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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52,101 | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$ where $X_i \sim N(0,1)$? | Assuming independent $X_i$, the mean $\frac{1}{n}\sum X_i$ is also normal, i.e. $N(0,1/n)$. Absolute value of it is Half-normal, which has mean $E[Y_1]=\frac{\sigma\sqrt{2}}{\sqrt{\pi}}=\sqrt{\frac{2}{n\pi}}$. For $Y_2$ we can find the expected value directly:
$$E[Y_2]=\frac{1}{n}\sum_{i=1}^n E[|X_i|]=E[|X_i|]=\sqrt\fr... | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$ | Assuming independent $X_i$, the mean $\frac{1}{n}\sum X_i$ is also normal, i.e. $N(0,1/n)$. Absolute value of it is Half-normal, which has mean $E[Y_1]=\frac{\sigma\sqrt{2}}{\sqrt{\pi}}=\sqrt{\frac{2} | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$ where $X_i \sim N(0,1)$?
Assuming independent $X_i$, the mean $\frac{1}{n}\sum X_i$ is also normal, i.e. $N(0,1/n)$. Absolute value of it is Half-normal, which has mean $E[Y_1]=\frac{\sigma\sqrt{2}}{\sqrt{\pi}}=\sqrt{\f... | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$
Assuming independent $X_i$, the mean $\frac{1}{n}\sum X_i$ is also normal, i.e. $N(0,1/n)$. Absolute value of it is Half-normal, which has mean $E[Y_1]=\frac{\sigma\sqrt{2}}{\sqrt{\pi}}=\sqrt{\frac{2} |
52,102 | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$ where $X_i \sim N(0,1)$? | Answer:
Whatever the distribution of $X_1,...,X_n$,
$$\mathbb{E} Y_2 \geq \mathbb{E} Y_1.$$
Details:
For any $n$ numbers $X_1,..., X_n$ it is true that
$$ \sum_i |X_i| \geq |\sum_i X_i|$$
and dividing both sides by $n$:
$$ \frac{1}{n}\sum_i |X_i| \geq \frac{1}{n}|\sum_i X_i| = |\frac{1}{n}\sum_i X_i|.$$
Now, the key ... | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$ | Answer:
Whatever the distribution of $X_1,...,X_n$,
$$\mathbb{E} Y_2 \geq \mathbb{E} Y_1.$$
Details:
For any $n$ numbers $X_1,..., X_n$ it is true that
$$ \sum_i |X_i| \geq |\sum_i X_i|$$
and dividi | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$ where $X_i \sim N(0,1)$?
Answer:
Whatever the distribution of $X_1,...,X_n$,
$$\mathbb{E} Y_2 \geq \mathbb{E} Y_1.$$
Details:
For any $n$ numbers $X_1,..., X_n$ it is true that
$$ \sum_i |X_i| \geq |\sum_i X_i|$$
and ... | How can I establish an inequality between $|\frac1n \sum_{i=1}^nX_i|$ and $\frac1n\sum^n_{i=1}|X_i|$
Answer:
Whatever the distribution of $X_1,...,X_n$,
$$\mathbb{E} Y_2 \geq \mathbb{E} Y_1.$$
Details:
For any $n$ numbers $X_1,..., X_n$ it is true that
$$ \sum_i |X_i| \geq |\sum_i X_i|$$
and dividi |
52,103 | Probability that any two people have the same birthday? | Unfortunately, yes, there is flaw. According to your purported formula, the probabilty of having two people with the same birthday, when you only have $n=1$ person, is:
$$P_1 = 1 - \Big( \frac{364}{365} \Big)^1 = 1 - \frac{364}{365} = \frac{1}{365} \neq 0.$$
So, you are ascribing a non-zero probability to an impossib... | Probability that any two people have the same birthday? | Unfortunately, yes, there is flaw. According to your purported formula, the probabilty of having two people with the same birthday, when you only have $n=1$ person, is:
$$P_1 = 1 - \Big( \frac{364}{3 | Probability that any two people have the same birthday?
Unfortunately, yes, there is flaw. According to your purported formula, the probabilty of having two people with the same birthday, when you only have $n=1$ person, is:
$$P_1 = 1 - \Big( \frac{364}{365} \Big)^1 = 1 - \frac{364}{365} = \frac{1}{365} \neq 0.$$
So,... | Probability that any two people have the same birthday?
Unfortunately, yes, there is flaw. According to your purported formula, the probabilty of having two people with the same birthday, when you only have $n=1$ person, is:
$$P_1 = 1 - \Big( \frac{364}{3 |
52,104 | Probability that any two people have the same birthday? | One way to find the probability of no birthday match in a room with $n=25$ people is shown in the Wikipedia link of my first Comment. Here is a slightly different way to write it:
$$P(\text{No Match}) = \frac{{}_{365}P_{25}}{365^{25}}
= \prod_{i=0}^{24}\left(1 - \frac{i}{365}\right) = 0.4313.$$
In R, this can be evalua... | Probability that any two people have the same birthday? | One way to find the probability of no birthday match in a room with $n=25$ people is shown in the Wikipedia link of my first Comment. Here is a slightly different way to write it:
$$P(\text{No Match}) | Probability that any two people have the same birthday?
One way to find the probability of no birthday match in a room with $n=25$ people is shown in the Wikipedia link of my first Comment. Here is a slightly different way to write it:
$$P(\text{No Match}) = \frac{{}_{365}P_{25}}{365^{25}}
= \prod_{i=0}^{24}\left(1 - \... | Probability that any two people have the same birthday?
One way to find the probability of no birthday match in a room with $n=25$ people is shown in the Wikipedia link of my first Comment. Here is a slightly different way to write it:
$$P(\text{No Match}) |
52,105 | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance? [duplicate] | Vertical distance is a "real distance". The distance from a given point to any point on the line is a "real distance". The question for how to fit the best regression line is which of the infinite possible distances makes the most sense for how we are thinking about our model. That is, any number of possible loss fu... | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance? | Vertical distance is a "real distance". The distance from a given point to any point on the line is a "real distance". The question for how to fit the best regression line is which of the infinite p | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance? [duplicate]
Vertical distance is a "real distance". The distance from a given point to any point on the line is a "real distance". The question for how to fit the best regression line is which of the infinite possible... | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance?
Vertical distance is a "real distance". The distance from a given point to any point on the line is a "real distance". The question for how to fit the best regression line is which of the infinite p |
52,106 | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance? [duplicate] | Summing up Michael Chernick comment and gung answer:
Both vertical and point distances are "real" - it all depends on the situation.
Ordinary linear regression assumes the $X$ value are known and the only error is in the $Y$'s. That is often a reasonable assumption.
If you assume error in the $X$'s as well, you get w... | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance? | Summing up Michael Chernick comment and gung answer:
Both vertical and point distances are "real" - it all depends on the situation.
Ordinary linear regression assumes the $X$ value are known and th | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance? [duplicate]
Summing up Michael Chernick comment and gung answer:
Both vertical and point distances are "real" - it all depends on the situation.
Ordinary linear regression assumes the $X$ value are known and the only ... | Why does linear regression use "vertical" distance to the best-fit-line, instead of actual distance?
Summing up Michael Chernick comment and gung answer:
Both vertical and point distances are "real" - it all depends on the situation.
Ordinary linear regression assumes the $X$ value are known and th |
52,107 | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$ | In this answer to the question
$$\dfrac{{n+1 \choose x}p^x(1-p)^{n+1-x}}{{n \choose x}p^x(1-p)^{n-x}} = \dfrac{n+1}{n+1-x}(1-p)$$
represents the likelihood ratio
$$\frac{L(n+1\mid x,p)}{L(n\mid x,p)}$$
If this ratio is larger than one (1), $${L(n+1\mid x,p)}>{L(n|\mid x,p)}$$ $-$ergo the likelihood increases$-$ and if ... | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$ | In this answer to the question
$$\dfrac{{n+1 \choose x}p^x(1-p)^{n+1-x}}{{n \choose x}p^x(1-p)^{n-x}} = \dfrac{n+1}{n+1-x}(1-p)$$
represents the likelihood ratio
$$\frac{L(n+1\mid x,p)}{L(n\mid x,p)}$ | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$
In this answer to the question
$$\dfrac{{n+1 \choose x}p^x(1-p)^{n+1-x}}{{n \choose x}p^x(1-p)^{n-x}} = \dfrac{n+1}{n+1-x}(1-p)$$
represents the likelihood ratio
$$\frac{L(n+1\mid x,p)}{L(n\mid x,p)}$$
If this ratio is larger than one (1), $${L(n+1\mid... | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$
In this answer to the question
$$\dfrac{{n+1 \choose x}p^x(1-p)^{n+1-x}}{{n \choose x}p^x(1-p)^{n-x}} = \dfrac{n+1}{n+1-x}(1-p)$$
represents the likelihood ratio
$$\frac{L(n+1\mid x,p)}{L(n\mid x,p)}$ |
52,108 | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$ | As Xi'an correctly points out, this is a maximisation problem over integers, not real numbers. The objective function is quasi-concave, so we can obtain the maximising value by finding the point at which the (forward) likelihood ratio first drops below one. His answer shows you how to do this, and I have nothing to a... | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$ | As Xi'an correctly points out, this is a maximisation problem over integers, not real numbers. The objective function is quasi-concave, so we can obtain the maximising value by finding the point at w | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$
As Xi'an correctly points out, this is a maximisation problem over integers, not real numbers. The objective function is quasi-concave, so we can obtain the maximising value by finding the point at which the (forward) likelihood ratio first drops belo... | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$
As Xi'an correctly points out, this is a maximisation problem over integers, not real numbers. The objective function is quasi-concave, so we can obtain the maximising value by finding the point at w |
52,109 | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$ | Binomial PMF is a discrete function of $n$, say $f(n)$, given others, i.e. $x,p$. We want to maximize it in terms of $n$. Typically, we would take the derivate and equate it to zero, but in discrete cases we shouldn't do that. This PDF is known to have its peak value(s) around its mean (not exactly but close). Its grap... | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$ | Binomial PMF is a discrete function of $n$, say $f(n)$, given others, i.e. $x,p$. We want to maximize it in terms of $n$. Typically, we would take the derivate and equate it to zero, but in discrete c | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$
Binomial PMF is a discrete function of $n$, say $f(n)$, given others, i.e. $x,p$. We want to maximize it in terms of $n$. Typically, we would take the derivate and equate it to zero, but in discrete cases we shouldn't do that. This PDF is known to have... | Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$
Binomial PMF is a discrete function of $n$, say $f(n)$, given others, i.e. $x,p$. We want to maximize it in terms of $n$. Typically, we would take the derivate and equate it to zero, but in discrete c |
52,110 | Fisher exact test on 4 x 3 table, with low count? | Having observed zeros is not an issue for a Fisher Exact test -- nor indeed is it a problem for a chi-squared test (it's not clear why you think this would be a difficulty with an exact test; if you can clarify the source of your concern, additional explanation/clarification may be possible). An entire row or column of... | Fisher exact test on 4 x 3 table, with low count? | Having observed zeros is not an issue for a Fisher Exact test -- nor indeed is it a problem for a chi-squared test (it's not clear why you think this would be a difficulty with an exact test; if you c | Fisher exact test on 4 x 3 table, with low count?
Having observed zeros is not an issue for a Fisher Exact test -- nor indeed is it a problem for a chi-squared test (it's not clear why you think this would be a difficulty with an exact test; if you can clarify the source of your concern, additional explanation/clarific... | Fisher exact test on 4 x 3 table, with low count?
Having observed zeros is not an issue for a Fisher Exact test -- nor indeed is it a problem for a chi-squared test (it's not clear why you think this would be a difficulty with an exact test; if you c |
52,111 | Fisher exact test on 4 x 3 table, with low count? | In principle, Fisher's exact test can be used on tables of any size, with any entries. The only issue is whether it is computationally feasible, which is an issue when you are using large tables with large values. In this case the fisher.test function in R can comfortably handle the matrix you are using, and the syst... | Fisher exact test on 4 x 3 table, with low count? | In principle, Fisher's exact test can be used on tables of any size, with any entries. The only issue is whether it is computationally feasible, which is an issue when you are using large tables with | Fisher exact test on 4 x 3 table, with low count?
In principle, Fisher's exact test can be used on tables of any size, with any entries. The only issue is whether it is computationally feasible, which is an issue when you are using large tables with large values. In this case the fisher.test function in R can comfort... | Fisher exact test on 4 x 3 table, with low count?
In principle, Fisher's exact test can be used on tables of any size, with any entries. The only issue is whether it is computationally feasible, which is an issue when you are using large tables with |
52,112 | Specify contrasts for lme with interactions | If you look at the summary of your fixed effects portion of the model, you can label each row as follows:
Value Std.Error DF t-value p-value
beta0 (Intercept) 204417.8 109088.33 168 1.87387 0.0627
beta1 Exposure2 -192542.9 58653.05 168 -3.28274 0... | Specify contrasts for lme with interactions | If you look at the summary of your fixed effects portion of the model, you can label each row as follows:
Value Std.Error DF t-value p-value
beta0 (Intercept) | Specify contrasts for lme with interactions
If you look at the summary of your fixed effects portion of the model, you can label each row as follows:
Value Std.Error DF t-value p-value
beta0 (Intercept) 204417.8 109088.33 168 1.87387 0.0627
beta1 Exposure2 ... | Specify contrasts for lme with interactions
If you look at the summary of your fixed effects portion of the model, you can label each row as follows:
Value Std.Error DF t-value p-value
beta0 (Intercept) |
52,113 | Specify contrasts for lme with interactions | You could also reparameterise your model and look at the parameter estimates
Something like
model2 <- lme(AUC ~ Exposure -1 + Exposure:Sex + Exposure:Genotype +
Basal,
random = ~ 1 | Date / Experiment / Cell,
data = mydata)
then look differences between sexes with Exposure categories a... | Specify contrasts for lme with interactions | You could also reparameterise your model and look at the parameter estimates
Something like
model2 <- lme(AUC ~ Exposure -1 + Exposure:Sex + Exposure:Genotype +
Basal,
random = | Specify contrasts for lme with interactions
You could also reparameterise your model and look at the parameter estimates
Something like
model2 <- lme(AUC ~ Exposure -1 + Exposure:Sex + Exposure:Genotype +
Basal,
random = ~ 1 | Date / Experiment / Cell,
data = mydata)
then look differen... | Specify contrasts for lme with interactions
You could also reparameterise your model and look at the parameter estimates
Something like
model2 <- lme(AUC ~ Exposure -1 + Exposure:Sex + Exposure:Genotype +
Basal,
random = |
52,114 | Specify contrasts for lme with interactions | I think for the kind of questions you are asking, you want to use post-hoc comparisons, such as with emmeans, rather than trying to interpret the summary output.
I have sample code below. I created some data and used a simpler model, so obviously my results will be different than yours.
Because your model is complex, ... | Specify contrasts for lme with interactions | I think for the kind of questions you are asking, you want to use post-hoc comparisons, such as with emmeans, rather than trying to interpret the summary output.
I have sample code below. I created s | Specify contrasts for lme with interactions
I think for the kind of questions you are asking, you want to use post-hoc comparisons, such as with emmeans, rather than trying to interpret the summary output.
I have sample code below. I created some data and used a simpler model, so obviously my results will be different... | Specify contrasts for lme with interactions
I think for the kind of questions you are asking, you want to use post-hoc comparisons, such as with emmeans, rather than trying to interpret the summary output.
I have sample code below. I created s |
52,115 | how is deep learning integrated into the reinforcement learning | The core of Q-learning is to learn a function $Q$ which maps state-action pairs to the expected discounted future reward.
This function can be represented in a variety of ways
As a look-up table (each row containing state, action, and expected reward)
As a linear or nonlinear regression model mapping state-action to r... | how is deep learning integrated into the reinforcement learning | The core of Q-learning is to learn a function $Q$ which maps state-action pairs to the expected discounted future reward.
This function can be represented in a variety of ways
As a look-up table (eac | how is deep learning integrated into the reinforcement learning
The core of Q-learning is to learn a function $Q$ which maps state-action pairs to the expected discounted future reward.
This function can be represented in a variety of ways
As a look-up table (each row containing state, action, and expected reward)
As ... | how is deep learning integrated into the reinforcement learning
The core of Q-learning is to learn a function $Q$ which maps state-action pairs to the expected discounted future reward.
This function can be represented in a variety of ways
As a look-up table (eac |
52,116 | how is deep learning integrated into the reinforcement learning | The input into the neural network is the current observation of the environment (for example, a screen shot of a game, or a list of values from some sensors).
The output from the neural network is a list of Q-values covering each of the choices that the agent can make (in Space Invaders for example, the list might be a... | how is deep learning integrated into the reinforcement learning | The input into the neural network is the current observation of the environment (for example, a screen shot of a game, or a list of values from some sensors).
The output from the neural network is a l | how is deep learning integrated into the reinforcement learning
The input into the neural network is the current observation of the environment (for example, a screen shot of a game, or a list of values from some sensors).
The output from the neural network is a list of Q-values covering each of the choices that the ag... | how is deep learning integrated into the reinforcement learning
The input into the neural network is the current observation of the environment (for example, a screen shot of a game, or a list of values from some sensors).
The output from the neural network is a l |
52,117 | Simplest way for ANN to learn F = MA? | Yes, the network will probably approximate some sort of multiplication, but it is unlikely to generalize outside the range of inputs you train it on.
You may have more luck learning and generalizing the rule by using a quadratic neuron, which is capable of multiplying inputs. RNTNs introduced here do something to that... | Simplest way for ANN to learn F = MA? | Yes, the network will probably approximate some sort of multiplication, but it is unlikely to generalize outside the range of inputs you train it on.
You may have more luck learning and generalizing | Simplest way for ANN to learn F = MA?
Yes, the network will probably approximate some sort of multiplication, but it is unlikely to generalize outside the range of inputs you train it on.
You may have more luck learning and generalizing the rule by using a quadratic neuron, which is capable of multiplying inputs. RNTN... | Simplest way for ANN to learn F = MA?
Yes, the network will probably approximate some sort of multiplication, but it is unlikely to generalize outside the range of inputs you train it on.
You may have more luck learning and generalizing |
52,118 | Simplest way for ANN to learn F = MA? | As Shimao said, a NNet will be able to learn some sigmoid based approximation of multiplication, but it will likely fail for new values that fall outside of the range of the training set.
Remember that a 3 layer feedforward neural net is a universal approximator, given a sufficient number of neurons. So you might end ... | Simplest way for ANN to learn F = MA? | As Shimao said, a NNet will be able to learn some sigmoid based approximation of multiplication, but it will likely fail for new values that fall outside of the range of the training set.
Remember th | Simplest way for ANN to learn F = MA?
As Shimao said, a NNet will be able to learn some sigmoid based approximation of multiplication, but it will likely fail for new values that fall outside of the range of the training set.
Remember that a 3 layer feedforward neural net is a universal approximator, given a sufficien... | Simplest way for ANN to learn F = MA?
As Shimao said, a NNet will be able to learn some sigmoid based approximation of multiplication, but it will likely fail for new values that fall outside of the range of the training set.
Remember th |
52,119 | Generalized Pareto distribution (GPD) | The replacement of $z$ with $\frac{x-\mu}{\sigma}$ allows the generalization to a "location-scale family". This is common when dealing with continuous distributions. That is, tweaking $\mu$ and $\sigma$ you can center the distribution and spread the distribution as you please.
Check out what happens to the distribution... | Generalized Pareto distribution (GPD) | The replacement of $z$ with $\frac{x-\mu}{\sigma}$ allows the generalization to a "location-scale family". This is common when dealing with continuous distributions. That is, tweaking $\mu$ and $\sigm | Generalized Pareto distribution (GPD)
The replacement of $z$ with $\frac{x-\mu}{\sigma}$ allows the generalization to a "location-scale family". This is common when dealing with continuous distributions. That is, tweaking $\mu$ and $\sigma$ you can center the distribution and spread the distribution as you please.
Chec... | Generalized Pareto distribution (GPD)
The replacement of $z$ with $\frac{x-\mu}{\sigma}$ allows the generalization to a "location-scale family". This is common when dealing with continuous distributions. That is, tweaking $\mu$ and $\sigm |
52,120 | Generalized Pareto distribution (GPD) | The max-stability property of the GEV distribution is quite well known
in relation with the Fisher-Tippett-Gnedenko theorem. The GPD has the
following remarkable property which can be named threshold
stability and relates to the Pickands-Balkema-de Haan theorem. It
helps to understand the relation between the location... | Generalized Pareto distribution (GPD) | The max-stability property of the GEV distribution is quite well known
in relation with the Fisher-Tippett-Gnedenko theorem. The GPD has the
following remarkable property which can be named threshold | Generalized Pareto distribution (GPD)
The max-stability property of the GEV distribution is quite well known
in relation with the Fisher-Tippett-Gnedenko theorem. The GPD has the
following remarkable property which can be named threshold
stability and relates to the Pickands-Balkema-de Haan theorem. It
helps to unders... | Generalized Pareto distribution (GPD)
The max-stability property of the GEV distribution is quite well known
in relation with the Fisher-Tippett-Gnedenko theorem. The GPD has the
following remarkable property which can be named threshold |
52,121 | When a prior distribution would not be overwhelmed by data, regardless of the sample size? | One way is to set a prior that is a constant. For example, take a simple linear regression context where you have an intercept, one slope, and an error term. If you set the prior on beta to be $\beta \sim \text{N}(5, 0)$, then no amount of data can overwhelm that prior. You are multiplying an arbitrarily large number o... | When a prior distribution would not be overwhelmed by data, regardless of the sample size? | One way is to set a prior that is a constant. For example, take a simple linear regression context where you have an intercept, one slope, and an error term. If you set the prior on beta to be $\beta | When a prior distribution would not be overwhelmed by data, regardless of the sample size?
One way is to set a prior that is a constant. For example, take a simple linear regression context where you have an intercept, one slope, and an error term. If you set the prior on beta to be $\beta \sim \text{N}(5, 0)$, then no... | When a prior distribution would not be overwhelmed by data, regardless of the sample size?
One way is to set a prior that is a constant. For example, take a simple linear regression context where you have an intercept, one slope, and an error term. If you set the prior on beta to be $\beta |
52,122 | When a prior distribution would not be overwhelmed by data, regardless of the sample size? | Another example would be lack of identification.
Assume a proper prior $\pi(\theta)$. We obtain that the posterior is equal to the prior, $\pi(\theta|y)=\pi(\theta)$, if $f(y|\theta)$ does not depend on $\theta$, i.e., if the likelihood is not informative about the parameter of interest:
\begin{eqnarray*}
\pi(\theta|y... | When a prior distribution would not be overwhelmed by data, regardless of the sample size? | Another example would be lack of identification.
Assume a proper prior $\pi(\theta)$. We obtain that the posterior is equal to the prior, $\pi(\theta|y)=\pi(\theta)$, if $f(y|\theta)$ does not depend | When a prior distribution would not be overwhelmed by data, regardless of the sample size?
Another example would be lack of identification.
Assume a proper prior $\pi(\theta)$. We obtain that the posterior is equal to the prior, $\pi(\theta|y)=\pi(\theta)$, if $f(y|\theta)$ does not depend on $\theta$, i.e., if the li... | When a prior distribution would not be overwhelmed by data, regardless of the sample size?
Another example would be lack of identification.
Assume a proper prior $\pi(\theta)$. We obtain that the posterior is equal to the prior, $\pi(\theta|y)=\pi(\theta)$, if $f(y|\theta)$ does not depend |
52,123 | Relationship between model over fitting and number of parameters | An exact answer depends on a particular statistical model and the data dimensionality. However, usually the more parameters the model has, the more functions it can represent. A common assumption is that the function generating the data is simpler than the exact random noise on the training samples, thus smaller models... | Relationship between model over fitting and number of parameters | An exact answer depends on a particular statistical model and the data dimensionality. However, usually the more parameters the model has, the more functions it can represent. A common assumption is t | Relationship between model over fitting and number of parameters
An exact answer depends on a particular statistical model and the data dimensionality. However, usually the more parameters the model has, the more functions it can represent. A common assumption is that the function generating the data is simpler than th... | Relationship between model over fitting and number of parameters
An exact answer depends on a particular statistical model and the data dimensionality. However, usually the more parameters the model has, the more functions it can represent. A common assumption is t |
52,124 | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)? | When I even use leave one out (LOOCV) to calculate LDA projection matrix, it is calculated by holding out just one observation. My question is why even in this case the projection matrix ($W$) is so over-fitted and sensitive to cross validation? Intuitively I've hold out just one sample but it seems the projection matr... | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)? | When I even use leave one out (LOOCV) to calculate LDA projection matrix, it is calculated by holding out just one observation. My question is why even in this case the projection matrix ($W$) is so o | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)?
When I even use leave one out (LOOCV) to calculate LDA projection matrix, it is calculated by holding out just one observation. My question is why even in this case the projection matrix ($W$) is so over-fitted and sensitive to cro... | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)?
When I even use leave one out (LOOCV) to calculate LDA projection matrix, it is calculated by holding out just one observation. My question is why even in this case the projection matrix ($W$) is so o |
52,125 | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)? | Looks like your sample size is not a lot bigger than the dimensionality of the data (feature set size). That can be a problem for LDA and it can overfit. Since it relies on computing the within-class scatter matrix which requires the scenario of N >> p (# samples >> # features).
One quick way to check if you are overfi... | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)? | Looks like your sample size is not a lot bigger than the dimensionality of the data (feature set size). That can be a problem for LDA and it can overfit. Since it relies on computing the within-class | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)?
Looks like your sample size is not a lot bigger than the dimensionality of the data (feature set size). That can be a problem for LDA and it can overfit. Since it relies on computing the within-class scatter matrix which requires t... | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)?
Looks like your sample size is not a lot bigger than the dimensionality of the data (feature set size). That can be a problem for LDA and it can overfit. Since it relies on computing the within-class |
52,126 | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)? | LDA is optimal when the distribution of features, conditional on the labels is Gaussian with equal, but unstructured covariance matrices. If conditional Gaussian model doesn't hold approximately, you may not want to use LDA. The results of your LOO-CV suggests
The conditional Gaussian model is a poor fit and/or
You... | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)? | LDA is optimal when the distribution of features, conditional on the labels is Gaussian with equal, but unstructured covariance matrices. If conditional Gaussian model doesn't hold approximately, you | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)?
LDA is optimal when the distribution of features, conditional on the labels is Gaussian with equal, but unstructured covariance matrices. If conditional Gaussian model doesn't hold approximately, you may not want to use LDA. The ... | Why linear discriminant analysis is sensitive to cross validation (LDA overfit problem)?
LDA is optimal when the distribution of features, conditional on the labels is Gaussian with equal, but unstructured covariance matrices. If conditional Gaussian model doesn't hold approximately, you |
52,127 | Loss vs. Classification Accuracy in applied problems | Accuracy is essentially the mean of the Losses under a zero-one loss function, so to answer your question, yes accuracy is just a loss function.
More specifically: For the Zero-one loss function is defined as:
$L(y,y^*) =\begin{cases}
0,& \text{if } y = y*\\
1, & \text{otherwise}
\end{cases}$
So th... | Loss vs. Classification Accuracy in applied problems | Accuracy is essentially the mean of the Losses under a zero-one loss function, so to answer your question, yes accuracy is just a loss function.
More specifically: For the Zero-one loss function is de | Loss vs. Classification Accuracy in applied problems
Accuracy is essentially the mean of the Losses under a zero-one loss function, so to answer your question, yes accuracy is just a loss function.
More specifically: For the Zero-one loss function is defined as:
$L(y,y^*) =\begin{cases}
0,& \text{if } y = y*\\
... | Loss vs. Classification Accuracy in applied problems
Accuracy is essentially the mean of the Losses under a zero-one loss function, so to answer your question, yes accuracy is just a loss function.
More specifically: For the Zero-one loss function is de |
52,128 | Loss vs. Classification Accuracy in applied problems | I want to argue that the premise of your question is flawed.
In practical problems, where we want to for instance predict if a subject has a certain disease or not, we usually take classification accuracy as a measure [...]
Maybe some people do, but I think there is a fair perspective that anyone doing this is not do... | Loss vs. Classification Accuracy in applied problems | I want to argue that the premise of your question is flawed.
In practical problems, where we want to for instance predict if a subject has a certain disease or not, we usually take classification acc | Loss vs. Classification Accuracy in applied problems
I want to argue that the premise of your question is flawed.
In practical problems, where we want to for instance predict if a subject has a certain disease or not, we usually take classification accuracy as a measure [...]
Maybe some people do, but I think there i... | Loss vs. Classification Accuracy in applied problems
I want to argue that the premise of your question is flawed.
In practical problems, where we want to for instance predict if a subject has a certain disease or not, we usually take classification acc |
52,129 | Loss vs. Classification Accuracy in applied problems | They are two different metrics to evaluate your model's performance usually being used in different phases.
Loss is often used in the training process to find the "best" parameter values for your model (e.g. weights in neural network). It is what you try to optimize in the training by updating weights.
Accuracy is more... | Loss vs. Classification Accuracy in applied problems | They are two different metrics to evaluate your model's performance usually being used in different phases.
Loss is often used in the training process to find the "best" parameter values for your mode | Loss vs. Classification Accuracy in applied problems
They are two different metrics to evaluate your model's performance usually being used in different phases.
Loss is often used in the training process to find the "best" parameter values for your model (e.g. weights in neural network). It is what you try to optimize ... | Loss vs. Classification Accuracy in applied problems
They are two different metrics to evaluate your model's performance usually being used in different phases.
Loss is often used in the training process to find the "best" parameter values for your mode |
52,130 | Loss vs. Classification Accuracy in applied problems | A related discussion can be found here: What are the impacts of choosing different loss functions in classification to approximate 0-1 loss
As mentioned by @Tilefish Poele Classification Accuracy is one type of Loss, which is 0-1 loss. There are other types of loss exist for different purpose.
I will give one example ... | Loss vs. Classification Accuracy in applied problems | A related discussion can be found here: What are the impacts of choosing different loss functions in classification to approximate 0-1 loss
As mentioned by @Tilefish Poele Classification Accuracy is o | Loss vs. Classification Accuracy in applied problems
A related discussion can be found here: What are the impacts of choosing different loss functions in classification to approximate 0-1 loss
As mentioned by @Tilefish Poele Classification Accuracy is one type of Loss, which is 0-1 loss. There are other types of loss e... | Loss vs. Classification Accuracy in applied problems
A related discussion can be found here: What are the impacts of choosing different loss functions in classification to approximate 0-1 loss
As mentioned by @Tilefish Poele Classification Accuracy is o |
52,131 | Ellipse formula from points | A straightforward way, especially when you expect the points to fall exactly on an ellipse (yet which works even when they don't), is to observe that an ellipse is the set of zeros of a second order polynomial
$$0 = P(x,y) = -1 + \beta_x\,x + \beta_y\,y + \beta_{xy}\,xy + \beta_{x^2}\,x^2 + \beta_{y^2}\,y^2$$
You can t... | Ellipse formula from points | A straightforward way, especially when you expect the points to fall exactly on an ellipse (yet which works even when they don't), is to observe that an ellipse is the set of zeros of a second order p | Ellipse formula from points
A straightforward way, especially when you expect the points to fall exactly on an ellipse (yet which works even when they don't), is to observe that an ellipse is the set of zeros of a second order polynomial
$$0 = P(x,y) = -1 + \beta_x\,x + \beta_y\,y + \beta_{xy}\,xy + \beta_{x^2}\,x^2 + ... | Ellipse formula from points
A straightforward way, especially when you expect the points to fall exactly on an ellipse (yet which works even when they don't), is to observe that an ellipse is the set of zeros of a second order p |
52,132 | What is the connection (if any) and difference between logistic regression and survival analysis? | They are different categories of things - survival analysis is the analysis of data where time to a given event is the dependent variable. The given event may include death, failure of a machine, a criminal's time to (re)offending or becoming ill, for example. It uses a number of techniques to analyse this data, includ... | What is the connection (if any) and difference between logistic regression and survival analysis? | They are different categories of things - survival analysis is the analysis of data where time to a given event is the dependent variable. The given event may include death, failure of a machine, a cr | What is the connection (if any) and difference between logistic regression and survival analysis?
They are different categories of things - survival analysis is the analysis of data where time to a given event is the dependent variable. The given event may include death, failure of a machine, a criminal's time to (re)o... | What is the connection (if any) and difference between logistic regression and survival analysis?
They are different categories of things - survival analysis is the analysis of data where time to a given event is the dependent variable. The given event may include death, failure of a machine, a cr |
52,133 | What is the connection (if any) and difference between logistic regression and survival analysis? | They have different dependent variables (for logistic 1/0 and for survival time to event).
So the short answer is no - you cannot compare the coefficients. | What is the connection (if any) and difference between logistic regression and survival analysis? | They have different dependent variables (for logistic 1/0 and for survival time to event).
So the short answer is no - you cannot compare the coefficients. | What is the connection (if any) and difference between logistic regression and survival analysis?
They have different dependent variables (for logistic 1/0 and for survival time to event).
So the short answer is no - you cannot compare the coefficients. | What is the connection (if any) and difference between logistic regression and survival analysis?
They have different dependent variables (for logistic 1/0 and for survival time to event).
So the short answer is no - you cannot compare the coefficients. |
52,134 | Probability for class in xgboost | predict_proba yields estimated probabilities that a sample is in class 1.
Note that the speaker in the comment is the author of xgboost, so this is the definitive answer on the subject. | Probability for class in xgboost | predict_proba yields estimated probabilities that a sample is in class 1.
Note that the speaker in the comment is the author of xgboost, so this is the definitive answer on the subject. | Probability for class in xgboost
predict_proba yields estimated probabilities that a sample is in class 1.
Note that the speaker in the comment is the author of xgboost, so this is the definitive answer on the subject. | Probability for class in xgboost
predict_proba yields estimated probabilities that a sample is in class 1.
Note that the speaker in the comment is the author of xgboost, so this is the definitive answer on the subject. |
52,135 | How to generate a sequence of timestamps in R? | Computers have different ways of storing time data. For example, R uses date-time classes POSIXlt and POSIXct. From the documentation
Class "POSIXct" represents the (signed) number of seconds since the
beginning of 1970 (in the UTC time zone) as a numeric vector.
So time is stored as a number of seconds
Sys.time()
... | How to generate a sequence of timestamps in R? | Computers have different ways of storing time data. For example, R uses date-time classes POSIXlt and POSIXct. From the documentation
Class "POSIXct" represents the (signed) number of seconds since t | How to generate a sequence of timestamps in R?
Computers have different ways of storing time data. For example, R uses date-time classes POSIXlt and POSIXct. From the documentation
Class "POSIXct" represents the (signed) number of seconds since the
beginning of 1970 (in the UTC time zone) as a numeric vector.
So ti... | How to generate a sequence of timestamps in R?
Computers have different ways of storing time data. For example, R uses date-time classes POSIXlt and POSIXct. From the documentation
Class "POSIXct" represents the (signed) number of seconds since t |
52,136 | Proportionality assumption in Cox Regression Model | The Cox proportional hazards model can be described as follows:
$$h(t|X)=h_{0}(t)e^{\beta X}$$
where $h(t)$ is the hazard rate at time $t$, $h_{0}(t)$ is the baseline hazard rate at time $t$, $\beta$ is a vector of coefficients and $X$ is a vector of covariates.
As you will know, the Cox model is a semi-parametric mode... | Proportionality assumption in Cox Regression Model | The Cox proportional hazards model can be described as follows:
$$h(t|X)=h_{0}(t)e^{\beta X}$$
where $h(t)$ is the hazard rate at time $t$, $h_{0}(t)$ is the baseline hazard rate at time $t$, $\beta$ | Proportionality assumption in Cox Regression Model
The Cox proportional hazards model can be described as follows:
$$h(t|X)=h_{0}(t)e^{\beta X}$$
where $h(t)$ is the hazard rate at time $t$, $h_{0}(t)$ is the baseline hazard rate at time $t$, $\beta$ is a vector of coefficients and $X$ is a vector of covariates.
As you... | Proportionality assumption in Cox Regression Model
The Cox proportional hazards model can be described as follows:
$$h(t|X)=h_{0}(t)e^{\beta X}$$
where $h(t)$ is the hazard rate at time $t$, $h_{0}(t)$ is the baseline hazard rate at time $t$, $\beta$ |
52,137 | Proportionality assumption in Cox Regression Model | Basically, if the effect is proportional, this means the effect is constant over time. In other words: the hazard rate ratio is constant over time. Simple methods of checking this are graphically through plotting Schoefeld residuals, or by adding an interaction with time to your cox model and checking whether it signif... | Proportionality assumption in Cox Regression Model | Basically, if the effect is proportional, this means the effect is constant over time. In other words: the hazard rate ratio is constant over time. Simple methods of checking this are graphically thro | Proportionality assumption in Cox Regression Model
Basically, if the effect is proportional, this means the effect is constant over time. In other words: the hazard rate ratio is constant over time. Simple methods of checking this are graphically through plotting Schoefeld residuals, or by adding an interaction with ti... | Proportionality assumption in Cox Regression Model
Basically, if the effect is proportional, this means the effect is constant over time. In other words: the hazard rate ratio is constant over time. Simple methods of checking this are graphically thro |
52,138 | Order of operations in statistics | Everything to the left of the $\mid$ is the event whose conditional probability is being talked about; everything to the right of the $\mid$
is the conditioning event, the one that we assume has occurred. Commas
generally mean intersection. Thus, $P(A\mid B, C)$ is the same
as $P(A\mid B\cap C)$ or $P(A\mid (B\cap C)... | Order of operations in statistics | Everything to the left of the $\mid$ is the event whose conditional probability is being talked about; everything to the right of the $\mid$
is the conditioning event, the one that we assume has occu | Order of operations in statistics
Everything to the left of the $\mid$ is the event whose conditional probability is being talked about; everything to the right of the $\mid$
is the conditioning event, the one that we assume has occurred. Commas
generally mean intersection. Thus, $P(A\mid B, C)$ is the same
as $P(A\m... | Order of operations in statistics
Everything to the left of the $\mid$ is the event whose conditional probability is being talked about; everything to the right of the $\mid$
is the conditioning event, the one that we assume has occu |
52,139 | Order of operations in statistics | Order doesn't matter
Order doesn't matter in this setting, so there isn't any order of operations to worry about. Explicitly:
$$P(a \mid b, c) = P(a \mid c, b)$$
This is because the AND logical concept doesn't depend on order. Consider the statement "It is Wednesday AND I am a student". This is an equivalent logical ... | Order of operations in statistics | Order doesn't matter
Order doesn't matter in this setting, so there isn't any order of operations to worry about. Explicitly:
$$P(a \mid b, c) = P(a \mid c, b)$$
This is because the AND logical conce | Order of operations in statistics
Order doesn't matter
Order doesn't matter in this setting, so there isn't any order of operations to worry about. Explicitly:
$$P(a \mid b, c) = P(a \mid c, b)$$
This is because the AND logical concept doesn't depend on order. Consider the statement "It is Wednesday AND I am a studen... | Order of operations in statistics
Order doesn't matter
Order doesn't matter in this setting, so there isn't any order of operations to worry about. Explicitly:
$$P(a \mid b, c) = P(a \mid c, b)$$
This is because the AND logical conce |
52,140 | Why is this definition of the Central Limit Theorem not incorrect? | Note that in your expression
$$ \lim_{n\to\infty} \Pr\bigg[\frac{\bar{X}_n-\mu}{\sigma/\sqrt n} \le z\bigg] $$
There is nowhere a reference to $\lim_{n\to\infty}\bar{X}_n$. It doesn't matter what this last part converges to - you're working with a different expression. It seems you were trying to do something like
$$ \... | Why is this definition of the Central Limit Theorem not incorrect? | Note that in your expression
$$ \lim_{n\to\infty} \Pr\bigg[\frac{\bar{X}_n-\mu}{\sigma/\sqrt n} \le z\bigg] $$
There is nowhere a reference to $\lim_{n\to\infty}\bar{X}_n$. It doesn't matter what this | Why is this definition of the Central Limit Theorem not incorrect?
Note that in your expression
$$ \lim_{n\to\infty} \Pr\bigg[\frac{\bar{X}_n-\mu}{\sigma/\sqrt n} \le z\bigg] $$
There is nowhere a reference to $\lim_{n\to\infty}\bar{X}_n$. It doesn't matter what this last part converges to - you're working with a diffe... | Why is this definition of the Central Limit Theorem not incorrect?
Note that in your expression
$$ \lim_{n\to\infty} \Pr\bigg[\frac{\bar{X}_n-\mu}{\sigma/\sqrt n} \le z\bigg] $$
There is nowhere a reference to $\lim_{n\to\infty}\bar{X}_n$. It doesn't matter what this |
52,141 | Why is this definition of the Central Limit Theorem not incorrect? | $\bar{X}$ is defined as $\frac{1}{n}\sum_{i=1}^nX_i$, your definition misses an average, and summation should start at $i=1$.
$\mu$ is the population mean, not the sample mean ($\bar{X}$ is). Likewise, $\sigma$ is the population standard deviation.
The crucial difference to the LLN is that the difference between $\bar{... | Why is this definition of the Central Limit Theorem not incorrect? | $\bar{X}$ is defined as $\frac{1}{n}\sum_{i=1}^nX_i$, your definition misses an average, and summation should start at $i=1$.
$\mu$ is the population mean, not the sample mean ($\bar{X}$ is). Likewise | Why is this definition of the Central Limit Theorem not incorrect?
$\bar{X}$ is defined as $\frac{1}{n}\sum_{i=1}^nX_i$, your definition misses an average, and summation should start at $i=1$.
$\mu$ is the population mean, not the sample mean ($\bar{X}$ is). Likewise, $\sigma$ is the population standard deviation.
The ... | Why is this definition of the Central Limit Theorem not incorrect?
$\bar{X}$ is defined as $\frac{1}{n}\sum_{i=1}^nX_i$, your definition misses an average, and summation should start at $i=1$.
$\mu$ is the population mean, not the sample mean ($\bar{X}$ is). Likewise |
52,142 | Likelihood Ratio Test for the variance of a normal distribution | I don't think your derivation of the likelihood ratio test is correct. Let's start from the beginning. I will write everything in terms of the variance since this way we can use some known results about normal distributions. This does not change the nature of the problem either.
We wish to test
$$ H _0 : \sigma^2 = \si... | Likelihood Ratio Test for the variance of a normal distribution | I don't think your derivation of the likelihood ratio test is correct. Let's start from the beginning. I will write everything in terms of the variance since this way we can use some known results abo | Likelihood Ratio Test for the variance of a normal distribution
I don't think your derivation of the likelihood ratio test is correct. Let's start from the beginning. I will write everything in terms of the variance since this way we can use some known results about normal distributions. This does not change the nature... | Likelihood Ratio Test for the variance of a normal distribution
I don't think your derivation of the likelihood ratio test is correct. Let's start from the beginning. I will write everything in terms of the variance since this way we can use some known results abo |
52,143 | How to obtain Tukey Table in R? | Here's part of the table you linked to:
The first few rows are obtained by:
> qtukey(p = 0.95, nmeans = 2:10, df = 5)
[1] 3.635351 4.601725 5.218325 5.673125 6.032903 6.329901 6.582301 6.801398
[9] 6.994698
> qtukey(p = 0.99, nmeans = 2:10, df = 5)
[1] 5.702311 6.975727 7.804156 8.421495 8.913107 9.320875 9.66... | How to obtain Tukey Table in R? | Here's part of the table you linked to:
The first few rows are obtained by:
> qtukey(p = 0.95, nmeans = 2:10, df = 5)
[1] 3.635351 4.601725 5.218325 5.673125 6.032903 6.329901 6.582301 6.801398
[9] 6 | How to obtain Tukey Table in R?
Here's part of the table you linked to:
The first few rows are obtained by:
> qtukey(p = 0.95, nmeans = 2:10, df = 5)
[1] 3.635351 4.601725 5.218325 5.673125 6.032903 6.329901 6.582301 6.801398
[9] 6.994698
> qtukey(p = 0.99, nmeans = 2:10, df = 5)
[1] 5.702311 6.975727 7.804156 8.... | How to obtain Tukey Table in R?
Here's part of the table you linked to:
The first few rows are obtained by:
> qtukey(p = 0.95, nmeans = 2:10, df = 5)
[1] 3.635351 4.601725 5.218325 5.673125 6.032903 6.329901 6.582301 6.801398
[9] 6 |
52,144 | How to obtain Tukey Table in R? | Here is a way to generate QTable into a data frame.
You can change the grid limits according to your needs.
QTable <- expand.grid(alpha=c(0.01,0.05),
groups=seq(2,10,1),
df=seq(2,120,1))
QTable$QVal=qtukey(1-QTable$alpha,QTable$groups,df=QTable$df)
head(QTable)
alpha gr... | How to obtain Tukey Table in R? | Here is a way to generate QTable into a data frame.
You can change the grid limits according to your needs.
QTable <- expand.grid(alpha=c(0.01,0.05),
groups=seq(2,10,1),
| How to obtain Tukey Table in R?
Here is a way to generate QTable into a data frame.
You can change the grid limits according to your needs.
QTable <- expand.grid(alpha=c(0.01,0.05),
groups=seq(2,10,1),
df=seq(2,120,1))
QTable$QVal=qtukey(1-QTable$alpha,QTable$groups,df=QTabl... | How to obtain Tukey Table in R?
Here is a way to generate QTable into a data frame.
You can change the grid limits according to your needs.
QTable <- expand.grid(alpha=c(0.01,0.05),
groups=seq(2,10,1),
|
52,145 | How to obtain Tukey Table in R? | For exaplanatory purpose, I tried to make up a function which provides full Tukey Table, see my comments inside. I still think that the R-help is misleading in this case:
QTable<-function(dfrange=10,nurange=20,alpha=0.05,digs=3){
ROWS<-dfrange
COLS<-nurange
tabl<-matrix(nrow=ROWS,ncol=COLS)
for(a in 2:COLS){
... | How to obtain Tukey Table in R? | For exaplanatory purpose, I tried to make up a function which provides full Tukey Table, see my comments inside. I still think that the R-help is misleading in this case:
QTable<-function(dfrange=10,n | How to obtain Tukey Table in R?
For exaplanatory purpose, I tried to make up a function which provides full Tukey Table, see my comments inside. I still think that the R-help is misleading in this case:
QTable<-function(dfrange=10,nurange=20,alpha=0.05,digs=3){
ROWS<-dfrange
COLS<-nurange
tabl<-matrix(nrow=ROWS,... | How to obtain Tukey Table in R?
For exaplanatory purpose, I tried to make up a function which provides full Tukey Table, see my comments inside. I still think that the R-help is misleading in this case:
QTable<-function(dfrange=10,n |
52,146 | How to interpret 95% confidence interval for Area Under Curve of ROC? | A confidence interval is an interval-estimate for some true value of a parameter. Let us (as an example) start with e.g. a confidence interval for the mean of a normal distribution and then move on to ROC and AUC so that one sees the analogy.
Assume that you have a random normal variable $X \sim N(\mu;\sigma)$. Where ... | How to interpret 95% confidence interval for Area Under Curve of ROC? | A confidence interval is an interval-estimate for some true value of a parameter. Let us (as an example) start with e.g. a confidence interval for the mean of a normal distribution and then move on to | How to interpret 95% confidence interval for Area Under Curve of ROC?
A confidence interval is an interval-estimate for some true value of a parameter. Let us (as an example) start with e.g. a confidence interval for the mean of a normal distribution and then move on to ROC and AUC so that one sees the analogy.
Assume... | How to interpret 95% confidence interval for Area Under Curve of ROC?
A confidence interval is an interval-estimate for some true value of a parameter. Let us (as an example) start with e.g. a confidence interval for the mean of a normal distribution and then move on to |
52,147 | How to interpret 95% confidence interval for Area Under Curve of ROC? | Probably the best interpretation would be in terms of the so-called $c$ statistic, which turns out to equal the area under the ROC curve. That is, if you are trying to predict some response $Y$ (which is often binary) using a score $X$, then the $c$ statistic is defined as $P(X^\prime > X \mid Y^\prime > Y)$, where $X... | How to interpret 95% confidence interval for Area Under Curve of ROC? | Probably the best interpretation would be in terms of the so-called $c$ statistic, which turns out to equal the area under the ROC curve. That is, if you are trying to predict some response $Y$ (whic | How to interpret 95% confidence interval for Area Under Curve of ROC?
Probably the best interpretation would be in terms of the so-called $c$ statistic, which turns out to equal the area under the ROC curve. That is, if you are trying to predict some response $Y$ (which is often binary) using a score $X$, then the $c$... | How to interpret 95% confidence interval for Area Under Curve of ROC?
Probably the best interpretation would be in terms of the so-called $c$ statistic, which turns out to equal the area under the ROC curve. That is, if you are trying to predict some response $Y$ (whic |
52,148 | Explaining Consistency of estimators to a non-statistical audience | This is an indirect approach that might help lead you toward considering the question in a different light.
Let me play devil's advocate for a moment.
In practice*, how much does consistency matter?
* (you might think about whether your lay audience would care about anything else)
When you have data, you have some pa... | Explaining Consistency of estimators to a non-statistical audience | This is an indirect approach that might help lead you toward considering the question in a different light.
Let me play devil's advocate for a moment.
In practice*, how much does consistency matter? | Explaining Consistency of estimators to a non-statistical audience
This is an indirect approach that might help lead you toward considering the question in a different light.
Let me play devil's advocate for a moment.
In practice*, how much does consistency matter?
* (you might think about whether your lay audience w... | Explaining Consistency of estimators to a non-statistical audience
This is an indirect approach that might help lead you toward considering the question in a different light.
Let me play devil's advocate for a moment.
In practice*, how much does consistency matter? |
52,149 | Explaining Consistency of estimators to a non-statistical audience | Create a simple but realistic example, with a known ‘feature of the population’ (i.e., parameter). Simulate from this example, and create a plot, with the number of observations on the x-axis and ‘cumulative’ parameter estimates on the y-axis. Mark the population parameter with a red horizontal line. Point out that the... | Explaining Consistency of estimators to a non-statistical audience | Create a simple but realistic example, with a known ‘feature of the population’ (i.e., parameter). Simulate from this example, and create a plot, with the number of observations on the x-axis and ‘cum | Explaining Consistency of estimators to a non-statistical audience
Create a simple but realistic example, with a known ‘feature of the population’ (i.e., parameter). Simulate from this example, and create a plot, with the number of observations on the x-axis and ‘cumulative’ parameter estimates on the y-axis. Mark the ... | Explaining Consistency of estimators to a non-statistical audience
Create a simple but realistic example, with a known ‘feature of the population’ (i.e., parameter). Simulate from this example, and create a plot, with the number of observations on the x-axis and ‘cum |
52,150 | Explaining Consistency of estimators to a non-statistical audience | Reasons to be Consistent, Part III:
1) Defense: smiling, an estimator property is "asymptotic" when we don't have a clue as to when it will actually start to visibly affect the behavior and the results of an estimator. It may take a sample of immense size, it may take a few dozens of observations. So we want to have ... | Explaining Consistency of estimators to a non-statistical audience | Reasons to be Consistent, Part III:
1) Defense: smiling, an estimator property is "asymptotic" when we don't have a clue as to when it will actually start to visibly affect the behavior and the resu | Explaining Consistency of estimators to a non-statistical audience
Reasons to be Consistent, Part III:
1) Defense: smiling, an estimator property is "asymptotic" when we don't have a clue as to when it will actually start to visibly affect the behavior and the results of an estimator. It may take a sample of immense ... | Explaining Consistency of estimators to a non-statistical audience
Reasons to be Consistent, Part III:
1) Defense: smiling, an estimator property is "asymptotic" when we don't have a clue as to when it will actually start to visibly affect the behavior and the resu |
52,151 | Explaining Consistency of estimators to a non-statistical audience | Thank you so much for your responses.
I have had a lot of people in the discipline ask me "Who cares what happens at infinity? We are never going to get there"..similar to what Glen posted and my response has been "Why don't you consider the first entry in your sample as the mean of the sample?" though this seems a rat... | Explaining Consistency of estimators to a non-statistical audience | Thank you so much for your responses.
I have had a lot of people in the discipline ask me "Who cares what happens at infinity? We are never going to get there"..similar to what Glen posted and my resp | Explaining Consistency of estimators to a non-statistical audience
Thank you so much for your responses.
I have had a lot of people in the discipline ask me "Who cares what happens at infinity? We are never going to get there"..similar to what Glen posted and my response has been "Why don't you consider the first entry... | Explaining Consistency of estimators to a non-statistical audience
Thank you so much for your responses.
I have had a lot of people in the discipline ask me "Who cares what happens at infinity? We are never going to get there"..similar to what Glen posted and my resp |
52,152 | R optim function - Setting constraints for individual parameters | I would recommend re-parametrizing the problem so that it is unconstrained.
Say by mapping the non-negative parameter with a log transform. | R optim function - Setting constraints for individual parameters | I would recommend re-parametrizing the problem so that it is unconstrained.
Say by mapping the non-negative parameter with a log transform. | R optim function - Setting constraints for individual parameters
I would recommend re-parametrizing the problem so that it is unconstrained.
Say by mapping the non-negative parameter with a log transform. | R optim function - Setting constraints for individual parameters
I would recommend re-parametrizing the problem so that it is unconstrained.
Say by mapping the non-negative parameter with a log transform. |
52,153 | R optim function - Setting constraints for individual parameters | You can set the constraints for the unconstrained parameters to $\pm \infty$ (and the ceiling for the non-negative parameters to $+\infty$).
optim(par=theta, fn=min.RSS, lower=c(0, -Inf, -Inf, 0), upper=rep(Inf, 4),
method="L-BFGS-B")
Technically the upper argument is unnecessary in this case, as its default v... | R optim function - Setting constraints for individual parameters | You can set the constraints for the unconstrained parameters to $\pm \infty$ (and the ceiling for the non-negative parameters to $+\infty$).
optim(par=theta, fn=min.RSS, lower=c(0, -Inf, -Inf, 0), up | R optim function - Setting constraints for individual parameters
You can set the constraints for the unconstrained parameters to $\pm \infty$ (and the ceiling for the non-negative parameters to $+\infty$).
optim(par=theta, fn=min.RSS, lower=c(0, -Inf, -Inf, 0), upper=rep(Inf, 4),
method="L-BFGS-B")
Technically... | R optim function - Setting constraints for individual parameters
You can set the constraints for the unconstrained parameters to $\pm \infty$ (and the ceiling for the non-negative parameters to $+\infty$).
optim(par=theta, fn=min.RSS, lower=c(0, -Inf, -Inf, 0), up |
52,154 | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function | predict() in lme4 does not work well unless the grouping factor specification is "realistic". If we use samples from the observed data, we get reasonable predictions. I think this is a bug in predict.merMod()
This is lme4 1.1-7
my.fit <- glmer(smoker ~ biomarker + year + sex + age + (1|id), data = df, family = binomial... | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function | predict() in lme4 does not work well unless the grouping factor specification is "realistic". If we use samples from the observed data, we get reasonable predictions. I think this is a bug in predict. | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function
predict() in lme4 does not work well unless the grouping factor specification is "realistic". If we use samples from the observed data, we get reasonable predictions. I think this is a bug in predict.merMod()
This is lme4 1.1-7
my.fit <- gl... | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function
predict() in lme4 does not work well unless the grouping factor specification is "realistic". If we use samples from the observed data, we get reasonable predictions. I think this is a bug in predict. |
52,155 | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function | To get the confidence interval, you could also try the effects package
lmer.1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
library("effects")
# obtain a fit at different estimates of the predictor
ef.1=effect(c("Days"),lmer.1)
df.ef=data.frame(ef.1)
df.ef
plot(effect(c("Days"),lmer.1),grid=TRUE)
here is fit... | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function | To get the confidence interval, you could also try the effects package
lmer.1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
library("effects")
# obtain a fit at different estimates of the pr | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function
To get the confidence interval, you could also try the effects package
lmer.1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
library("effects")
# obtain a fit at different estimates of the predictor
ef.1=effect(c("Days"),lmer.1)
df... | Obtaining adjusted (predicted) proportions with lme4 - using the glmer-function
To get the confidence interval, you could also try the effects package
lmer.1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
library("effects")
# obtain a fit at different estimates of the pr |
52,156 | Find the mode of a probability distribution function | Consider that there are shapes of pdf that have a mode, but at which the derivative of the pdf is not zero (the Laplace being an obvious example).
There are also cases where there's no mode in the domain of the variable (examples below).
That is, we can't say as a general statement "the mode can be obtained by takin... | Find the mode of a probability distribution function | Consider that there are shapes of pdf that have a mode, but at which the derivative of the pdf is not zero (the Laplace being an obvious example).
There are also cases where there's no mode in the d | Find the mode of a probability distribution function
Consider that there are shapes of pdf that have a mode, but at which the derivative of the pdf is not zero (the Laplace being an obvious example).
There are also cases where there's no mode in the domain of the variable (examples below).
That is, we can't say as a... | Find the mode of a probability distribution function
Consider that there are shapes of pdf that have a mode, but at which the derivative of the pdf is not zero (the Laplace being an obvious example).
There are also cases where there's no mode in the d |
52,157 | Why is p for 8 times heads out of 21 flips not 8/21? | 8/21 is the proportion of heads in the result.
Instead of calculating the probability of 8 heads, you can calculate the probability that the proportion of heads in 21 coin flips will be 8/21. They both turn out 0.097 (assuming your calculation is correct) | Why is p for 8 times heads out of 21 flips not 8/21? | 8/21 is the proportion of heads in the result.
Instead of calculating the probability of 8 heads, you can calculate the probability that the proportion of heads in 21 coin flips will be 8/21. They bot | Why is p for 8 times heads out of 21 flips not 8/21?
8/21 is the proportion of heads in the result.
Instead of calculating the probability of 8 heads, you can calculate the probability that the proportion of heads in 21 coin flips will be 8/21. They both turn out 0.097 (assuming your calculation is correct) | Why is p for 8 times heads out of 21 flips not 8/21?
8/21 is the proportion of heads in the result.
Instead of calculating the probability of 8 heads, you can calculate the probability that the proportion of heads in 21 coin flips will be 8/21. They bot |
52,158 | Why is p for 8 times heads out of 21 flips not 8/21? | Think of one fair die with $21$ sides, of which $8$ have the letter $H$ inscribed, and the other $13$ have the letter $T$ inscribed.
Throw the die once. What is the probability that you will get an $H$? It is $8/21$. Now compact the $21$ dimensions into just $2$, taking into account how many time each letter appeared... | Why is p for 8 times heads out of 21 flips not 8/21? | Think of one fair die with $21$ sides, of which $8$ have the letter $H$ inscribed, and the other $13$ have the letter $T$ inscribed.
Throw the die once. What is the probability that you will get an | Why is p for 8 times heads out of 21 flips not 8/21?
Think of one fair die with $21$ sides, of which $8$ have the letter $H$ inscribed, and the other $13$ have the letter $T$ inscribed.
Throw the die once. What is the probability that you will get an $H$? It is $8/21$. Now compact the $21$ dimensions into just $2$, t... | Why is p for 8 times heads out of 21 flips not 8/21?
Think of one fair die with $21$ sides, of which $8$ have the letter $H$ inscribed, and the other $13$ have the letter $T$ inscribed.
Throw the die once. What is the probability that you will get an |
52,159 | Why is p for 8 times heads out of 21 flips not 8/21? | What am I then calculating by $8/21=0.38$?
You're calculating an estimate of the probability that one future coin flip will turn up heads.
Of course, by doing so you're ignoring everything else you know about the coin, including your expectation that the coin is fair, and treating it as a binomial experiment with an u... | Why is p for 8 times heads out of 21 flips not 8/21? | What am I then calculating by $8/21=0.38$?
You're calculating an estimate of the probability that one future coin flip will turn up heads.
Of course, by doing so you're ignoring everything else you k | Why is p for 8 times heads out of 21 flips not 8/21?
What am I then calculating by $8/21=0.38$?
You're calculating an estimate of the probability that one future coin flip will turn up heads.
Of course, by doing so you're ignoring everything else you know about the coin, including your expectation that the coin is fai... | Why is p for 8 times heads out of 21 flips not 8/21?
What am I then calculating by $8/21=0.38$?
You're calculating an estimate of the probability that one future coin flip will turn up heads.
Of course, by doing so you're ignoring everything else you k |
52,160 | How do you pronounce "LASSO"? | Rob Tibshirani pronounces it the first way ("LAS-so"), which seems fairly definitive to me. However, Trevor Hastie pronounces it the second way ("las-SOO") and is from South Africa, so I'd agree with @Glen_b and say that any common local pronunciation of the word would be appropriate. | How do you pronounce "LASSO"? | Rob Tibshirani pronounces it the first way ("LAS-so"), which seems fairly definitive to me. However, Trevor Hastie pronounces it the second way ("las-SOO") and is from South Africa, so I'd agree with | How do you pronounce "LASSO"?
Rob Tibshirani pronounces it the first way ("LAS-so"), which seems fairly definitive to me. However, Trevor Hastie pronounces it the second way ("las-SOO") and is from South Africa, so I'd agree with @Glen_b and say that any common local pronunciation of the word would be appropriate. | How do you pronounce "LASSO"?
Rob Tibshirani pronounces it the first way ("LAS-so"), which seems fairly definitive to me. However, Trevor Hastie pronounces it the second way ("las-SOO") and is from South Africa, so I'd agree with |
52,161 | K-means cluster analysis with K=2 as a binary classifier | It depends on what you mean by "did pretty well" and on the population. For general adult populations in the developed world I would not expect this to work very well: heights and weights alone are not great at distinguishing the genders.
The best and easiest way to assess the situation is to make a scatterplot of hei... | K-means cluster analysis with K=2 as a binary classifier | It depends on what you mean by "did pretty well" and on the population. For general adult populations in the developed world I would not expect this to work very well: heights and weights alone are n | K-means cluster analysis with K=2 as a binary classifier
It depends on what you mean by "did pretty well" and on the population. For general adult populations in the developed world I would not expect this to work very well: heights and weights alone are not great at distinguishing the genders.
The best and easiest wa... | K-means cluster analysis with K=2 as a binary classifier
It depends on what you mean by "did pretty well" and on the population. For general adult populations in the developed world I would not expect this to work very well: heights and weights alone are n |
52,162 | K-means cluster analysis with K=2 as a binary classifier | Yes, it does sound sensible. I am not sure why you would suspect it did not.
Men tend to be both taller and heavier than women. Exact numbers vary with country (some data here on weight and here on height. Combining them ought to make the classification even better. | K-means cluster analysis with K=2 as a binary classifier | Yes, it does sound sensible. I am not sure why you would suspect it did not.
Men tend to be both taller and heavier than women. Exact numbers vary with country (some data here on weight and here on he | K-means cluster analysis with K=2 as a binary classifier
Yes, it does sound sensible. I am not sure why you would suspect it did not.
Men tend to be both taller and heavier than women. Exact numbers vary with country (some data here on weight and here on height. Combining them ought to make the classification even bett... | K-means cluster analysis with K=2 as a binary classifier
Yes, it does sound sensible. I am not sure why you would suspect it did not.
Men tend to be both taller and heavier than women. Exact numbers vary with country (some data here on weight and here on he |
52,163 | K-means cluster analysis with K=2 as a binary classifier | Be careful of artifacts.
K-means assumes that every attribute has the same weight.
If, say, one attribute is the height in meters, and the other is the weight in g, then the result of k-means will depend almost exclusively on the weight.
If this attribute then is useful for separating your two classes, the outcome will... | K-means cluster analysis with K=2 as a binary classifier | Be careful of artifacts.
K-means assumes that every attribute has the same weight.
If, say, one attribute is the height in meters, and the other is the weight in g, then the result of k-means will dep | K-means cluster analysis with K=2 as a binary classifier
Be careful of artifacts.
K-means assumes that every attribute has the same weight.
If, say, one attribute is the height in meters, and the other is the weight in g, then the result of k-means will depend almost exclusively on the weight.
If this attribute then is... | K-means cluster analysis with K=2 as a binary classifier
Be careful of artifacts.
K-means assumes that every attribute has the same weight.
If, say, one attribute is the height in meters, and the other is the weight in g, then the result of k-means will dep |
52,164 | How to explain borderline p-values to non-stats people | Use "words", do not talk to non-technical people about p-values. They won't understand.
Use your domain knowledge. It might be on the borderline of the 5% significance level, but your domain knowledge might tell you that it is an important factor.
If your domain knowledge tells you that the coefficient must be positive... | How to explain borderline p-values to non-stats people | Use "words", do not talk to non-technical people about p-values. They won't understand.
Use your domain knowledge. It might be on the borderline of the 5% significance level, but your domain knowledge | How to explain borderline p-values to non-stats people
Use "words", do not talk to non-technical people about p-values. They won't understand.
Use your domain knowledge. It might be on the borderline of the 5% significance level, but your domain knowledge might tell you that it is an important factor.
If your domain kn... | How to explain borderline p-values to non-stats people
Use "words", do not talk to non-technical people about p-values. They won't understand.
Use your domain knowledge. It might be on the borderline of the 5% significance level, but your domain knowledge |
52,165 | How to explain borderline p-values to non-stats people | Tell the story you found out, not to explain the maths behind your findings.
Non statistical-people wants to know about the stories behind the data. Usually, they use your analysis to take decision in a fast way. | How to explain borderline p-values to non-stats people | Tell the story you found out, not to explain the maths behind your findings.
Non statistical-people wants to know about the stories behind the data. Usually, they use your analysis to take decision in | How to explain borderline p-values to non-stats people
Tell the story you found out, not to explain the maths behind your findings.
Non statistical-people wants to know about the stories behind the data. Usually, they use your analysis to take decision in a fast way. | How to explain borderline p-values to non-stats people
Tell the story you found out, not to explain the maths behind your findings.
Non statistical-people wants to know about the stories behind the data. Usually, they use your analysis to take decision in |
52,166 | How to explain borderline p-values to non-stats people | Drop the hypothesis test and the p value altogether. I'm not confident that 95% of "stats people" really understand p values; with "non-stats people", I'd bet it's less than half. Don't go there unless you must.
In your example, it sounds like you're trying to reject the null that the slope parameter for the predictor ... | How to explain borderline p-values to non-stats people | Drop the hypothesis test and the p value altogether. I'm not confident that 95% of "stats people" really understand p values; with "non-stats people", I'd bet it's less than half. Don't go there unles | How to explain borderline p-values to non-stats people
Drop the hypothesis test and the p value altogether. I'm not confident that 95% of "stats people" really understand p values; with "non-stats people", I'd bet it's less than half. Don't go there unless you must.
In your example, it sounds like you're trying to reje... | How to explain borderline p-values to non-stats people
Drop the hypothesis test and the p value altogether. I'm not confident that 95% of "stats people" really understand p values; with "non-stats people", I'd bet it's less than half. Don't go there unles |
52,167 | How to explain borderline p-values to non-stats people | Keep it simple.
I believe this correlation to be valid, but with the data I have at
the moment, it may or may not be. I need at least twice (or 3X or
10X, etc.) the data to be sure, one way or the other.
If that doesn't get a satisfactory response, consider an analogy.
We all know that home prices are related... | How to explain borderline p-values to non-stats people | Keep it simple.
I believe this correlation to be valid, but with the data I have at
the moment, it may or may not be. I need at least twice (or 3X or
10X, etc.) the data to be sure, one way or t | How to explain borderline p-values to non-stats people
Keep it simple.
I believe this correlation to be valid, but with the data I have at
the moment, it may or may not be. I need at least twice (or 3X or
10X, etc.) the data to be sure, one way or the other.
If that doesn't get a satisfactory response, consider ... | How to explain borderline p-values to non-stats people
Keep it simple.
I believe this correlation to be valid, but with the data I have at
the moment, it may or may not be. I need at least twice (or 3X or
10X, etc.) the data to be sure, one way or t |
52,168 | How to explain borderline p-values to non-stats people | If you think 300 points is limited, than that's the most important argumentation. Hypothesis tests are designed towards keeping the null, unless there is strong evidence against it.
Absence of evidence is not evidence of absence.
I guess also non-stats people should get this. | How to explain borderline p-values to non-stats people | If you think 300 points is limited, than that's the most important argumentation. Hypothesis tests are designed towards keeping the null, unless there is strong evidence against it.
Absence of evide | How to explain borderline p-values to non-stats people
If you think 300 points is limited, than that's the most important argumentation. Hypothesis tests are designed towards keeping the null, unless there is strong evidence against it.
Absence of evidence is not evidence of absence.
I guess also non-stats people sh... | How to explain borderline p-values to non-stats people
If you think 300 points is limited, than that's the most important argumentation. Hypothesis tests are designed towards keeping the null, unless there is strong evidence against it.
Absence of evide |
52,169 | How to explain borderline p-values to non-stats people | I think even non-stats people can understand a distribution curve - most people have seen that in high school and/or college. So you could also show it visually in the sense that people will understand rejection regions vis-a-vis your null hypothesis, etc. You could literally shade those in - "here's where we make this... | How to explain borderline p-values to non-stats people | I think even non-stats people can understand a distribution curve - most people have seen that in high school and/or college. So you could also show it visually in the sense that people will understan | How to explain borderline p-values to non-stats people
I think even non-stats people can understand a distribution curve - most people have seen that in high school and/or college. So you could also show it visually in the sense that people will understand rejection regions vis-a-vis your null hypothesis, etc. You coul... | How to explain borderline p-values to non-stats people
I think even non-stats people can understand a distribution curve - most people have seen that in high school and/or college. So you could also show it visually in the sense that people will understan |
52,170 | Does a Neural Network actually need an activation function or is that just for Back Propagation? | You built a multilayer neural network with a linear hidden layer. Linear units in the hidden layer negates the purpose of having a hidden layer. The weights between your inputs and the hidden layer, and the weights between the hidden layer and the output layer are effectively a single set of weights. A neural network w... | Does a Neural Network actually need an activation function or is that just for Back Propagation? | You built a multilayer neural network with a linear hidden layer. Linear units in the hidden layer negates the purpose of having a hidden layer. The weights between your inputs and the hidden layer, a | Does a Neural Network actually need an activation function or is that just for Back Propagation?
You built a multilayer neural network with a linear hidden layer. Linear units in the hidden layer negates the purpose of having a hidden layer. The weights between your inputs and the hidden layer, and the weights between ... | Does a Neural Network actually need an activation function or is that just for Back Propagation?
You built a multilayer neural network with a linear hidden layer. Linear units in the hidden layer negates the purpose of having a hidden layer. The weights between your inputs and the hidden layer, a |
52,171 | Does a Neural Network actually need an activation function or is that just for Back Propagation? | If you don't have non-linear activation functions, then you end up with a network as powerful in its expressive power as a linear model. Simply view it as a linear algebra problem. Intuitively if you have linear transformation encoded by a matrix $A$ and you compose an initial vector $x$ with multiple linear transforma... | Does a Neural Network actually need an activation function or is that just for Back Propagation? | If you don't have non-linear activation functions, then you end up with a network as powerful in its expressive power as a linear model. Simply view it as a linear algebra problem. Intuitively if you | Does a Neural Network actually need an activation function or is that just for Back Propagation?
If you don't have non-linear activation functions, then you end up with a network as powerful in its expressive power as a linear model. Simply view it as a linear algebra problem. Intuitively if you have linear transformat... | Does a Neural Network actually need an activation function or is that just for Back Propagation?
If you don't have non-linear activation functions, then you end up with a network as powerful in its expressive power as a linear model. Simply view it as a linear algebra problem. Intuitively if you |
52,172 | median(a)/median(b) not equal median(a/b) | This is a property of mathematics, it is actually rare that the order of operations does not matter, e.g. the log of the square root is not the same as the square root of the log (except for a few special cases).
We often focus on some of those special cases where due to operations distributing, associating, and commut... | median(a)/median(b) not equal median(a/b) | This is a property of mathematics, it is actually rare that the order of operations does not matter, e.g. the log of the square root is not the same as the square root of the log (except for a few spe | median(a)/median(b) not equal median(a/b)
This is a property of mathematics, it is actually rare that the order of operations does not matter, e.g. the log of the square root is not the same as the square root of the log (except for a few special cases).
We often focus on some of those special cases where due to operat... | median(a)/median(b) not equal median(a/b)
This is a property of mathematics, it is actually rare that the order of operations does not matter, e.g. the log of the square root is not the same as the square root of the log (except for a few spe |
52,173 | median(a)/median(b) not equal median(a/b) | You might find it even more surprising to discover that even with a nice linear operator like expectation, you still have this issue (median is non linear, mean is linear):
$$\text{mean}(A)/\text{mean}(B) \neq \text{mean}(A/B)$$
For example:
a=1:5
b=6:10
mean(a)/mean(b)
[1] 0.375
mean(a/b)
[1] 0.3543651
But then y... | median(a)/median(b) not equal median(a/b) | You might find it even more surprising to discover that even with a nice linear operator like expectation, you still have this issue (median is non linear, mean is linear):
$$\text{mean}(A)/\text{mean | median(a)/median(b) not equal median(a/b)
You might find it even more surprising to discover that even with a nice linear operator like expectation, you still have this issue (median is non linear, mean is linear):
$$\text{mean}(A)/\text{mean}(B) \neq \text{mean}(A/B)$$
For example:
a=1:5
b=6:10
mean(a)/mean(b)
[1] ... | median(a)/median(b) not equal median(a/b)
You might find it even more surprising to discover that even with a nice linear operator like expectation, you still have this issue (median is non linear, mean is linear):
$$\text{mean}(A)/\text{mean |
52,174 | median(a)/median(b) not equal median(a/b) | Erm, for the (obvious?) reason that the fractional representation of a number is not unique, the medians can't be the same.
EDIT: as per Glen's request
The location of the median relies on the ordering of numbers in your set. Suppose you order your numbers from smallest to largest, so you have something like this {1,2... | median(a)/median(b) not equal median(a/b) | Erm, for the (obvious?) reason that the fractional representation of a number is not unique, the medians can't be the same.
EDIT: as per Glen's request
The location of the median relies on the orderi | median(a)/median(b) not equal median(a/b)
Erm, for the (obvious?) reason that the fractional representation of a number is not unique, the medians can't be the same.
EDIT: as per Glen's request
The location of the median relies on the ordering of numbers in your set. Suppose you order your numbers from smallest to lar... | median(a)/median(b) not equal median(a/b)
Erm, for the (obvious?) reason that the fractional representation of a number is not unique, the medians can't be the same.
EDIT: as per Glen's request
The location of the median relies on the orderi |
52,175 | Concerns about the size of odds-ratio estimates in binary logistic regression model | Thanks for adding the table
Given this, I think the OR is fine. The logistic regression you posted also included another variable, but, in the table, the OR for L1 = 4 vs. L1 = 0 is $\frac{17537*1328}{1284*44} = 412.23$ which is actually a little larger than the one from the regression.
It's a very strong relationship. | Concerns about the size of odds-ratio estimates in binary logistic regression model | Thanks for adding the table
Given this, I think the OR is fine. The logistic regression you posted also included another variable, but, in the table, the OR for L1 = 4 vs. L1 = 0 is $\frac{17537*1328} | Concerns about the size of odds-ratio estimates in binary logistic regression model
Thanks for adding the table
Given this, I think the OR is fine. The logistic regression you posted also included another variable, but, in the table, the OR for L1 = 4 vs. L1 = 0 is $\frac{17537*1328}{1284*44} = 412.23$ which is actuall... | Concerns about the size of odds-ratio estimates in binary logistic regression model
Thanks for adding the table
Given this, I think the OR is fine. The logistic regression you posted also included another variable, but, in the table, the OR for L1 = 4 vs. L1 = 0 is $\frac{17537*1328} |
52,176 | Concerns about the size of odds-ratio estimates in binary logistic regression model | An important point needs to be added to Peter's good answer:
372 times as likely
is definitely not correct, although you would be about the ten gazillionth person to make this mistake. A number close to 400 is the ratio not of two probabilities but of two odds. The ratio of the two corresponding probabilities is [... | Concerns about the size of odds-ratio estimates in binary logistic regression model | An important point needs to be added to Peter's good answer:
372 times as likely
is definitely not correct, although you would be about the ten gazillionth person to make this mistake. A number cl | Concerns about the size of odds-ratio estimates in binary logistic regression model
An important point needs to be added to Peter's good answer:
372 times as likely
is definitely not correct, although you would be about the ten gazillionth person to make this mistake. A number close to 400 is the ratio not of two p... | Concerns about the size of odds-ratio estimates in binary logistic regression model
An important point needs to be added to Peter's good answer:
372 times as likely
is definitely not correct, although you would be about the ten gazillionth person to make this mistake. A number cl |
52,177 | Can someone give a simple guide of Dirichlet process clustering? | What is the difference between (Dirichlet) distribution and (Dirichlet) process?
The difference between a Dirichlet distribution and a Dirichlet process is perhaps easier to understand when you understand the difference between a Gaussian distribution and a Gaussian process. A Gaussian distribution pertains to the poss... | Can someone give a simple guide of Dirichlet process clustering? | What is the difference between (Dirichlet) distribution and (Dirichlet) process?
The difference between a Dirichlet distribution and a Dirichlet process is perhaps easier to understand when you unders | Can someone give a simple guide of Dirichlet process clustering?
What is the difference between (Dirichlet) distribution and (Dirichlet) process?
The difference between a Dirichlet distribution and a Dirichlet process is perhaps easier to understand when you understand the difference between a Gaussian distribution and... | Can someone give a simple guide of Dirichlet process clustering?
What is the difference between (Dirichlet) distribution and (Dirichlet) process?
The difference between a Dirichlet distribution and a Dirichlet process is perhaps easier to understand when you unders |
52,178 | Can someone give a simple guide of Dirichlet process clustering? | These are two great tutorials,
"Introduction to the Dirichlet Distribution and Related Processes"
"A Very Gentle Note on the Construction of Dirichlet Process"
specially the first one, with a reference to a very succinct tutorial on measure theory. I would start with the first one, because it starts by introducing the ... | Can someone give a simple guide of Dirichlet process clustering? | These are two great tutorials,
"Introduction to the Dirichlet Distribution and Related Processes"
"A Very Gentle Note on the Construction of Dirichlet Process"
specially the first one, with a referenc | Can someone give a simple guide of Dirichlet process clustering?
These are two great tutorials,
"Introduction to the Dirichlet Distribution and Related Processes"
"A Very Gentle Note on the Construction of Dirichlet Process"
specially the first one, with a reference to a very succinct tutorial on measure theory. I woul... | Can someone give a simple guide of Dirichlet process clustering?
These are two great tutorials,
"Introduction to the Dirichlet Distribution and Related Processes"
"A Very Gentle Note on the Construction of Dirichlet Process"
specially the first one, with a referenc |
52,179 | When do you use AIC vs. BIC [duplicate] | The AIC and BIC optimize different things.
AIC is basically suitable for a situation where you don't necessarily think there's 'a model' so much as a bunch of effects of different sizes, and you're in a situation you want to get good prediction error. As such, as the sample size expands, the AIC choice of model expand... | When do you use AIC vs. BIC [duplicate] | The AIC and BIC optimize different things.
AIC is basically suitable for a situation where you don't necessarily think there's 'a model' so much as a bunch of effects of different sizes, and you're i | When do you use AIC vs. BIC [duplicate]
The AIC and BIC optimize different things.
AIC is basically suitable for a situation where you don't necessarily think there's 'a model' so much as a bunch of effects of different sizes, and you're in a situation you want to get good prediction error. As such, as the sample size... | When do you use AIC vs. BIC [duplicate]
The AIC and BIC optimize different things.
AIC is basically suitable for a situation where you don't necessarily think there's 'a model' so much as a bunch of effects of different sizes, and you're i |
52,180 | When do you use AIC vs. BIC [duplicate] | When used for forward or backward model selection, the BIC penalizes the number of parameters in the model to a greater extent than AIC. Consequently, you'll arrive at a model with fewer parameters in it, on average. | When do you use AIC vs. BIC [duplicate] | When used for forward or backward model selection, the BIC penalizes the number of parameters in the model to a greater extent than AIC. Consequently, you'll arrive at a model with fewer parameters in | When do you use AIC vs. BIC [duplicate]
When used for forward or backward model selection, the BIC penalizes the number of parameters in the model to a greater extent than AIC. Consequently, you'll arrive at a model with fewer parameters in it, on average. | When do you use AIC vs. BIC [duplicate]
When used for forward or backward model selection, the BIC penalizes the number of parameters in the model to a greater extent than AIC. Consequently, you'll arrive at a model with fewer parameters in |
52,181 | R model.tables() incorrect means – possible bug? | As you point out, the individual cell means match, but where you see the problem is in the marginal means. There are multiple ways to calculate the marginal means. Suppose that the data has information on sex (male/female) and age (old/young) and we want to calculate the margin for sex. One approach is to ignore the... | R model.tables() incorrect means – possible bug? | As you point out, the individual cell means match, but where you see the problem is in the marginal means. There are multiple ways to calculate the marginal means. Suppose that the data has informat | R model.tables() incorrect means – possible bug?
As you point out, the individual cell means match, but where you see the problem is in the marginal means. There are multiple ways to calculate the marginal means. Suppose that the data has information on sex (male/female) and age (old/young) and we want to calculate t... | R model.tables() incorrect means – possible bug?
As you point out, the individual cell means match, but where you see the problem is in the marginal means. There are multiple ways to calculate the marginal means. Suppose that the data has informat |
52,182 | R model.tables() incorrect means – possible bug? | @mnel is correct in that because of the unbalanced design, the order of the terms matter in the output of model.tables.
ADDED: In the help file for aov, we read that it "is designed for balanced designs, and the results can be hard to interpret without balance." So if you want simple descriptive statistics, better t... | R model.tables() incorrect means – possible bug? | @mnel is correct in that because of the unbalanced design, the order of the terms matter in the output of model.tables.
ADDED: In the help file for aov, we read that it "is designed for balanced des | R model.tables() incorrect means – possible bug?
@mnel is correct in that because of the unbalanced design, the order of the terms matter in the output of model.tables.
ADDED: In the help file for aov, we read that it "is designed for balanced designs, and the results can be hard to interpret without balance." So if... | R model.tables() incorrect means – possible bug?
@mnel is correct in that because of the unbalanced design, the order of the terms matter in the output of model.tables.
ADDED: In the help file for aov, we read that it "is designed for balanced des |
52,183 | R model.tables() incorrect means – possible bug? | Watch out: the model.tables() function only works with balanced designs. If you want to have the marginal means for unbalanced design you should use the popMeans() function. Imagine you have the following model:
Check.Model <- aov(dependent ~ factor1 + factor2, data=data.data)
If you would want the marginal means for ... | R model.tables() incorrect means – possible bug? | Watch out: the model.tables() function only works with balanced designs. If you want to have the marginal means for unbalanced design you should use the popMeans() function. Imagine you have the follo | R model.tables() incorrect means – possible bug?
Watch out: the model.tables() function only works with balanced designs. If you want to have the marginal means for unbalanced design you should use the popMeans() function. Imagine you have the following model:
Check.Model <- aov(dependent ~ factor1 + factor2, data=data... | R model.tables() incorrect means – possible bug?
Watch out: the model.tables() function only works with balanced designs. If you want to have the marginal means for unbalanced design you should use the popMeans() function. Imagine you have the follo |
52,184 | Why doesn't the Cramér-Rao lower bound apply? | Are you aware of the three regularity conditions that must be satisfied for the CR lower bound to apply? It looks like it violates the condition that the bounds of the distribution function must not depend upon the quantity being estimated. $\theta$ determines the bounds of the distribution. See the Wikipedia article, ... | Why doesn't the Cramér-Rao lower bound apply? | Are you aware of the three regularity conditions that must be satisfied for the CR lower bound to apply? It looks like it violates the condition that the bounds of the distribution function must not d | Why doesn't the Cramér-Rao lower bound apply?
Are you aware of the three regularity conditions that must be satisfied for the CR lower bound to apply? It looks like it violates the condition that the bounds of the distribution function must not depend upon the quantity being estimated. $\theta$ determines the bounds of... | Why doesn't the Cramér-Rao lower bound apply?
Are you aware of the three regularity conditions that must be satisfied for the CR lower bound to apply? It looks like it violates the condition that the bounds of the distribution function must not d |
52,185 | Why doesn't the Cramér-Rao lower bound apply? | The Cramer-Rao Lower Bound (CRLB) is valid only for densities that are sufficiently regular. In particular, the support of the density f(x; θ) cannot depend upon the parameter θ. This is because f(x; θ) must be such that the order of integration of f(x; θ) with respect to x and differentiation of f(x; θ) with respect... | Why doesn't the Cramér-Rao lower bound apply? | The Cramer-Rao Lower Bound (CRLB) is valid only for densities that are sufficiently regular. In particular, the support of the density f(x; θ) cannot depend upon the parameter θ. This is because f(x | Why doesn't the Cramér-Rao lower bound apply?
The Cramer-Rao Lower Bound (CRLB) is valid only for densities that are sufficiently regular. In particular, the support of the density f(x; θ) cannot depend upon the parameter θ. This is because f(x; θ) must be such that the order of integration of f(x; θ) with respect to... | Why doesn't the Cramér-Rao lower bound apply?
The Cramer-Rao Lower Bound (CRLB) is valid only for densities that are sufficiently regular. In particular, the support of the density f(x; θ) cannot depend upon the parameter θ. This is because f(x |
52,186 | Pie charts vs. dot plots | There are two different types of chart that that are referred to as 'dotplots' and I think that you are getting the two confused. The type of dotplot that it looks like you are thinking about is really a variation on a histogram and does not convey the same type of information that a pie chart would.
The type of dotpl... | Pie charts vs. dot plots | There are two different types of chart that that are referred to as 'dotplots' and I think that you are getting the two confused. The type of dotplot that it looks like you are thinking about is real | Pie charts vs. dot plots
There are two different types of chart that that are referred to as 'dotplots' and I think that you are getting the two confused. The type of dotplot that it looks like you are thinking about is really a variation on a histogram and does not convey the same type of information that a pie chart... | Pie charts vs. dot plots
There are two different types of chart that that are referred to as 'dotplots' and I think that you are getting the two confused. The type of dotplot that it looks like you are thinking about is real |
52,187 | Pie charts vs. dot plots | Greg Snow's response has covered much about dot plot. I'd just like to suggest an alternative which you can compress the dimension further:
Sorry the legend is missing but the idea is pretty much here. Instead of displaying the four pieces of data on four horizontal lines, we can put them in one line with accumulative... | Pie charts vs. dot plots | Greg Snow's response has covered much about dot plot. I'd just like to suggest an alternative which you can compress the dimension further:
Sorry the legend is missing but the idea is pretty much her | Pie charts vs. dot plots
Greg Snow's response has covered much about dot plot. I'd just like to suggest an alternative which you can compress the dimension further:
Sorry the legend is missing but the idea is pretty much here. Instead of displaying the four pieces of data on four horizontal lines, we can put them in o... | Pie charts vs. dot plots
Greg Snow's response has covered much about dot plot. I'd just like to suggest an alternative which you can compress the dimension further:
Sorry the legend is missing but the idea is pretty much her |
52,188 | The most common extracted features for image recognition | Different categories of image features come to mind:
Color features such as color histograms which could for instance be in RGB or HSV space
Other histogram approaches, e.g. histogram of oriented gradients (HOG)
Texture features such as Tamura's or Haralick's
SIFT and SURF features are popular as well
Luckily librari... | The most common extracted features for image recognition | Different categories of image features come to mind:
Color features such as color histograms which could for instance be in RGB or HSV space
Other histogram approaches, e.g. histogram of oriented gra | The most common extracted features for image recognition
Different categories of image features come to mind:
Color features such as color histograms which could for instance be in RGB or HSV space
Other histogram approaches, e.g. histogram of oriented gradients (HOG)
Texture features such as Tamura's or Haralick's
SI... | The most common extracted features for image recognition
Different categories of image features come to mind:
Color features such as color histograms which could for instance be in RGB or HSV space
Other histogram approaches, e.g. histogram of oriented gra |
52,189 | The most common extracted features for image recognition | One standard approach is to use a restricted Boltzmann machine to do the feature extraction, and then reconsider the RBM as a neural network and finish the training using back-propagation. See, for example,
G. E. Hinton, "To Recognize Shapes, First Learn to Generate images," Progress in brain research, vol. 165, pp. 5... | The most common extracted features for image recognition | One standard approach is to use a restricted Boltzmann machine to do the feature extraction, and then reconsider the RBM as a neural network and finish the training using back-propagation. See, for e | The most common extracted features for image recognition
One standard approach is to use a restricted Boltzmann machine to do the feature extraction, and then reconsider the RBM as a neural network and finish the training using back-propagation. See, for example,
G. E. Hinton, "To Recognize Shapes, First Learn to Gene... | The most common extracted features for image recognition
One standard approach is to use a restricted Boltzmann machine to do the feature extraction, and then reconsider the RBM as a neural network and finish the training using back-propagation. See, for e |
52,190 | How to visualize two bar charts with very different scales without looking redundant | In general, if you have two different measurements on each of a set of observations, and you think there may be a relationship between them, I think it's best to visualize them with a scatterplot. I don't know if you use R, but here is some simple code and a sample plot:
speed = c(2.2, 4.7, 7.3, 3.1)
weight = c(500... | How to visualize two bar charts with very different scales without looking redundant | In general, if you have two different measurements on each of a set of observations, and you think there may be a relationship between them, I think it's best to visualize them with a scatterplot. I | How to visualize two bar charts with very different scales without looking redundant
In general, if you have two different measurements on each of a set of observations, and you think there may be a relationship between them, I think it's best to visualize them with a scatterplot. I don't know if you use R, but here i... | How to visualize two bar charts with very different scales without looking redundant
In general, if you have two different measurements on each of a set of observations, and you think there may be a relationship between them, I think it's best to visualize them with a scatterplot. I |
52,191 | How to visualize two bar charts with very different scales without looking redundant | It's OK to have two graphs share an axis.
But it's best to avoid one graph with two scales in the same dimension. There is too much potential for misreading (mainly assuming the alignment carries some significance). See the Stephen Few article Dual-Scaled Axes in Graphs: Are They Ever the Best Solution?. | How to visualize two bar charts with very different scales without looking redundant | It's OK to have two graphs share an axis.
But it's best to avoid one graph with two scales in the same dimension. There is too much potential for misreading (mainly assuming the alignment carries som | How to visualize two bar charts with very different scales without looking redundant
It's OK to have two graphs share an axis.
But it's best to avoid one graph with two scales in the same dimension. There is too much potential for misreading (mainly assuming the alignment carries some significance). See the Stephen Fe... | How to visualize two bar charts with very different scales without looking redundant
It's OK to have two graphs share an axis.
But it's best to avoid one graph with two scales in the same dimension. There is too much potential for misreading (mainly assuming the alignment carries som |
52,192 | How to visualize two bar charts with very different scales without looking redundant | You could also transform absolute scales into relative by using z-transformation (or any other that you think is more suitable).
speed = c(2.2, 4.7, 7.3, 3.1)
weight = c(500, 222, 999, 1000)
speed=scale(speed)
weight=scale(weight)
rng=extendrange(range(c(speed,weight)))
plot(speed, type="b", col="red", ylim=rng,ylab... | How to visualize two bar charts with very different scales without looking redundant | You could also transform absolute scales into relative by using z-transformation (or any other that you think is more suitable).
speed = c(2.2, 4.7, 7.3, 3.1)
weight = c(500, 222, 999, 1000)
speed=s | How to visualize two bar charts with very different scales without looking redundant
You could also transform absolute scales into relative by using z-transformation (or any other that you think is more suitable).
speed = c(2.2, 4.7, 7.3, 3.1)
weight = c(500, 222, 999, 1000)
speed=scale(speed)
weight=scale(weight)
rn... | How to visualize two bar charts with very different scales without looking redundant
You could also transform absolute scales into relative by using z-transformation (or any other that you think is more suitable).
speed = c(2.2, 4.7, 7.3, 3.1)
weight = c(500, 222, 999, 1000)
speed=s |
52,193 | How to visualize two bar charts with very different scales without looking redundant | Given that your data sets are different by orders of magnitude you might want to use logarithmic scale for your x-axis (or take the log of all samples before plotting.) That way the you can still see the variation within the same order of magnitude relatively clearly while the empty space between the sets is condensed.... | How to visualize two bar charts with very different scales without looking redundant | Given that your data sets are different by orders of magnitude you might want to use logarithmic scale for your x-axis (or take the log of all samples before plotting.) That way the you can still see | How to visualize two bar charts with very different scales without looking redundant
Given that your data sets are different by orders of magnitude you might want to use logarithmic scale for your x-axis (or take the log of all samples before plotting.) That way the you can still see the variation within the same order... | How to visualize two bar charts with very different scales without looking redundant
Given that your data sets are different by orders of magnitude you might want to use logarithmic scale for your x-axis (or take the log of all samples before plotting.) That way the you can still see |
52,194 | Plotting a logistic GAM model in R - why is the scale not 0-1? | The individual plots are on the scale of the linear predictor, i.e. a scale that is -Inf to +Inf. The inverse of the link function is used to map from this scale to the 0, ..., 1 scale of the response. Further note that each smooth is subject to centring constraints and so is centred about 0. | Plotting a logistic GAM model in R - why is the scale not 0-1? | The individual plots are on the scale of the linear predictor, i.e. a scale that is -Inf to +Inf. The inverse of the link function is used to map from this scale to the 0, ..., 1 scale of the response | Plotting a logistic GAM model in R - why is the scale not 0-1?
The individual plots are on the scale of the linear predictor, i.e. a scale that is -Inf to +Inf. The inverse of the link function is used to map from this scale to the 0, ..., 1 scale of the response. Further note that each smooth is subject to centring co... | Plotting a logistic GAM model in R - why is the scale not 0-1?
The individual plots are on the scale of the linear predictor, i.e. a scale that is -Inf to +Inf. The inverse of the link function is used to map from this scale to the 0, ..., 1 scale of the response |
52,195 | Plotting a logistic GAM model in R - why is the scale not 0-1? | What is being plotted is the log-odds. It's log(p/(1-p)). That's the space of the logistic regression. You can convert the values using the logistic distribution and the qlogis and plogis functions.
I don't know what GAM functions you're using but often times there are options to get the p-values out. | Plotting a logistic GAM model in R - why is the scale not 0-1? | What is being plotted is the log-odds. It's log(p/(1-p)). That's the space of the logistic regression. You can convert the values using the logistic distribution and the qlogis and plogis functions | Plotting a logistic GAM model in R - why is the scale not 0-1?
What is being plotted is the log-odds. It's log(p/(1-p)). That's the space of the logistic regression. You can convert the values using the logistic distribution and the qlogis and plogis functions.
I don't know what GAM functions you're using but often ... | Plotting a logistic GAM model in R - why is the scale not 0-1?
What is being plotted is the log-odds. It's log(p/(1-p)). That's the space of the logistic regression. You can convert the values using the logistic distribution and the qlogis and plogis functions |
52,196 | Plotting a logistic GAM model in R - why is the scale not 0-1? | The other answers already provide a good enough explanation, but I wanted to provide a worked example to show the differences in case somebody discovers this question down the road. I have fit a model using the biopsy data in the MASS package in R. The only adaptation to this data that I made was converting the charact... | Plotting a logistic GAM model in R - why is the scale not 0-1? | The other answers already provide a good enough explanation, but I wanted to provide a worked example to show the differences in case somebody discovers this question down the road. I have fit a model | Plotting a logistic GAM model in R - why is the scale not 0-1?
The other answers already provide a good enough explanation, but I wanted to provide a worked example to show the differences in case somebody discovers this question down the road. I have fit a model using the biopsy data in the MASS package in R. The only... | Plotting a logistic GAM model in R - why is the scale not 0-1?
The other answers already provide a good enough explanation, but I wanted to provide a worked example to show the differences in case somebody discovers this question down the road. I have fit a model |
52,197 | If there was a certification exam for statisticians, what would be the syllabus? | The Royal Statistical Society offers three levels of professional exam in statistics. Their documentation includes the syllabuses (pdf) and a series of reading lists. Far too much material to summarise here! | If there was a certification exam for statisticians, what would be the syllabus? | The Royal Statistical Society offers three levels of professional exam in statistics. Their documentation includes the syllabuses (pdf) and a series of reading lists. Far too much material to summaris | If there was a certification exam for statisticians, what would be the syllabus?
The Royal Statistical Society offers three levels of professional exam in statistics. Their documentation includes the syllabuses (pdf) and a series of reading lists. Far too much material to summarise here! | If there was a certification exam for statisticians, what would be the syllabus?
The Royal Statistical Society offers three levels of professional exam in statistics. Their documentation includes the syllabuses (pdf) and a series of reading lists. Far too much material to summaris |
52,198 | If there was a certification exam for statisticians, what would be the syllabus? | The American Statistical Association, The Royal Statistical Society, and the australian and Canadian societies all have certification. In the case of ASA where I have certification and RSS where I have an application in, there is not a required test. They look for information from your CV and references. | If there was a certification exam for statisticians, what would be the syllabus? | The American Statistical Association, The Royal Statistical Society, and the australian and Canadian societies all have certification. In the case of ASA where I have certification and RSS where I ha | If there was a certification exam for statisticians, what would be the syllabus?
The American Statistical Association, The Royal Statistical Society, and the australian and Canadian societies all have certification. In the case of ASA where I have certification and RSS where I have an application in, there is not a re... | If there was a certification exam for statisticians, what would be the syllabus?
The American Statistical Association, The Royal Statistical Society, and the australian and Canadian societies all have certification. In the case of ASA where I have certification and RSS where I ha |
52,199 | Best method to visualize large interaction between two factors | If you are interested in visualizing an interaction effect specifically, you can subtract main effects (i.e., average factor effect, say $x_i$ and $x_j$) from each treatment mean (combination of factor levels, indexed by $i$ and $j$) based on the relation
$$\gamma_{ij} = \bar x_{ij} - \bar x_i - \bar x_j + \bar x$$
Thi... | Best method to visualize large interaction between two factors | If you are interested in visualizing an interaction effect specifically, you can subtract main effects (i.e., average factor effect, say $x_i$ and $x_j$) from each treatment mean (combination of facto | Best method to visualize large interaction between two factors
If you are interested in visualizing an interaction effect specifically, you can subtract main effects (i.e., average factor effect, say $x_i$ and $x_j$) from each treatment mean (combination of factor levels, indexed by $i$ and $j$) based on the relation
$... | Best method to visualize large interaction between two factors
If you are interested in visualizing an interaction effect specifically, you can subtract main effects (i.e., average factor effect, say $x_i$ and $x_j$) from each treatment mean (combination of facto |
52,200 | Best method to visualize large interaction between two factors | In R, there is a function coplot which plots your main effect and outcome in a grid of domains for each conditioning factor in a scatter-plot matrix. By examining the change between trends in the panel of plots, you can assess the extent of interaction present in the data. | Best method to visualize large interaction between two factors | In R, there is a function coplot which plots your main effect and outcome in a grid of domains for each conditioning factor in a scatter-plot matrix. By examining the change between trends in the pane | Best method to visualize large interaction between two factors
In R, there is a function coplot which plots your main effect and outcome in a grid of domains for each conditioning factor in a scatter-plot matrix. By examining the change between trends in the panel of plots, you can assess the extent of interaction pres... | Best method to visualize large interaction between two factors
In R, there is a function coplot which plots your main effect and outcome in a grid of domains for each conditioning factor in a scatter-plot matrix. By examining the change between trends in the pane |
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