The p-value is computed for each separate observation, and can be different for two obser... | Confused about rejection region and P-value
The rejection region is fixed beforehand. If the null hypothesis is true then some $\alpha \%$ of the observations will be in the region.
The p-value is not the same as this $\alpha \%$.
The p-value i |
52,256 | Where does the binary logistic regression model equation come from? | I wouldn’t say it was “derived”, but rather designed. In generalized linear models
$$C(Y|X)=E(Y|X)=X\beta$$
$C$ is a link function. For linear regression its inverse, $C^{-1}$, is an identity function; for logistic regression it’s the logit function. $Y$ is assumed to follow a Bernoulli distinction parametrized by prob... | Where does the binary logistic regression model equation come from? | I wouldn’t say it was “derived”, but rather designed. In generalized linear models
$$C(Y|X)=E(Y|X)=X\beta$$
$C$ is a link function. For linear regression its inverse, $C^{-1}$, is an identity function | Where does the binary logistic regression model equation come from?
I wouldn’t say it was “derived”, but rather designed. In generalized linear models
$$C(Y|X)=E(Y|X)=X\beta$$
$C$ is a link function. For linear regression its inverse, $C^{-1}$, is an identity function; for logistic regression it’s the logit function. $... | Where does the binary logistic regression model equation come from?
I wouldn’t say it was “derived”, but rather designed. In generalized linear models
$$C(Y|X)=E(Y|X)=X\beta$$
$C$ is a link function. For linear regression its inverse, $C^{-1}$, is an identity function |
52,257 | Where does the binary logistic regression model equation come from? | 1 Convenient transformation
The logistic function is often used as a mapping from $(-\infty,\infty)$ to $(0,1)$ (as others mention).
However the logistic function as link function also relates to being the canonical link function, or sometimes it relates to a particular mechanism/model. See the two points below.
2 Cano... | Where does the binary logistic regression model equation come from? | 1 Convenient transformation
The logistic function is often used as a mapping from $(-\infty,\infty)$ to $(0,1)$ (as others mention).
However the logistic function as link function also relates to bein | Where does the binary logistic regression model equation come from?
1 Convenient transformation
The logistic function is often used as a mapping from $(-\infty,\infty)$ to $(0,1)$ (as others mention).
However the logistic function as link function also relates to being the canonical link function, or sometimes it relat... | Where does the binary logistic regression model equation come from?
1 Convenient transformation
The logistic function is often used as a mapping from $(-\infty,\infty)$ to $(0,1)$ (as others mention).
However the logistic function as link function also relates to bein |
52,258 | Where does the binary logistic regression model equation come from? | To me, this paper from John Mount was instructive. He derives the logistic regression formula using two approaches, one them using the maximum entropy principle. | Where does the binary logistic regression model equation come from? | To me, this paper from John Mount was instructive. He derives the logistic regression formula using two approaches, one them using the maximum entropy principle. | Where does the binary logistic regression model equation come from?
To me, this paper from John Mount was instructive. He derives the logistic regression formula using two approaches, one them using the maximum entropy principle. | Where does the binary logistic regression model equation come from?
To me, this paper from John Mount was instructive. He derives the logistic regression formula using two approaches, one them using the maximum entropy principle. |
52,259 | Where does the binary logistic regression model equation come from? | You obtain the sigmoid function by making the assumption that a linear combination of your inputs gives you the log-odds of the two classes. That is the log of the ratio of the probabilities of class $1$ to class $0$,
$$
X \beta = \log\left(\frac{p_1}{p_0}\right) = \log\left(\frac{p_1}{1-p_1}\right).
$$
This is an assu... | Where does the binary logistic regression model equation come from? | You obtain the sigmoid function by making the assumption that a linear combination of your inputs gives you the log-odds of the two classes. That is the log of the ratio of the probabilities of class | Where does the binary logistic regression model equation come from?
You obtain the sigmoid function by making the assumption that a linear combination of your inputs gives you the log-odds of the two classes. That is the log of the ratio of the probabilities of class $1$ to class $0$,
$$
X \beta = \log\left(\frac{p_1}{... | Where does the binary logistic regression model equation come from?
You obtain the sigmoid function by making the assumption that a linear combination of your inputs gives you the log-odds of the two classes. That is the log of the ratio of the probabilities of class |
52,260 | Where does the binary logistic regression model equation come from? | Contrary to some of the answers in this thread, I would like to give a derivation of the formula which I like.
Suppose we have a random variable that can take either of two classes $C_1$ or $C_2$. We are interested in finding the probability of $C_k$ conditioned on some observation $x$, i.e., we want to estimate $p(C_k... | Where does the binary logistic regression model equation come from? | Contrary to some of the answers in this thread, I would like to give a derivation of the formula which I like.
Suppose we have a random variable that can take either of two classes $C_1$ or $C_2$. We | Where does the binary logistic regression model equation come from?
Contrary to some of the answers in this thread, I would like to give a derivation of the formula which I like.
Suppose we have a random variable that can take either of two classes $C_1$ or $C_2$. We are interested in finding the probability of $C_k$ c... | Where does the binary logistic regression model equation come from?
Contrary to some of the answers in this thread, I would like to give a derivation of the formula which I like.
Suppose we have a random variable that can take either of two classes $C_1$ or $C_2$. We |
52,261 | May using more features decrease the accuracy of a classifier? | This is an instructive encounter with Hughes phenomenon. Naïvely, one would think that the more information one has the better one can model a system and make predictions. However, this prejudice ignores the so-called curse of dimensionality.
Suppose for convenience that each feature (or variable) can only take on a f... | May using more features decrease the accuracy of a classifier? | This is an instructive encounter with Hughes phenomenon. Naïvely, one would think that the more information one has the better one can model a system and make predictions. However, this prejudice igno | May using more features decrease the accuracy of a classifier?
This is an instructive encounter with Hughes phenomenon. Naïvely, one would think that the more information one has the better one can model a system and make predictions. However, this prejudice ignores the so-called curse of dimensionality.
Suppose for c... | May using more features decrease the accuracy of a classifier?
This is an instructive encounter with Hughes phenomenon. Naïvely, one would think that the more information one has the better one can model a system and make predictions. However, this prejudice igno |
52,262 | May using more features decrease the accuracy of a classifier? | Adding too many predictors will lead to overfitting. Always. Take a look at our overfitting tag.
Don't just throw predictors into your model. (Cross-validation and regularization help somewhat, but they will not prevent all overfitting.)
Also: Why is accuracy not the best measure for assessing classification models? | May using more features decrease the accuracy of a classifier? | Adding too many predictors will lead to overfitting. Always. Take a look at our overfitting tag.
Don't just throw predictors into your model. (Cross-validation and regularization help somewhat, but th | May using more features decrease the accuracy of a classifier?
Adding too many predictors will lead to overfitting. Always. Take a look at our overfitting tag.
Don't just throw predictors into your model. (Cross-validation and regularization help somewhat, but they will not prevent all overfitting.)
Also: Why is accura... | May using more features decrease the accuracy of a classifier?
Adding too many predictors will lead to overfitting. Always. Take a look at our overfitting tag.
Don't just throw predictors into your model. (Cross-validation and regularization help somewhat, but th |
52,263 | May using more features decrease the accuracy of a classifier? | This has been answered but here are a few more tips. When creating a model, you must always be conscious of the bias/variance trade off curves of the model. If a model has many features, it will predict with high variance, causing less accurate results. Too few features, and the model will have high bias, causing the m... | May using more features decrease the accuracy of a classifier? | This has been answered but here are a few more tips. When creating a model, you must always be conscious of the bias/variance trade off curves of the model. If a model has many features, it will predi | May using more features decrease the accuracy of a classifier?
This has been answered but here are a few more tips. When creating a model, you must always be conscious of the bias/variance trade off curves of the model. If a model has many features, it will predict with high variance, causing less accurate results. Too... | May using more features decrease the accuracy of a classifier?
This has been answered but here are a few more tips. When creating a model, you must always be conscious of the bias/variance trade off curves of the model. If a model has many features, it will predi |
52,264 | What does it mean L1 loss is not differentiable? | $L_1$ loss uses the absolute value of the difference between the predicted and the actual value to measure the loss (or the error) made by the model. The absolute value (or the modulus function), i.e. $f(x) = |x|$ is not differentiable is the way of saying that its derivative is not defined for its whole domain. For mo... | What does it mean L1 loss is not differentiable? | $L_1$ loss uses the absolute value of the difference between the predicted and the actual value to measure the loss (or the error) made by the model. The absolute value (or the modulus function), i.e. | What does it mean L1 loss is not differentiable?
$L_1$ loss uses the absolute value of the difference between the predicted and the actual value to measure the loss (or the error) made by the model. The absolute value (or the modulus function), i.e. $f(x) = |x|$ is not differentiable is the way of saying that its deriv... | What does it mean L1 loss is not differentiable?
$L_1$ loss uses the absolute value of the difference between the predicted and the actual value to measure the loss (or the error) made by the model. The absolute value (or the modulus function), i.e. |
52,265 | What does it mean L1 loss is not differentiable? | I understand that derivative not exist at x=0, but what practical problems can arise from this fact?
$$ L = |x*a - y|; $$
$$ \frac{\partial L}{\partial a} = \dfrac{x\left(xa-y\right)}{\left|xa-y\right|} $$
When faced with loss equals zero for any sample you train your model with, the gradient calculator will need to d... | What does it mean L1 loss is not differentiable? | I understand that derivative not exist at x=0, but what practical problems can arise from this fact?
$$ L = |x*a - y|; $$
$$ \frac{\partial L}{\partial a} = \dfrac{x\left(xa-y\right)}{\left|xa-y\righ | What does it mean L1 loss is not differentiable?
I understand that derivative not exist at x=0, but what practical problems can arise from this fact?
$$ L = |x*a - y|; $$
$$ \frac{\partial L}{\partial a} = \dfrac{x\left(xa-y\right)}{\left|xa-y\right|} $$
When faced with loss equals zero for any sample you train your m... | What does it mean L1 loss is not differentiable?
I understand that derivative not exist at x=0, but what practical problems can arise from this fact?
$$ L = |x*a - y|; $$
$$ \frac{\partial L}{\partial a} = \dfrac{x\left(xa-y\right)}{\left|xa-y\righ |
52,266 | What does it mean L1 loss is not differentiable? | +1 to both Tomasz and Alexey posts.
I would add that a good surrogate for the $L_1$ loss is the Pseudo-Huber loss function: $ L_{\delta }(x) =$ $\delta ^{2}\left({\sqrt {1+(x/\delta )^{2}}}-1\right)$ with $\delta = 1$. It allows us to approximate the $L_1$ rather faithfully away from $x=1$ and within $[-1,1]$ behaves l... | What does it mean L1 loss is not differentiable? | +1 to both Tomasz and Alexey posts.
I would add that a good surrogate for the $L_1$ loss is the Pseudo-Huber loss function: $ L_{\delta }(x) =$ $\delta ^{2}\left({\sqrt {1+(x/\delta )^{2}}}-1\right)$ | What does it mean L1 loss is not differentiable?
+1 to both Tomasz and Alexey posts.
I would add that a good surrogate for the $L_1$ loss is the Pseudo-Huber loss function: $ L_{\delta }(x) =$ $\delta ^{2}\left({\sqrt {1+(x/\delta )^{2}}}-1\right)$ with $\delta = 1$. It allows us to approximate the $L_1$ rather faithfu... | What does it mean L1 loss is not differentiable?
+1 to both Tomasz and Alexey posts.
I would add that a good surrogate for the $L_1$ loss is the Pseudo-Huber loss function: $ L_{\delta }(x) =$ $\delta ^{2}\left({\sqrt {1+(x/\delta )^{2}}}-1\right)$ |
52,267 | regression with multiple independent variables vs multiple regressions with one independent variable | Note at first I understood your question as 'making multiple regressions with one variable' this gives rise to part 1 in which I explain the effect of an interaction term. In the image of part one the left image relates to doing six different simple regressions (a different one for each single age class, resulting in s... | regression with multiple independent variables vs multiple regressions with one independent variable | Note at first I understood your question as 'making multiple regressions with one variable' this gives rise to part 1 in which I explain the effect of an interaction term. In the image of part one the | regression with multiple independent variables vs multiple regressions with one independent variable
Note at first I understood your question as 'making multiple regressions with one variable' this gives rise to part 1 in which I explain the effect of an interaction term. In the image of part one the left image relates... | regression with multiple independent variables vs multiple regressions with one independent variable
Note at first I understood your question as 'making multiple regressions with one variable' this gives rise to part 1 in which I explain the effect of an interaction term. In the image of part one the |
52,268 | regression with multiple independent variables vs multiple regressions with one independent variable | To explain a little more. Multiple regression tests for the unique contribution of each predictor. So let's take your example and assume that IQ and age are correlated.
If you run a regression with IQ only the contribution of IQ can be visualized like this (red part):
But once you add age to the analysis, it looks som... | regression with multiple independent variables vs multiple regressions with one independent variable | To explain a little more. Multiple regression tests for the unique contribution of each predictor. So let's take your example and assume that IQ and age are correlated.
If you run a regression with IQ | regression with multiple independent variables vs multiple regressions with one independent variable
To explain a little more. Multiple regression tests for the unique contribution of each predictor. So let's take your example and assume that IQ and age are correlated.
If you run a regression with IQ only the contribut... | regression with multiple independent variables vs multiple regressions with one independent variable
To explain a little more. Multiple regression tests for the unique contribution of each predictor. So let's take your example and assume that IQ and age are correlated.
If you run a regression with IQ |
52,269 | regression with multiple independent variables vs multiple regressions with one independent variable | You can do that. It answers a different question.
If you include both independent variables then the results for each are controlling for the other. If you do them separately then they are not. | regression with multiple independent variables vs multiple regressions with one independent variable | You can do that. It answers a different question.
If you include both independent variables then the results for each are controlling for the other. If you do them separately then they are not. | regression with multiple independent variables vs multiple regressions with one independent variable
You can do that. It answers a different question.
If you include both independent variables then the results for each are controlling for the other. If you do them separately then they are not. | regression with multiple independent variables vs multiple regressions with one independent variable
You can do that. It answers a different question.
If you include both independent variables then the results for each are controlling for the other. If you do them separately then they are not. |
52,270 | regression with multiple independent variables vs multiple regressions with one independent variable | What this would do is answer drastically different questions.
Multiple regressions of one independent variable will give you an understand of
the target variable varies with each output of each variable
A regression with multiple independent variables would give you
coefficient estimates that let you know how the tar... | regression with multiple independent variables vs multiple regressions with one independent variable | What this would do is answer drastically different questions.
Multiple regressions of one independent variable will give you an understand of
the target variable varies with each output of each vari | regression with multiple independent variables vs multiple regressions with one independent variable
What this would do is answer drastically different questions.
Multiple regressions of one independent variable will give you an understand of
the target variable varies with each output of each variable
A regression w... | regression with multiple independent variables vs multiple regressions with one independent variable
What this would do is answer drastically different questions.
Multiple regressions of one independent variable will give you an understand of
the target variable varies with each output of each vari |
52,271 | regression with multiple independent variables vs multiple regressions with one independent variable | Your question says "Which method is better?". Better what for? If you want to predict GPA you might want to use both variables. If your question is about the relation between IQ and GPA, then you have no reason to add age to the Model. Hence, it depends on your research question what Model suits better. One point that ... | regression with multiple independent variables vs multiple regressions with one independent variable | Your question says "Which method is better?". Better what for? If you want to predict GPA you might want to use both variables. If your question is about the relation between IQ and GPA, then you have | regression with multiple independent variables vs multiple regressions with one independent variable
Your question says "Which method is better?". Better what for? If you want to predict GPA you might want to use both variables. If your question is about the relation between IQ and GPA, then you have no reason to add a... | regression with multiple independent variables vs multiple regressions with one independent variable
Your question says "Which method is better?". Better what for? If you want to predict GPA you might want to use both variables. If your question is about the relation between IQ and GPA, then you have |
52,272 | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set? | Yes, but the most focused treatment takes a different approach. You need to choose a model type that will train each class on an "is or is-not" basis. This is also called "one-vs-all". Your result will be, effectively, a separate set of weights for each of the five classes, i.e. five models that will decide whether or... | How can I create a neural network that can recognize objects without having data for objects that ar | Yes, but the most focused treatment takes a different approach. You need to choose a model type that will train each class on an "is or is-not" basis. This is also called "one-vs-all". Your result wi | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set?
Yes, but the most focused treatment takes a different approach. You need to choose a model type that will train each class on an "is or is-not" basis. This is also called "one-vs-all". Yo... | How can I create a neural network that can recognize objects without having data for objects that ar
Yes, but the most focused treatment takes a different approach. You need to choose a model type that will train each class on an "is or is-not" basis. This is also called "one-vs-all". Your result wi |
52,273 | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set? | Yes, and this is called: one-class classification when you train a model only on the positive data and try to predict the outliers.
check this it might help: https://medium.com/squad-engineering/one-class-classification-for-images-with-deep-features-69182fb4c9c5 | How can I create a neural network that can recognize objects without having data for objects that ar | Yes, and this is called: one-class classification when you train a model only on the positive data and try to predict the outliers.
check this it might help: https://medium.com/squad-engineering/one-c | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set?
Yes, and this is called: one-class classification when you train a model only on the positive data and try to predict the outliers.
check this it might help: https://medium.com/squad-engin... | How can I create a neural network that can recognize objects without having data for objects that ar
Yes, and this is called: one-class classification when you train a model only on the positive data and try to predict the outliers.
check this it might help: https://medium.com/squad-engineering/one-c |
52,274 | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set? | I think you need to look at this problem in a different aspect. Based on your case, instead of training your model to recognize 'if this item is recyclable', you can approach this problem as 'if this item is not recyclable'. The reason is you only have 5 recyclable items, which is much less that those of in reality. So... | How can I create a neural network that can recognize objects without having data for objects that ar | I think you need to look at this problem in a different aspect. Based on your case, instead of training your model to recognize 'if this item is recyclable', you can approach this problem as 'if this | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set?
I think you need to look at this problem in a different aspect. Based on your case, instead of training your model to recognize 'if this item is recyclable', you can approach this problem ... | How can I create a neural network that can recognize objects without having data for objects that ar
I think you need to look at this problem in a different aspect. Based on your case, instead of training your model to recognize 'if this item is recyclable', you can approach this problem as 'if this |
52,275 | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set? | I would suggest you to get more data and build a binary classifier.
First combine all of your data into 1 class (recyclable)
Then craw internet and find items not recyclable. We should found items that people usually throw in the trash. But not trying to get irrelevant images such as cats and dogs. | How can I create a neural network that can recognize objects without having data for objects that ar | I would suggest you to get more data and build a binary classifier.
First combine all of your data into 1 class (recyclable)
Then craw internet and find items not recyclable. We should found items th | How can I create a neural network that can recognize objects without having data for objects that aren't in the classification set?
I would suggest you to get more data and build a binary classifier.
First combine all of your data into 1 class (recyclable)
Then craw internet and find items not recyclable. We should fo... | How can I create a neural network that can recognize objects without having data for objects that ar
I would suggest you to get more data and build a binary classifier.
First combine all of your data into 1 class (recyclable)
Then craw internet and find items not recyclable. We should found items th |
52,276 | Does it make sense to do Cross Validation with a Small Sample? | I have concerns about involving 250 predictors when you have 16 samples. However, let's set that aside for now and focus on cross-validation.
You don't have much data, so any split from the full set to the training and validation set is going to result in really very few observations on which you can train. However, th... | Does it make sense to do Cross Validation with a Small Sample? | I have concerns about involving 250 predictors when you have 16 samples. However, let's set that aside for now and focus on cross-validation.
You don't have much data, so any split from the full set t | Does it make sense to do Cross Validation with a Small Sample?
I have concerns about involving 250 predictors when you have 16 samples. However, let's set that aside for now and focus on cross-validation.
You don't have much data, so any split from the full set to the training and validation set is going to result in r... | Does it make sense to do Cross Validation with a Small Sample?
I have concerns about involving 250 predictors when you have 16 samples. However, let's set that aside for now and focus on cross-validation.
You don't have much data, so any split from the full set t |
52,277 | Does it make sense to do Cross Validation with a Small Sample? | I'm being asked to perform CV on the set.
I'm going to assume that this cross validation will be for internal validation (part of verification) of the performance of the model you get from your 16 x 250 data set.
That is, you are not going to do any data-driven hyperparameter optimization (which can also use cross val... | Does it make sense to do Cross Validation with a Small Sample? | I'm being asked to perform CV on the set.
I'm going to assume that this cross validation will be for internal validation (part of verification) of the performance of the model you get from your 16 x | Does it make sense to do Cross Validation with a Small Sample?
I'm being asked to perform CV on the set.
I'm going to assume that this cross validation will be for internal validation (part of verification) of the performance of the model you get from your 16 x 250 data set.
That is, you are not going to do any data-d... | Does it make sense to do Cross Validation with a Small Sample?
I'm being asked to perform CV on the set.
I'm going to assume that this cross validation will be for internal validation (part of verification) of the performance of the model you get from your 16 x |
52,278 | Does it make sense to do Cross Validation with a Small Sample? | The theory behind cross validation works all the way down the case where $k = n$, which is called leave-one-out cross-validation. LOOCV is the best choice when $n$ is small. The upside to using cross validation is that your estimate of generalization error will be unbiased and you'll be able to form a non-parametric co... | Does it make sense to do Cross Validation with a Small Sample? | The theory behind cross validation works all the way down the case where $k = n$, which is called leave-one-out cross-validation. LOOCV is the best choice when $n$ is small. The upside to using cross | Does it make sense to do Cross Validation with a Small Sample?
The theory behind cross validation works all the way down the case where $k = n$, which is called leave-one-out cross-validation. LOOCV is the best choice when $n$ is small. The upside to using cross validation is that your estimate of generalization error ... | Does it make sense to do Cross Validation with a Small Sample?
The theory behind cross validation works all the way down the case where $k = n$, which is called leave-one-out cross-validation. LOOCV is the best choice when $n$ is small. The upside to using cross |
52,279 | Does it make sense to do Cross Validation with a Small Sample? | No, not only does cross-validation make no sense here, but no analysis makes any sense at all. You cannot validly analyze 250 features on a sample size of 16. Cross-validation cannot validly help you with that.
Let's go to the raw, absolute minimum: suppose you had only one predictor and you want to estimate an outcome... | Does it make sense to do Cross Validation with a Small Sample? | No, not only does cross-validation make no sense here, but no analysis makes any sense at all. You cannot validly analyze 250 features on a sample size of 16. Cross-validation cannot validly help you | Does it make sense to do Cross Validation with a Small Sample?
No, not only does cross-validation make no sense here, but no analysis makes any sense at all. You cannot validly analyze 250 features on a sample size of 16. Cross-validation cannot validly help you with that.
Let's go to the raw, absolute minimum: suppose... | Does it make sense to do Cross Validation with a Small Sample?
No, not only does cross-validation make no sense here, but no analysis makes any sense at all. You cannot validly analyze 250 features on a sample size of 16. Cross-validation cannot validly help you |
52,280 | Binomial distribution intituition for N | Note that the values of $X \sim Binomial(n,p)$ correspond to number of "positive" trials, not probability. As $n$ grows, the values of $\hat{p} = X/n$ converge to the true $p$, hence the probability as a long-run frequency definition. Values of $X = n\hat{p}$ clearly don't converge.
Same distinction might help understa... | Binomial distribution intituition for N | Note that the values of $X \sim Binomial(n,p)$ correspond to number of "positive" trials, not probability. As $n$ grows, the values of $\hat{p} = X/n$ converge to the true $p$, hence the probability a | Binomial distribution intituition for N
Note that the values of $X \sim Binomial(n,p)$ correspond to number of "positive" trials, not probability. As $n$ grows, the values of $\hat{p} = X/n$ converge to the true $p$, hence the probability as a long-run frequency definition. Values of $X = n\hat{p}$ clearly don't conver... | Binomial distribution intituition for N
Note that the values of $X \sim Binomial(n,p)$ correspond to number of "positive" trials, not probability. As $n$ grows, the values of $\hat{p} = X/n$ converge to the true $p$, hence the probability a |
52,281 | Binomial distribution intituition for N | The variance of the distribution increases with N as you are measuring the total number of successes, not the ratio. Imagine you throw a coin once. The variance is tiny as all possible results are 0 heads and 1 heads (1/2 of a success from the mean).
If you throw it a million times, you won't often get results that cl... | Binomial distribution intituition for N | The variance of the distribution increases with N as you are measuring the total number of successes, not the ratio. Imagine you throw a coin once. The variance is tiny as all possible results are 0 h | Binomial distribution intituition for N
The variance of the distribution increases with N as you are measuring the total number of successes, not the ratio. Imagine you throw a coin once. The variance is tiny as all possible results are 0 heads and 1 heads (1/2 of a success from the mean).
If you throw it a million ti... | Binomial distribution intituition for N
The variance of the distribution increases with N as you are measuring the total number of successes, not the ratio. Imagine you throw a coin once. The variance is tiny as all possible results are 0 h |
52,282 | Binomial distribution intituition for N | What binomial distribution describes, is the distribution of "successes" in $n$ Bernoulli trials, each having probability of success $p$. The most popular handbook example, is that you have a biased coin with probability of tossing heads equal to $p$, you throw it $n$ times and count the total number of heads tossed.
I... | Binomial distribution intituition for N | What binomial distribution describes, is the distribution of "successes" in $n$ Bernoulli trials, each having probability of success $p$. The most popular handbook example, is that you have a biased c | Binomial distribution intituition for N
What binomial distribution describes, is the distribution of "successes" in $n$ Bernoulli trials, each having probability of success $p$. The most popular handbook example, is that you have a biased coin with probability of tossing heads equal to $p$, you throw it $n$ times and c... | Binomial distribution intituition for N
What binomial distribution describes, is the distribution of "successes" in $n$ Bernoulli trials, each having probability of success $p$. The most popular handbook example, is that you have a biased c |
52,283 | Why do two implementations of the Anderson-Darling test produce such different p-values? | The Anderson-Darling test is a good test--but it has to be correctly applied and, as in most distributional tests, there is a subtle pitfall. Many analysts have fallen for it.
Distributional tests are Cinderella tests. In the fairy tale, the prince's men searched for a mysterious princess by comparing the feet of yo... | Why do two implementations of the Anderson-Darling test produce such different p-values? | The Anderson-Darling test is a good test--but it has to be correctly applied and, as in most distributional tests, there is a subtle pitfall. Many analysts have fallen for it.
Distributional tests a | Why do two implementations of the Anderson-Darling test produce such different p-values?
The Anderson-Darling test is a good test--but it has to be correctly applied and, as in most distributional tests, there is a subtle pitfall. Many analysts have fallen for it.
Distributional tests are Cinderella tests. In the fa... | Why do two implementations of the Anderson-Darling test produce such different p-values?
The Anderson-Darling test is a good test--but it has to be correctly applied and, as in most distributional tests, there is a subtle pitfall. Many analysts have fallen for it.
Distributional tests a |
52,284 | Derivation of the closed-form solution to minimizing the least-squares cost function | Our loss function is $RSS(\beta) = (y - X\beta)^T(y -X\beta)$. Expanding this and using the fact that $(u - v)^T = u^T - v^T$, we have
$$
RSS(\beta) = y^Ty - y^TX\beta - \beta^TX^Ty + \beta^T X^T X \beta.
$$
Noting that $y^TX\beta$ is a scalar, and for any scalar $r \in \mathbb R$ we have $r = r^T$ we have $y^T X \bet... | Derivation of the closed-form solution to minimizing the least-squares cost function | Our loss function is $RSS(\beta) = (y - X\beta)^T(y -X\beta)$. Expanding this and using the fact that $(u - v)^T = u^T - v^T$, we have
$$
RSS(\beta) = y^Ty - y^TX\beta - \beta^TX^Ty + \beta^T X^T X \ | Derivation of the closed-form solution to minimizing the least-squares cost function
Our loss function is $RSS(\beta) = (y - X\beta)^T(y -X\beta)$. Expanding this and using the fact that $(u - v)^T = u^T - v^T$, we have
$$
RSS(\beta) = y^Ty - y^TX\beta - \beta^TX^Ty + \beta^T X^T X \beta.
$$
Noting that $y^TX\beta$ is... | Derivation of the closed-form solution to minimizing the least-squares cost function
Our loss function is $RSS(\beta) = (y - X\beta)^T(y -X\beta)$. Expanding this and using the fact that $(u - v)^T = u^T - v^T$, we have
$$
RSS(\beta) = y^Ty - y^TX\beta - \beta^TX^Ty + \beta^T X^T X \ |
52,285 | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$? | Let $\mu = E(X)$. Then
$$Var(X) = E\left((X - \mu)(X - \mu)^T\right) = E\left(XX^T - \mu X^T - X \mu^T +
\mu \mu^T\right) \\ = E(XX^T) - \mu\mu^T$$
which generalizes the well-known scalar equality $Var(Z) = E(Z^2) - E(Z)^2$.
The natural estimator of $\Sigma := Var(X)$ is $\hat \Sigma = \frac 1{n-1}XX^T - \hat \mu \h... | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$? | Let $\mu = E(X)$. Then
$$Var(X) = E\left((X - \mu)(X - \mu)^T\right) = E\left(XX^T - \mu X^T - X \mu^T +
\mu \mu^T\right) \\ = E(XX^T) - \mu\mu^T$$
which generalizes the well-known scalar equality $ | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$?
Let $\mu = E(X)$. Then
$$Var(X) = E\left((X - \mu)(X - \mu)^T\right) = E\left(XX^T - \mu X^T - X \mu^T +
\mu \mu^T\right) \\ = E(XX^T) - \mu\mu^T$$
which generalizes the well-known scalar equality $Var(Z) = E(Z^2) - E(Z)^2$.
The natural estimator of $... | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$?
Let $\mu = E(X)$. Then
$$Var(X) = E\left((X - \mu)(X - \mu)^T\right) = E\left(XX^T - \mu X^T - X \mu^T +
\mu \mu^T\right) \\ = E(XX^T) - \mu\mu^T$$
which generalizes the well-known scalar equality $ |
52,286 | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$? | COMMENT:
@Chacone's answer is great as is, but I think there is one step that is left unexplained, and it is clearer with expectation notation. To reflect @GeoMatt22's comment in the following proof $X$ is a $p\times 1$ random vector:
$$
\begin{align}
\text{Cov}(X)&=\mathbb E\left[\,\left(X- \mathbb E[X] \right) \, \le... | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$? | COMMENT:
@Chacone's answer is great as is, but I think there is one step that is left unexplained, and it is clearer with expectation notation. To reflect @GeoMatt22's comment in the following proof $ | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$?
COMMENT:
@Chacone's answer is great as is, but I think there is one step that is left unexplained, and it is clearer with expectation notation. To reflect @GeoMatt22's comment in the following proof $X$ is a $p\times 1$ random vector:
$$
\begin{align}
\t... | Why can the covariance matrix be computed as $\frac{X X^T}{n-1}$?
COMMENT:
@Chacone's answer is great as is, but I think there is one step that is left unexplained, and it is clearer with expectation notation. To reflect @GeoMatt22's comment in the following proof $ |
52,287 | The p value for the random forest regression model | When in doubt, simulate or permute.
In this specific case:
Randomly permute your dependent variable.
Fit a random forest.
Note the % variance explained.
Do steps 1-3 multiple times, say 1,000-10,000 times. You now have an empirical distribution of % variance explained through a random forest, under the null hypothesi... | The p value for the random forest regression model | When in doubt, simulate or permute.
In this specific case:
Randomly permute your dependent variable.
Fit a random forest.
Note the % variance explained.
Do steps 1-3 multiple times, say 1,000-10,000 | The p value for the random forest regression model
When in doubt, simulate or permute.
In this specific case:
Randomly permute your dependent variable.
Fit a random forest.
Note the % variance explained.
Do steps 1-3 multiple times, say 1,000-10,000 times. You now have an empirical distribution of % variance explaine... | The p value for the random forest regression model
When in doubt, simulate or permute.
In this specific case:
Randomly permute your dependent variable.
Fit a random forest.
Note the % variance explained.
Do steps 1-3 multiple times, say 1,000-10,000 |
52,288 | what is suitable probability distribution for count data | Two common distributions for count data are the poisson or the negative-binomial one. If we fit these to your data, the NB works a lot better:
library(MASS) # for fitdistr()
xx <- 0:20
counts <- c(49, 36, 42, 26, 22, 22, 8, 12, 2, 4, 7, 0, 1, 1, 1, 1, 2, 1, 0, 1, 0)
obs <- rep(xx,counts)
poisson.density <- length(obs... | what is suitable probability distribution for count data | Two common distributions for count data are the poisson or the negative-binomial one. If we fit these to your data, the NB works a lot better:
library(MASS) # for fitdistr()
xx <- 0:20
counts <- c(49 | what is suitable probability distribution for count data
Two common distributions for count data are the poisson or the negative-binomial one. If we fit these to your data, the NB works a lot better:
library(MASS) # for fitdistr()
xx <- 0:20
counts <- c(49, 36, 42, 26, 22, 22, 8, 12, 2, 4, 7, 0, 1, 1, 1, 1, 2, 1, 0, 1... | what is suitable probability distribution for count data
Two common distributions for count data are the poisson or the negative-binomial one. If we fit these to your data, the NB works a lot better:
library(MASS) # for fitdistr()
xx <- 0:20
counts <- c(49 |
52,289 | Principle of Analogy and Method of Moments | Least squares estimator in the classical linear regression model is a Method of Moments estimator.
The model is
$$\mathbf y = \mathbf X\beta + \mathbf u$$
Instead of minimizing the sum of squared residuals, we can obtain the OLS estimator by noting that under the assumptions of the specific model, it holds that ("or... | Principle of Analogy and Method of Moments | Least squares estimator in the classical linear regression model is a Method of Moments estimator.
The model is
$$\mathbf y = \mathbf X\beta + \mathbf u$$
Instead of minimizing the sum of squared r | Principle of Analogy and Method of Moments
Least squares estimator in the classical linear regression model is a Method of Moments estimator.
The model is
$$\mathbf y = \mathbf X\beta + \mathbf u$$
Instead of minimizing the sum of squared residuals, we can obtain the OLS estimator by noting that under the assumption... | Principle of Analogy and Method of Moments
Least squares estimator in the classical linear regression model is a Method of Moments estimator.
The model is
$$\mathbf y = \mathbf X\beta + \mathbf u$$
Instead of minimizing the sum of squared r |
52,290 | Is AIC a measure of goodness of fit? [duplicate] | Just to expand a little on Hossein's answer: AIC is a measure of relative goodness of fit. If you take a model and calculate its AIC then you might get a value of, say, 2000. That number on its own is meaningless, and tells you nothing about how well your model fits. However, say you then fit another model which contai... | Is AIC a measure of goodness of fit? [duplicate] | Just to expand a little on Hossein's answer: AIC is a measure of relative goodness of fit. If you take a model and calculate its AIC then you might get a value of, say, 2000. That number on its own is | Is AIC a measure of goodness of fit? [duplicate]
Just to expand a little on Hossein's answer: AIC is a measure of relative goodness of fit. If you take a model and calculate its AIC then you might get a value of, say, 2000. That number on its own is meaningless, and tells you nothing about how well your model fits. How... | Is AIC a measure of goodness of fit? [duplicate]
Just to expand a little on Hossein's answer: AIC is a measure of relative goodness of fit. If you take a model and calculate its AIC then you might get a value of, say, 2000. That number on its own is |
52,291 | Is AIC a measure of goodness of fit? [duplicate] | AIC like many other model quality measures has two parts: goodness of fit and model simplicity. If you only measure the quality of a model by its goodness of fit, it favors overfitted models. On the other hand, if you only measure the model quality by its simplicity, it favors underfitted models. Therefore, AIC conside... | Is AIC a measure of goodness of fit? [duplicate] | AIC like many other model quality measures has two parts: goodness of fit and model simplicity. If you only measure the quality of a model by its goodness of fit, it favors overfitted models. On the o | Is AIC a measure of goodness of fit? [duplicate]
AIC like many other model quality measures has two parts: goodness of fit and model simplicity. If you only measure the quality of a model by its goodness of fit, it favors overfitted models. On the other hand, if you only measure the model quality by its simplicity, it ... | Is AIC a measure of goodness of fit? [duplicate]
AIC like many other model quality measures has two parts: goodness of fit and model simplicity. If you only measure the quality of a model by its goodness of fit, it favors overfitted models. On the o |
52,292 | Need a smoother fit curve | This seems to be a case of dose-response modelling. There is an excellent paper by Ritz et al. (2015) that describes how these analyses can be performed using R. An introduction is provided here.
Using your data and the R package drc (which is the package described in the paper by Ritz et al.), I fitted a 4-parameter l... | Need a smoother fit curve | This seems to be a case of dose-response modelling. There is an excellent paper by Ritz et al. (2015) that describes how these analyses can be performed using R. An introduction is provided here.
Usin | Need a smoother fit curve
This seems to be a case of dose-response modelling. There is an excellent paper by Ritz et al. (2015) that describes how these analyses can be performed using R. An introduction is provided here.
Using your data and the R package drc (which is the package described in the paper by Ritz et al.)... | Need a smoother fit curve
This seems to be a case of dose-response modelling. There is an excellent paper by Ritz et al. (2015) that describes how these analyses can be performed using R. An introduction is provided here.
Usin |
52,293 | Need a smoother fit curve | I also think the original plot is smooth to some extent already. Another approach is to have ggplot do the smoothing for you. Not sure if this is what you want.
ggplot(XY, aes(x=log(Concn), y = Values)) + geom_smooth(method="loess") | Need a smoother fit curve | I also think the original plot is smooth to some extent already. Another approach is to have ggplot do the smoothing for you. Not sure if this is what you want.
ggplot(XY, aes(x=log(Concn), y = Values | Need a smoother fit curve
I also think the original plot is smooth to some extent already. Another approach is to have ggplot do the smoothing for you. Not sure if this is what you want.
ggplot(XY, aes(x=log(Concn), y = Values)) + geom_smooth(method="loess") | Need a smoother fit curve
I also think the original plot is smooth to some extent already. Another approach is to have ggplot do the smoothing for you. Not sure if this is what you want.
ggplot(XY, aes(x=log(Concn), y = Values |
52,294 | Need a smoother fit curve | You've plotted your curve as a linear interpolation between eleven data points. Even if the true underlying curve smooth, drawing it by taking eleven sample points and interpolating linearly is going to look pointy.
You need more sample points when drawing the curve. Create a sequence of x-values to use as sample poi... | Need a smoother fit curve | You've plotted your curve as a linear interpolation between eleven data points. Even if the true underlying curve smooth, drawing it by taking eleven sample points and interpolating linearly is going | Need a smoother fit curve
You've plotted your curve as a linear interpolation between eleven data points. Even if the true underlying curve smooth, drawing it by taking eleven sample points and interpolating linearly is going to look pointy.
You need more sample points when drawing the curve. Create a sequence of x-v... | Need a smoother fit curve
You've plotted your curve as a linear interpolation between eleven data points. Even if the true underlying curve smooth, drawing it by taking eleven sample points and interpolating linearly is going |
52,295 | Need a smoother fit curve | Your function looks pretty smooth to me, and what I think you want is more flexibility.
So here's a spline with 8 degrees of freedom:
library(splines)
my_glm <- glm(Values ~ ns(Concn, df = 8), data = XY)
plot(XY$Values ~ XY$Concn , data = XY, col = 4,
main = "XY Std curve", log = "x")
lines(XY$Concn, predict(my_gl... | Need a smoother fit curve | Your function looks pretty smooth to me, and what I think you want is more flexibility.
So here's a spline with 8 degrees of freedom:
library(splines)
my_glm <- glm(Values ~ ns(Concn, df = 8), data = | Need a smoother fit curve
Your function looks pretty smooth to me, and what I think you want is more flexibility.
So here's a spline with 8 degrees of freedom:
library(splines)
my_glm <- glm(Values ~ ns(Concn, df = 8), data = XY)
plot(XY$Values ~ XY$Concn , data = XY, col = 4,
main = "XY Std curve", log = "x")
lin... | Need a smoother fit curve
Your function looks pretty smooth to me, and what I think you want is more flexibility.
So here's a spline with 8 degrees of freedom:
library(splines)
my_glm <- glm(Values ~ ns(Concn, df = 8), data = |
52,296 | Bayesian inference: numerically sampling from the posterior predictive | If you can simulate values from $P(x_{\text{new}}|\theta)$, you can simply use your $N$ samples from posterior predictive and generate $x_{\text{new},i}$ for each posterior sample from this model to get a sample from the posterior predictive $\{x_{\text{new}}\}_{i=1}^N$.
This amounts to obtaining a collection $\{x_{\... | Bayesian inference: numerically sampling from the posterior predictive | If you can simulate values from $P(x_{\text{new}}|\theta)$, you can simply use your $N$ samples from posterior predictive and generate $x_{\text{new},i}$ for each posterior sample from this model to g | Bayesian inference: numerically sampling from the posterior predictive
If you can simulate values from $P(x_{\text{new}}|\theta)$, you can simply use your $N$ samples from posterior predictive and generate $x_{\text{new},i}$ for each posterior sample from this model to get a sample from the posterior predictive $\{x_{\... | Bayesian inference: numerically sampling from the posterior predictive
If you can simulate values from $P(x_{\text{new}}|\theta)$, you can simply use your $N$ samples from posterior predictive and generate $x_{\text{new},i}$ for each posterior sample from this model to g |
52,297 | Bayesian inference: numerically sampling from the posterior predictive | Here is an instantiated example of the answer provided by lbelzile. The application is linear regression, and the goal is to find the posterior predicted distribution of $y$ values at a probed $x$ value:
http://doingbayesiandataanalysis.blogspot.com/2016/10/posterior-predictive-distribution-for.html
The key idea is tha... | Bayesian inference: numerically sampling from the posterior predictive | Here is an instantiated example of the answer provided by lbelzile. The application is linear regression, and the goal is to find the posterior predicted distribution of $y$ values at a probed $x$ val | Bayesian inference: numerically sampling from the posterior predictive
Here is an instantiated example of the answer provided by lbelzile. The application is linear regression, and the goal is to find the posterior predicted distribution of $y$ values at a probed $x$ value:
http://doingbayesiandataanalysis.blogspot.com... | Bayesian inference: numerically sampling from the posterior predictive
Here is an instantiated example of the answer provided by lbelzile. The application is linear regression, and the goal is to find the posterior predicted distribution of $y$ values at a probed $x$ val |
52,298 | Variance of Cohen's $d$ for within subjects designs | There is no know derivation of the variance of $d_{av}$. In fact, this is not how one should compute the $d$ value for a within-subjects design (neither with $d_{rm}$ or the $d_{av}$).
There are two approaches for computing a $d$ value for a within-subjects design. The first uses change score standardization and is giv... | Variance of Cohen's $d$ for within subjects designs | There is no know derivation of the variance of $d_{av}$. In fact, this is not how one should compute the $d$ value for a within-subjects design (neither with $d_{rm}$ or the $d_{av}$).
There are two a | Variance of Cohen's $d$ for within subjects designs
There is no know derivation of the variance of $d_{av}$. In fact, this is not how one should compute the $d$ value for a within-subjects design (neither with $d_{rm}$ or the $d_{av}$).
There are two approaches for computing a $d$ value for a within-subjects design. Th... | Variance of Cohen's $d$ for within subjects designs
There is no know derivation of the variance of $d_{av}$. In fact, this is not how one should compute the $d$ value for a within-subjects design (neither with $d_{rm}$ or the $d_{av}$).
There are two a |
52,299 | Variance of Cohen's $d$ for within subjects designs | Structural equation modeling (SEM) is your friend in this case. We need the sample means and the covariance matrix as inputs. We may label the parameters (m1, m2, sd1, and sd2) and define $d_{av}$=(m2-m1)/((sd1+sd2)/2). SEM automatically calculates $Var(d_{av})$ by taken the correlation between the pre- and post-test s... | Variance of Cohen's $d$ for within subjects designs | Structural equation modeling (SEM) is your friend in this case. We need the sample means and the covariance matrix as inputs. We may label the parameters (m1, m2, sd1, and sd2) and define $d_{av}$=(m2 | Variance of Cohen's $d$ for within subjects designs
Structural equation modeling (SEM) is your friend in this case. We need the sample means and the covariance matrix as inputs. We may label the parameters (m1, m2, sd1, and sd2) and define $d_{av}$=(m2-m1)/((sd1+sd2)/2). SEM automatically calculates $Var(d_{av})$ by ta... | Variance of Cohen's $d$ for within subjects designs
Structural equation modeling (SEM) is your friend in this case. We need the sample means and the covariance matrix as inputs. We may label the parameters (m1, m2, sd1, and sd2) and define $d_{av}$=(m2 |
52,300 | What is collinearity and how does it differ from multicollinearity? | In statistics, the terms collinearity and multicollinearity are overlapping. Collinearity is a linear association between two explanatory variables. Multicollinearity in a multiple regression model are highly linearly related associations between two or more explanatory variables.
In case of perfect multicollinearity t... | What is collinearity and how does it differ from multicollinearity? | In statistics, the terms collinearity and multicollinearity are overlapping. Collinearity is a linear association between two explanatory variables. Multicollinearity in a multiple regression model ar | What is collinearity and how does it differ from multicollinearity?
In statistics, the terms collinearity and multicollinearity are overlapping. Collinearity is a linear association between two explanatory variables. Multicollinearity in a multiple regression model are highly linearly related associations between two o... | What is collinearity and how does it differ from multicollinearity?
In statistics, the terms collinearity and multicollinearity are overlapping. Collinearity is a linear association between two explanatory variables. Multicollinearity in a multiple regression model ar |
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