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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5,201 | Intuitive difference between hidden Markov models and conditional random fields | "Conditional Random Fields can be understood as a sequential extension to the Maximum Entropy Model". This sentence is from a technical report related to "Classical Probabilistic Models and Conditional Random Fields".
It is probably the best read for topics such as HMM, CRF and Maximum Entropy.
PS: Figure 1 in the link... | Intuitive difference between hidden Markov models and conditional random fields | "Conditional Random Fields can be understood as a sequential extension to the Maximum Entropy Model". This sentence is from a technical report related to "Classical Probabilistic Models and Conditiona | Intuitive difference between hidden Markov models and conditional random fields
"Conditional Random Fields can be understood as a sequential extension to the Maximum Entropy Model". This sentence is from a technical report related to "Classical Probabilistic Models and Conditional Random Fields".
It is probably the bes... | Intuitive difference between hidden Markov models and conditional random fields
"Conditional Random Fields can be understood as a sequential extension to the Maximum Entropy Model". This sentence is from a technical report related to "Classical Probabilistic Models and Conditiona |
5,202 | Multiple regression or partial correlation coefficient? And relations between the two | Multiple linear regression coefficient and partial correlation are directly linked and have the same significance (p-value). Partial r is just another way of standardizing the coefficient, along with beta coefficient (standardized regression coefficient)$^1$. So, if the dependent variable is $y$ and the independents ar... | Multiple regression or partial correlation coefficient? And relations between the two | Multiple linear regression coefficient and partial correlation are directly linked and have the same significance (p-value). Partial r is just another way of standardizing the coefficient, along with | Multiple regression or partial correlation coefficient? And relations between the two
Multiple linear regression coefficient and partial correlation are directly linked and have the same significance (p-value). Partial r is just another way of standardizing the coefficient, along with beta coefficient (standardized reg... | Multiple regression or partial correlation coefficient? And relations between the two
Multiple linear regression coefficient and partial correlation are directly linked and have the same significance (p-value). Partial r is just another way of standardizing the coefficient, along with |
5,203 | Multiple regression or partial correlation coefficient? And relations between the two | Just bumped to this tread by chance. In the original answer,
in the formula for $\beta_{x_1}$ the factor $\sqrt{SSY/SSX_1}$ is
missing, that is
$$ \beta_{x_1} = \frac{r_{yx_1} - r_{y x_2} ~r_{x_1 x_2}}
{1-r^2_{x_1 x_2}} \times \sqrt{\frac{SSY}{SSX_1}},
$$
where $SSY=\sum_i (y_i-\bar y)^2$ and $SSX_1 = \sum_i {(x_{1i} ... | Multiple regression or partial correlation coefficient? And relations between the two | Just bumped to this tread by chance. In the original answer,
in the formula for $\beta_{x_1}$ the factor $\sqrt{SSY/SSX_1}$ is
missing, that is
$$ \beta_{x_1} = \frac{r_{yx_1} - r_{y x_2} ~r_{x_1 x_2 | Multiple regression or partial correlation coefficient? And relations between the two
Just bumped to this tread by chance. In the original answer,
in the formula for $\beta_{x_1}$ the factor $\sqrt{SSY/SSX_1}$ is
missing, that is
$$ \beta_{x_1} = \frac{r_{yx_1} - r_{y x_2} ~r_{x_1 x_2}}
{1-r^2_{x_1 x_2}} \times \sqrt{... | Multiple regression or partial correlation coefficient? And relations between the two
Just bumped to this tread by chance. In the original answer,
in the formula for $\beta_{x_1}$ the factor $\sqrt{SSY/SSX_1}$ is
missing, that is
$$ \beta_{x_1} = \frac{r_{yx_1} - r_{y x_2} ~r_{x_1 x_2 |
5,204 | Choosing variables to include in a multiple linear regression model | Based on your reaction to my comment:
You are looking for prediction. Thus, you should not really rely on (in)significance of the coefficients. You would be better to
Pick a criterion that describes your prediction needs best (e.g.
missclassification rate, AUC of ROC, some form of these with
weights,...)
For each mode... | Choosing variables to include in a multiple linear regression model | Based on your reaction to my comment:
You are looking for prediction. Thus, you should not really rely on (in)significance of the coefficients. You would be better to
Pick a criterion that describes | Choosing variables to include in a multiple linear regression model
Based on your reaction to my comment:
You are looking for prediction. Thus, you should not really rely on (in)significance of the coefficients. You would be better to
Pick a criterion that describes your prediction needs best (e.g.
missclassification ... | Choosing variables to include in a multiple linear regression model
Based on your reaction to my comment:
You are looking for prediction. Thus, you should not really rely on (in)significance of the coefficients. You would be better to
Pick a criterion that describes |
5,205 | Choosing variables to include in a multiple linear regression model | There is no simple answer to this. When you remove some of the non-significant explanatory variables, others that are correlated with those may become significant. There is nothing wrong with this, but it makes model selection at least partly art rather than science. This is why experiments aim for keeping explanato... | Choosing variables to include in a multiple linear regression model | There is no simple answer to this. When you remove some of the non-significant explanatory variables, others that are correlated with those may become significant. There is nothing wrong with this, | Choosing variables to include in a multiple linear regression model
There is no simple answer to this. When you remove some of the non-significant explanatory variables, others that are correlated with those may become significant. There is nothing wrong with this, but it makes model selection at least partly art rat... | Choosing variables to include in a multiple linear regression model
There is no simple answer to this. When you remove some of the non-significant explanatory variables, others that are correlated with those may become significant. There is nothing wrong with this, |
5,206 | Choosing variables to include in a multiple linear regression model | If you are only interested in predictive performance, then it is probably better to use all of the features and use ridge-regression to avoid over-fitting the training sample. This is essentially the advice given in the appendix of Millar's monograph on "subset selection in regression", so it comes with a reasonable p... | Choosing variables to include in a multiple linear regression model | If you are only interested in predictive performance, then it is probably better to use all of the features and use ridge-regression to avoid over-fitting the training sample. This is essentially the | Choosing variables to include in a multiple linear regression model
If you are only interested in predictive performance, then it is probably better to use all of the features and use ridge-regression to avoid over-fitting the training sample. This is essentially the advice given in the appendix of Millar's monograph ... | Choosing variables to include in a multiple linear regression model
If you are only interested in predictive performance, then it is probably better to use all of the features and use ridge-regression to avoid over-fitting the training sample. This is essentially the |
5,207 | Choosing variables to include in a multiple linear regression model | You can also use the step function in the Akaike information criterion. Example below. https://en.wikipedia.org/wiki/Akaike_information_criterion
StepModel = step(ClimateChangeModel) | Choosing variables to include in a multiple linear regression model | You can also use the step function in the Akaike information criterion. Example below. https://en.wikipedia.org/wiki/Akaike_information_criterion
StepModel = step(ClimateChangeModel) | Choosing variables to include in a multiple linear regression model
You can also use the step function in the Akaike information criterion. Example below. https://en.wikipedia.org/wiki/Akaike_information_criterion
StepModel = step(ClimateChangeModel) | Choosing variables to include in a multiple linear regression model
You can also use the step function in the Akaike information criterion. Example below. https://en.wikipedia.org/wiki/Akaike_information_criterion
StepModel = step(ClimateChangeModel) |
5,208 | Choosing variables to include in a multiple linear regression model | Use the leaps library. When you plot the variables the y-axis shows R^2 adjusted. You look at where the boxes are black at the highest R^2. This will show the variables you should use for your multiple linear regression.
Wine example below:
library(leaps)
regsubsets.out <-
regsubsets(Price ~ Year + WinterRain + AGST... | Choosing variables to include in a multiple linear regression model | Use the leaps library. When you plot the variables the y-axis shows R^2 adjusted. You look at where the boxes are black at the highest R^2. This will show the variables you should use for your multipl | Choosing variables to include in a multiple linear regression model
Use the leaps library. When you plot the variables the y-axis shows R^2 adjusted. You look at where the boxes are black at the highest R^2. This will show the variables you should use for your multiple linear regression.
Wine example below:
library(le... | Choosing variables to include in a multiple linear regression model
Use the leaps library. When you plot the variables the y-axis shows R^2 adjusted. You look at where the boxes are black at the highest R^2. This will show the variables you should use for your multipl |
5,209 | Choosing variables to include in a multiple linear regression model | Why not doing correlation analysis First and then onclude in regression only those that corelate with Dv? | Choosing variables to include in a multiple linear regression model | Why not doing correlation analysis First and then onclude in regression only those that corelate with Dv? | Choosing variables to include in a multiple linear regression model
Why not doing correlation analysis First and then onclude in regression only those that corelate with Dv? | Choosing variables to include in a multiple linear regression model
Why not doing correlation analysis First and then onclude in regression only those that corelate with Dv? |
5,210 | Choosing variables to include in a multiple linear regression model | My advisor offered another possible way to go about this. Run all of your variables once, and then remove those that fail to meet some threshold (we set our threshold as p < .25). Continue iterating that way until all variables fall below that .25 value, then report those values which are significant. | Choosing variables to include in a multiple linear regression model | My advisor offered another possible way to go about this. Run all of your variables once, and then remove those that fail to meet some threshold (we set our threshold as p < .25). Continue iterating t | Choosing variables to include in a multiple linear regression model
My advisor offered another possible way to go about this. Run all of your variables once, and then remove those that fail to meet some threshold (we set our threshold as p < .25). Continue iterating that way until all variables fall below that .25 valu... | Choosing variables to include in a multiple linear regression model
My advisor offered another possible way to go about this. Run all of your variables once, and then remove those that fail to meet some threshold (we set our threshold as p < .25). Continue iterating t |
5,211 | PCA and the train/test split | For measuring the generalization error, you need to do the latter: a separate PCA for every training set (which would mean doing a separate PCA for every classifier and for every CV fold).
You then apply the same transformation to the test set: i.e. you do not do a separate PCA on the test set! You subtract the mean (a... | PCA and the train/test split | For measuring the generalization error, you need to do the latter: a separate PCA for every training set (which would mean doing a separate PCA for every classifier and for every CV fold).
You then ap | PCA and the train/test split
For measuring the generalization error, you need to do the latter: a separate PCA for every training set (which would mean doing a separate PCA for every classifier and for every CV fold).
You then apply the same transformation to the test set: i.e. you do not do a separate PCA on the test ... | PCA and the train/test split
For measuring the generalization error, you need to do the latter: a separate PCA for every training set (which would mean doing a separate PCA for every classifier and for every CV fold).
You then ap |
5,212 | PCA and the train/test split | The answer to this question depends on your experimental design. PCA can be done on the whole data set so long as you don't need to build your model in advance of knowing the data you are trying to predict. If you have a dataset where you have a bunch of samples some of which are known and some are unknown and you wa... | PCA and the train/test split | The answer to this question depends on your experimental design. PCA can be done on the whole data set so long as you don't need to build your model in advance of knowing the data you are trying to p | PCA and the train/test split
The answer to this question depends on your experimental design. PCA can be done on the whole data set so long as you don't need to build your model in advance of knowing the data you are trying to predict. If you have a dataset where you have a bunch of samples some of which are known an... | PCA and the train/test split
The answer to this question depends on your experimental design. PCA can be done on the whole data set so long as you don't need to build your model in advance of knowing the data you are trying to p |
5,213 | PCA and the train/test split | Do the latter, PCA on training set each time
In PCA, we learn the reduced matrix : U which helps us get the projection Z_train = U x X_train
At test time, we use the same U learned from the training phase and then compute the projection Z_test = U x X_test
So, essentially we are projecting the test set onto the reduced... | PCA and the train/test split | Do the latter, PCA on training set each time
In PCA, we learn the reduced matrix : U which helps us get the projection Z_train = U x X_train
At test time, we use the same U learned from the training p | PCA and the train/test split
Do the latter, PCA on training set each time
In PCA, we learn the reduced matrix : U which helps us get the projection Z_train = U x X_train
At test time, we use the same U learned from the training phase and then compute the projection Z_test = U x X_test
So, essentially we are projecting ... | PCA and the train/test split
Do the latter, PCA on training set each time
In PCA, we learn the reduced matrix : U which helps us get the projection Z_train = U x X_train
At test time, we use the same U learned from the training p |
5,214 | How does the Adam method of stochastic gradient descent work? | The Adam paper says, "...many objective functions are composed of a sum of subfunctions evaluated at different subsamples of data; in this case optimization can be made more efficient by taking gradient steps w.r.t. individual subfunctions..." Here, they just mean that the objective function is a sum of errors over tr... | How does the Adam method of stochastic gradient descent work? | The Adam paper says, "...many objective functions are composed of a sum of subfunctions evaluated at different subsamples of data; in this case optimization can be made more efficient by taking gradie | How does the Adam method of stochastic gradient descent work?
The Adam paper says, "...many objective functions are composed of a sum of subfunctions evaluated at different subsamples of data; in this case optimization can be made more efficient by taking gradient steps w.r.t. individual subfunctions..." Here, they ju... | How does the Adam method of stochastic gradient descent work?
The Adam paper says, "...many objective functions are composed of a sum of subfunctions evaluated at different subsamples of data; in this case optimization can be made more efficient by taking gradie |
5,215 | Variational inference versus MCMC: when to choose one over the other? | For a long answer, see Blei, Kucukelbir and McAuliffe here. This short answer draws heavily therefrom.
MCMC is asymptotically exact; VI is not. In the limit, MCMC will exactly approximate the target distribution. VI comes without warranty.
MCMC is computationally expensive. In general, VI is faster.
Meaning, when we ... | Variational inference versus MCMC: when to choose one over the other? | For a long answer, see Blei, Kucukelbir and McAuliffe here. This short answer draws heavily therefrom.
MCMC is asymptotically exact; VI is not. In the limit, MCMC will exactly approximate the target | Variational inference versus MCMC: when to choose one over the other?
For a long answer, see Blei, Kucukelbir and McAuliffe here. This short answer draws heavily therefrom.
MCMC is asymptotically exact; VI is not. In the limit, MCMC will exactly approximate the target distribution. VI comes without warranty.
MCMC is c... | Variational inference versus MCMC: when to choose one over the other?
For a long answer, see Blei, Kucukelbir and McAuliffe here. This short answer draws heavily therefrom.
MCMC is asymptotically exact; VI is not. In the limit, MCMC will exactly approximate the target |
5,216 | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably? | My understanding is that AIC, DIC, and WAIC are all estimating the same thing: the expected out-of-sample deviance associated with a model. This is also the same thing that cross-validation estimates. In Gelman et al. (2013), they say this explicitly:
A natural way to estimate out-of-sample prediction error is cross-... | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably? | My understanding is that AIC, DIC, and WAIC are all estimating the same thing: the expected out-of-sample deviance associated with a model. This is also the same thing that cross-validation estimates | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably?
My understanding is that AIC, DIC, and WAIC are all estimating the same thing: the expected out-of-sample deviance associated with a model. This is also the same thing that cross-validation estimates. In Gelman et al. (2013), they say this explici... | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably?
My understanding is that AIC, DIC, and WAIC are all estimating the same thing: the expected out-of-sample deviance associated with a model. This is also the same thing that cross-validation estimates |
5,217 | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably? | "Interchangeably" is too strong a word. All of them are criteria that seek to compare models and find a "best" model, but each defines "best" differently and may identify different models as "best". | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably? | "Interchangeably" is too strong a word. All of them are criteria that seek to compare models and find a "best" model, but each defines "best" differently and may identify different models as "best". | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably?
"Interchangeably" is too strong a word. All of them are criteria that seek to compare models and find a "best" model, but each defines "best" differently and may identify different models as "best". | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably?
"Interchangeably" is too strong a word. All of them are criteria that seek to compare models and find a "best" model, but each defines "best" differently and may identify different models as "best". |
5,218 | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably? | “Propose a referendum”. Just to vote! ;-)
I liked the CAIC (Bozdogan, 1987) and BIC purely from my personal practice, because these criteria gives a serious penalty for complexity, we got more parsimony, but I always displayed the list of good models - to delta 4-6-8 (instead of 2). In step of investigating parameters ... | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably? | “Propose a referendum”. Just to vote! ;-)
I liked the CAIC (Bozdogan, 1987) and BIC purely from my personal practice, because these criteria gives a serious penalty for complexity, we got more parsimo | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably?
“Propose a referendum”. Just to vote! ;-)
I liked the CAIC (Bozdogan, 1987) and BIC purely from my personal practice, because these criteria gives a serious penalty for complexity, we got more parsimony, but I always displayed the list of good mode... | AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC --- Can I use them interchangeably?
“Propose a referendum”. Just to vote! ;-)
I liked the CAIC (Bozdogan, 1987) and BIC purely from my personal practice, because these criteria gives a serious penalty for complexity, we got more parsimo |
5,219 | Are splines overfitting the data? | Overfitting comes from allowing too large a class of models. This gets a bit tricky with models with continuous parameters (like splines and polynomials), but if you discretize the parameters into some number of distinct values, you'll see that increasing the number of knots/coefficients will increase the number of ava... | Are splines overfitting the data? | Overfitting comes from allowing too large a class of models. This gets a bit tricky with models with continuous parameters (like splines and polynomials), but if you discretize the parameters into som | Are splines overfitting the data?
Overfitting comes from allowing too large a class of models. This gets a bit tricky with models with continuous parameters (like splines and polynomials), but if you discretize the parameters into some number of distinct values, you'll see that increasing the number of knots/coefficien... | Are splines overfitting the data?
Overfitting comes from allowing too large a class of models. This gets a bit tricky with models with continuous parameters (like splines and polynomials), but if you discretize the parameters into som |
5,220 | Are splines overfitting the data? | Statisticians have been arguing about polynomial fitting for ages, and in my experience, it comes down to this:
Splines are basically a series of different equations pieced together, which tends to increase the accuracy of interpolated values at the cost of the ability to project outside the data range. This is fine i... | Are splines overfitting the data? | Statisticians have been arguing about polynomial fitting for ages, and in my experience, it comes down to this:
Splines are basically a series of different equations pieced together, which tends to in | Are splines overfitting the data?
Statisticians have been arguing about polynomial fitting for ages, and in my experience, it comes down to this:
Splines are basically a series of different equations pieced together, which tends to increase the accuracy of interpolated values at the cost of the ability to project outsi... | Are splines overfitting the data?
Statisticians have been arguing about polynomial fitting for ages, and in my experience, it comes down to this:
Splines are basically a series of different equations pieced together, which tends to in |
5,221 | Are splines overfitting the data? | choice between splines and polinomial interpolation (either Newton or Lagrange - deterministic ones) stops at really huge data - splines are more flexible ("using many polynomials in a piece-wise function rather than defining one overall polynomial")...
And the problem of overfitting is really the problem of another ca... | Are splines overfitting the data? | choice between splines and polinomial interpolation (either Newton or Lagrange - deterministic ones) stops at really huge data - splines are more flexible ("using many polynomials in a piece-wise func | Are splines overfitting the data?
choice between splines and polinomial interpolation (either Newton or Lagrange - deterministic ones) stops at really huge data - splines are more flexible ("using many polynomials in a piece-wise function rather than defining one overall polynomial")...
And the problem of overfitting i... | Are splines overfitting the data?
choice between splines and polinomial interpolation (either Newton or Lagrange - deterministic ones) stops at really huge data - splines are more flexible ("using many polynomials in a piece-wise func |
5,222 | Is it possible to interpret the bootstrap from a Bayesian perspective? | Section 8.4 of The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is "Relationship Between the Bootstrap and Bayesian Inference." That might be just what you are looking for. I believe that this book is freely available through a Stanford website, although I don't have the link on hand.
Edit:
Here... | Is it possible to interpret the bootstrap from a Bayesian perspective? | Section 8.4 of The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is "Relationship Between the Bootstrap and Bayesian Inference." That might be just what you are looking for. I b | Is it possible to interpret the bootstrap from a Bayesian perspective?
Section 8.4 of The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is "Relationship Between the Bootstrap and Bayesian Inference." That might be just what you are looking for. I believe that this book is freely available through... | Is it possible to interpret the bootstrap from a Bayesian perspective?
Section 8.4 of The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is "Relationship Between the Bootstrap and Bayesian Inference." That might be just what you are looking for. I b |
5,223 | Is it possible to interpret the bootstrap from a Bayesian perspective? | This is the latest paper I've seen on the subject:
@article{efr13bay,
author={Efron, Bradley},
title={Bayesian inference and the parametric bootstrap},
journal={Annals of Applied Statistics},
volume=6,
number=4,
pages={1971-1997},
year=2012,
doi={10.1214/12-AOAS571},
abstract={Summary: The parametric bootstrap can be u... | Is it possible to interpret the bootstrap from a Bayesian perspective? | This is the latest paper I've seen on the subject:
@article{efr13bay,
author={Efron, Bradley},
title={Bayesian inference and the parametric bootstrap},
journal={Annals of Applied Statistics},
volume=6 | Is it possible to interpret the bootstrap from a Bayesian perspective?
This is the latest paper I've seen on the subject:
@article{efr13bay,
author={Efron, Bradley},
title={Bayesian inference and the parametric bootstrap},
journal={Annals of Applied Statistics},
volume=6,
number=4,
pages={1971-1997},
year=2012,
doi={10... | Is it possible to interpret the bootstrap from a Bayesian perspective?
This is the latest paper I've seen on the subject:
@article{efr13bay,
author={Efron, Bradley},
title={Bayesian inference and the parametric bootstrap},
journal={Annals of Applied Statistics},
volume=6 |
5,224 | Is it possible to interpret the bootstrap from a Bayesian perspective? | I too was seduced by both bootstrapping and Bayes' theorem, but I couldn't make much sense of the justifications of bootstrapping until I looked at it from a Bayesian perspective. Then - as I explain below - the bootstrap distribution can be seen as a Bayesian posterior distribution, which makes the (a?) rationale behi... | Is it possible to interpret the bootstrap from a Bayesian perspective? | I too was seduced by both bootstrapping and Bayes' theorem, but I couldn't make much sense of the justifications of bootstrapping until I looked at it from a Bayesian perspective. Then - as I explain | Is it possible to interpret the bootstrap from a Bayesian perspective?
I too was seduced by both bootstrapping and Bayes' theorem, but I couldn't make much sense of the justifications of bootstrapping until I looked at it from a Bayesian perspective. Then - as I explain below - the bootstrap distribution can be seen as... | Is it possible to interpret the bootstrap from a Bayesian perspective?
I too was seduced by both bootstrapping and Bayes' theorem, but I couldn't make much sense of the justifications of bootstrapping until I looked at it from a Bayesian perspective. Then - as I explain |
5,225 | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP) | Short answer is: YES. Average Precision is a single number used to summarise a Precision-Recall curve:
You can approximate the integral (area under the curve) with:
Please take a look at this link for a good explanation. | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP) | Short answer is: YES. Average Precision is a single number used to summarise a Precision-Recall curve:
You can approximate the integral (area under the curve) with:
Please take a look at this link f | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP)
Short answer is: YES. Average Precision is a single number used to summarise a Precision-Recall curve:
You can approximate the integral (area under the curve) with:
Please take a look at this link for a good explanation. | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP)
Short answer is: YES. Average Precision is a single number used to summarise a Precision-Recall curve:
You can approximate the integral (area under the curve) with:
Please take a look at this link f |
5,226 | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP) | average_precision_score function expect confidence or probability as second parameter.
so you should use it as below,
average_precision_score(y_test, clf.predict_proba(X_test)[:,1])
and then it's same result of auc function. | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP) | average_precision_score function expect confidence or probability as second parameter.
so you should use it as below,
average_precision_score(y_test, clf.predict_proba(X_test)[:,1])
and then it's sam | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP)
average_precision_score function expect confidence or probability as second parameter.
so you should use it as below,
average_precision_score(y_test, clf.predict_proba(X_test)[:,1])
and then it's same result of auc function. | Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP)
average_precision_score function expect confidence or probability as second parameter.
so you should use it as below,
average_precision_score(y_test, clf.predict_proba(X_test)[:,1])
and then it's sam |
5,227 | How are kernels applied to feature maps to produce other feature maps? | The kernels are 3-dimensional, where width and height can be chosen, while the depth is equal to the number of maps in the input layer - in general.
They are certainly not 2-dimensional and replicated across the input feature maps at the same 2D location! That would mean a kernel wouldn't be able to distinguish betwee... | How are kernels applied to feature maps to produce other feature maps? | The kernels are 3-dimensional, where width and height can be chosen, while the depth is equal to the number of maps in the input layer - in general.
They are certainly not 2-dimensional and replicate | How are kernels applied to feature maps to produce other feature maps?
The kernels are 3-dimensional, where width and height can be chosen, while the depth is equal to the number of maps in the input layer - in general.
They are certainly not 2-dimensional and replicated across the input feature maps at the same 2D lo... | How are kernels applied to feature maps to produce other feature maps?
The kernels are 3-dimensional, where width and height can be chosen, while the depth is equal to the number of maps in the input layer - in general.
They are certainly not 2-dimensional and replicate |
5,228 | How are kernels applied to feature maps to produce other feature maps? | There is not a one-to-one correspondence between layers and kernels necessarily. That depends on the particular architecture. The figure you posted suggests that in the S2 layers you have 6 feature maps, each combining all feature maps of the previous layers, i.e. different possible combinations of the features.
Withou... | How are kernels applied to feature maps to produce other feature maps? | There is not a one-to-one correspondence between layers and kernels necessarily. That depends on the particular architecture. The figure you posted suggests that in the S2 layers you have 6 feature ma | How are kernels applied to feature maps to produce other feature maps?
There is not a one-to-one correspondence between layers and kernels necessarily. That depends on the particular architecture. The figure you posted suggests that in the S2 layers you have 6 feature maps, each combining all feature maps of the previo... | How are kernels applied to feature maps to produce other feature maps?
There is not a one-to-one correspondence between layers and kernels necessarily. That depends on the particular architecture. The figure you posted suggests that in the S2 layers you have 6 feature ma |
5,229 | How are kernels applied to feature maps to produce other feature maps? | Table 1 and Section 2a of Yann LeCun's "Gradient Based Learning Applied to Document Recognition" explains this well: http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf Not all regions of the 5x5 convolution are used to generate the 2nd convolutional layer. | How are kernels applied to feature maps to produce other feature maps? | Table 1 and Section 2a of Yann LeCun's "Gradient Based Learning Applied to Document Recognition" explains this well: http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf Not all regions of the 5x5 con | How are kernels applied to feature maps to produce other feature maps?
Table 1 and Section 2a of Yann LeCun's "Gradient Based Learning Applied to Document Recognition" explains this well: http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf Not all regions of the 5x5 convolution are used to generate the 2nd convolution... | How are kernels applied to feature maps to produce other feature maps?
Table 1 and Section 2a of Yann LeCun's "Gradient Based Learning Applied to Document Recognition" explains this well: http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf Not all regions of the 5x5 con |
5,230 | How are kernels applied to feature maps to produce other feature maps? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
This article can be helpful: Understanding Convolution... | How are kernels applied to feature maps to produce other feature maps? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How are kernels applied to feature maps to produce other feature maps?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | How are kernels applied to feature maps to produce other feature maps?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
5,231 | Normality of dependent variable = normality of residuals? | One point that may help your understanding:
If $x$ is normally distributed and $a$ and $b$ are constants, then $y=\frac{x-a}{b}$ is also normally distributed (but with a possibly different mean and variance).
Since the residuals are just the y values minus the estimated mean (standardized residuals are also divided by ... | Normality of dependent variable = normality of residuals? | One point that may help your understanding:
If $x$ is normally distributed and $a$ and $b$ are constants, then $y=\frac{x-a}{b}$ is also normally distributed (but with a possibly different mean and va | Normality of dependent variable = normality of residuals?
One point that may help your understanding:
If $x$ is normally distributed and $a$ and $b$ are constants, then $y=\frac{x-a}{b}$ is also normally distributed (but with a possibly different mean and variance).
Since the residuals are just the y values minus the e... | Normality of dependent variable = normality of residuals?
One point that may help your understanding:
If $x$ is normally distributed and $a$ and $b$ are constants, then $y=\frac{x-a}{b}$ is also normally distributed (but with a possibly different mean and va |
5,232 | Normality of dependent variable = normality of residuals? | The short answers:
residuals
no
depends, both approaches have advantages and disadvantages
why not? It may make more sense to compare medians instead of means.
from what you have told us, the normality assumption is probably violated
The longer answer:
The assumption is that the dependent variable (y) is normally dis... | Normality of dependent variable = normality of residuals? | The short answers:
residuals
no
depends, both approaches have advantages and disadvantages
why not? It may make more sense to compare medians instead of means.
from what you have told us, the normali | Normality of dependent variable = normality of residuals?
The short answers:
residuals
no
depends, both approaches have advantages and disadvantages
why not? It may make more sense to compare medians instead of means.
from what you have told us, the normality assumption is probably violated
The longer answer:
The ass... | Normality of dependent variable = normality of residuals?
The short answers:
residuals
no
depends, both approaches have advantages and disadvantages
why not? It may make more sense to compare medians instead of means.
from what you have told us, the normali |
5,233 | Normality of dependent variable = normality of residuals? | By definition of assumptions, the random variable $Y$ is a linear combination of $X$ and the residuals, all other things being constant.
If $X$ is not stochastic, and the error terms are normal, then $Y$ is normal and so are the residuals.
Question 1)
The assumptions refers to two things. First, to the normality of the... | Normality of dependent variable = normality of residuals? | By definition of assumptions, the random variable $Y$ is a linear combination of $X$ and the residuals, all other things being constant.
If $X$ is not stochastic, and the error terms are normal, then | Normality of dependent variable = normality of residuals?
By definition of assumptions, the random variable $Y$ is a linear combination of $X$ and the residuals, all other things being constant.
If $X$ is not stochastic, and the error terms are normal, then $Y$ is normal and so are the residuals.
Question 1)
The assump... | Normality of dependent variable = normality of residuals?
By definition of assumptions, the random variable $Y$ is a linear combination of $X$ and the residuals, all other things being constant.
If $X$ is not stochastic, and the error terms are normal, then |
5,234 | Normality of dependent variable = normality of residuals? | A clarification on Question 3: Normality of the residuals definitely does not imply normality within groups. The marginal distribution of residuals can be normal while the conditionals are not. This is true because a mixture of non-normal distributions can possibly be normal; see https://stats.stackexchange.com/a/486... | Normality of dependent variable = normality of residuals? | A clarification on Question 3: Normality of the residuals definitely does not imply normality within groups. The marginal distribution of residuals can be normal while the conditionals are not. This | Normality of dependent variable = normality of residuals?
A clarification on Question 3: Normality of the residuals definitely does not imply normality within groups. The marginal distribution of residuals can be normal while the conditionals are not. This is true because a mixture of non-normal distributions can pos... | Normality of dependent variable = normality of residuals?
A clarification on Question 3: Normality of the residuals definitely does not imply normality within groups. The marginal distribution of residuals can be normal while the conditionals are not. This |
5,235 | Normality of dependent variable = normality of residuals? | The assumptions refers to two things. First, to the normality of the error terms. Second, to the linearity and completeness of the model. Both things are necessary for inference. But if these assumptions are met, then both the residuals e and Y are normally distributed and the solution can be calculated quite easily, b... | Normality of dependent variable = normality of residuals? | The assumptions refers to two things. First, to the normality of the error terms. Second, to the linearity and completeness of the model. Both things are necessary for inference. But if these assumpti | Normality of dependent variable = normality of residuals?
The assumptions refers to two things. First, to the normality of the error terms. Second, to the linearity and completeness of the model. Both things are necessary for inference. But if these assumptions are met, then both the residuals e and Y are normally dist... | Normality of dependent variable = normality of residuals?
The assumptions refers to two things. First, to the normality of the error terms. Second, to the linearity and completeness of the model. Both things are necessary for inference. But if these assumpti |
5,236 | Can machine learning decode the SHA256 hashes? | This isn't really a stats answer, but:
No, you can't determine the first character of the plaintext from the hash, because there's no such thing as "the plaintext" for a given hash.
SHA-256 is a hashing algorithm. No matter what your plaintext, you get out a 32-byte signature, often expressed as a 64-character hex stri... | Can machine learning decode the SHA256 hashes? | This isn't really a stats answer, but:
No, you can't determine the first character of the plaintext from the hash, because there's no such thing as "the plaintext" for a given hash.
SHA-256 is a hashi | Can machine learning decode the SHA256 hashes?
This isn't really a stats answer, but:
No, you can't determine the first character of the plaintext from the hash, because there's no such thing as "the plaintext" for a given hash.
SHA-256 is a hashing algorithm. No matter what your plaintext, you get out a 32-byte signat... | Can machine learning decode the SHA256 hashes?
This isn't really a stats answer, but:
No, you can't determine the first character of the plaintext from the hash, because there's no such thing as "the plaintext" for a given hash.
SHA-256 is a hashi |
5,237 | Can machine learning decode the SHA256 hashes? | SHA256 is designed to be as random as possible, so it is unlikely you would be able to separate hashes that came from 1-prefixed plaintext from those that do not; there should simply be no feature of the hash string that would give that information away. | Can machine learning decode the SHA256 hashes? | SHA256 is designed to be as random as possible, so it is unlikely you would be able to separate hashes that came from 1-prefixed plaintext from those that do not; there should simply be no feature of | Can machine learning decode the SHA256 hashes?
SHA256 is designed to be as random as possible, so it is unlikely you would be able to separate hashes that came from 1-prefixed plaintext from those that do not; there should simply be no feature of the hash string that would give that information away. | Can machine learning decode the SHA256 hashes?
SHA256 is designed to be as random as possible, so it is unlikely you would be able to separate hashes that came from 1-prefixed plaintext from those that do not; there should simply be no feature of |
5,238 | Can machine learning decode the SHA256 hashes? | Regardless if this is "Possible", what algorithm would be the best approach?
Sorry, but that's a nonsensical question. If something is impossible, then you can't search for the best approach to the problem.
In this case, this definitely should be impossible because hashing is a one-way function: several inputs (infinit... | Can machine learning decode the SHA256 hashes? | Regardless if this is "Possible", what algorithm would be the best approach?
Sorry, but that's a nonsensical question. If something is impossible, then you can't search for the best approach to the pr | Can machine learning decode the SHA256 hashes?
Regardless if this is "Possible", what algorithm would be the best approach?
Sorry, but that's a nonsensical question. If something is impossible, then you can't search for the best approach to the problem.
In this case, this definitely should be impossible because hashing... | Can machine learning decode the SHA256 hashes?
Regardless if this is "Possible", what algorithm would be the best approach?
Sorry, but that's a nonsensical question. If something is impossible, then you can't search for the best approach to the pr |
5,239 | Can machine learning decode the SHA256 hashes? | While one can't prove a negative with an example.
Still I feel an example would be suggestive; and perhaps useful.
And it does show how one would (attempt to) solve similar problems.
In the case of
I want to make binary predictions, using features that are binary vectors,
a Random Forest is a solid choice.
I guess t... | Can machine learning decode the SHA256 hashes? | While one can't prove a negative with an example.
Still I feel an example would be suggestive; and perhaps useful.
And it does show how one would (attempt to) solve similar problems.
In the case of | Can machine learning decode the SHA256 hashes?
While one can't prove a negative with an example.
Still I feel an example would be suggestive; and perhaps useful.
And it does show how one would (attempt to) solve similar problems.
In the case of
I want to make binary predictions, using features that are binary vector... | Can machine learning decode the SHA256 hashes?
While one can't prove a negative with an example.
Still I feel an example would be suggestive; and perhaps useful.
And it does show how one would (attempt to) solve similar problems.
In the case of |
5,240 | Can machine learning decode the SHA256 hashes? | Hash functions are (by design) extremely badly suited for doing anything machine learning with them.
ML is essentially a family of methods for modelling / estimating locally continuous functions. I.e., you're trying to describe some physical system that, while it may have certain discontinuities, is in some sense in mo... | Can machine learning decode the SHA256 hashes? | Hash functions are (by design) extremely badly suited for doing anything machine learning with them.
ML is essentially a family of methods for modelling / estimating locally continuous functions. I.e. | Can machine learning decode the SHA256 hashes?
Hash functions are (by design) extremely badly suited for doing anything machine learning with them.
ML is essentially a family of methods for modelling / estimating locally continuous functions. I.e., you're trying to describe some physical system that, while it may have ... | Can machine learning decode the SHA256 hashes?
Hash functions are (by design) extremely badly suited for doing anything machine learning with them.
ML is essentially a family of methods for modelling / estimating locally continuous functions. I.e. |
5,241 | Can machine learning decode the SHA256 hashes? | This is an interesting question because it raises issues about what counts as "machine learning." There is certainly an algorithm that will eventually solve this problem if it can be solved. It goes like this:
Pick your favorite programming language, and decide on an encoding that maps every string to a (potentially v... | Can machine learning decode the SHA256 hashes? | This is an interesting question because it raises issues about what counts as "machine learning." There is certainly an algorithm that will eventually solve this problem if it can be solved. It goes l | Can machine learning decode the SHA256 hashes?
This is an interesting question because it raises issues about what counts as "machine learning." There is certainly an algorithm that will eventually solve this problem if it can be solved. It goes like this:
Pick your favorite programming language, and decide on an enco... | Can machine learning decode the SHA256 hashes?
This is an interesting question because it raises issues about what counts as "machine learning." There is certainly an algorithm that will eventually solve this problem if it can be solved. It goes l |
5,242 | Can machine learning decode the SHA256 hashes? | It is next to impossible. However, people observed some patterns in SHA256 which might suggest its non-randomness A distinguisher for SHA256 using Bitcoin (mining faster along the way). Their tldr:
"To distinguish between an ideal random permutation hash and SHA256, hash a large amount (~2^80) of candidate 1024 bit blo... | Can machine learning decode the SHA256 hashes? | It is next to impossible. However, people observed some patterns in SHA256 which might suggest its non-randomness A distinguisher for SHA256 using Bitcoin (mining faster along the way). Their tldr:
"T | Can machine learning decode the SHA256 hashes?
It is next to impossible. However, people observed some patterns in SHA256 which might suggest its non-randomness A distinguisher for SHA256 using Bitcoin (mining faster along the way). Their tldr:
"To distinguish between an ideal random permutation hash and SHA256, hash a... | Can machine learning decode the SHA256 hashes?
It is next to impossible. However, people observed some patterns in SHA256 which might suggest its non-randomness A distinguisher for SHA256 using Bitcoin (mining faster along the way). Their tldr:
"T |
5,243 | Can machine learning decode the SHA256 hashes? | I'll answer with a program. To reduce computational requirements I'll use a variant of sha256 I call sha16, which is just the first 16 bits of sha256.
#!/usr/bin/python3
import hashlib
from itertools import count
def sha16(plaintext):
h = hashlib.sha256()
h.update(plaintext)
return h.hexdigest()[:4]
def ... | Can machine learning decode the SHA256 hashes? | I'll answer with a program. To reduce computational requirements I'll use a variant of sha256 I call sha16, which is just the first 16 bits of sha256.
#!/usr/bin/python3
import hashlib
from itertools | Can machine learning decode the SHA256 hashes?
I'll answer with a program. To reduce computational requirements I'll use a variant of sha256 I call sha16, which is just the first 16 bits of sha256.
#!/usr/bin/python3
import hashlib
from itertools import count
def sha16(plaintext):
h = hashlib.sha256()
h.updat... | Can machine learning decode the SHA256 hashes?
I'll answer with a program. To reduce computational requirements I'll use a variant of sha256 I call sha16, which is just the first 16 bits of sha256.
#!/usr/bin/python3
import hashlib
from itertools |
5,244 | Can machine learning decode the SHA256 hashes? | What you describe is basically a pre-image attack. You're trying to find an input such that, when it is hashed, the output has some property like "a leading 1".*
It is an explicit goal of cryptographic hashes to prevent such pre-image attacks. If you can make such an attack, we tend to consider that algorithm to be i... | Can machine learning decode the SHA256 hashes? | What you describe is basically a pre-image attack. You're trying to find an input such that, when it is hashed, the output has some property like "a leading 1".*
It is an explicit goal of cryptograph | Can machine learning decode the SHA256 hashes?
What you describe is basically a pre-image attack. You're trying to find an input such that, when it is hashed, the output has some property like "a leading 1".*
It is an explicit goal of cryptographic hashes to prevent such pre-image attacks. If you can make such an att... | Can machine learning decode the SHA256 hashes?
What you describe is basically a pre-image attack. You're trying to find an input such that, when it is hashed, the output has some property like "a leading 1".*
It is an explicit goal of cryptograph |
5,245 | Can machine learning decode the SHA256 hashes? | Most all the answers here are telling you why you can't do this but here's the direct answer to:
Regardless if this is "Possible", what algorithm would be the best approach?
Assuming the input is sufficiently large:
Take the count of the set of valid characters.
Take the reciprocal of the number from step 1.
That's... | Can machine learning decode the SHA256 hashes? | Most all the answers here are telling you why you can't do this but here's the direct answer to:
Regardless if this is "Possible", what algorithm would be the best approach?
Assuming the input is su | Can machine learning decode the SHA256 hashes?
Most all the answers here are telling you why you can't do this but here's the direct answer to:
Regardless if this is "Possible", what algorithm would be the best approach?
Assuming the input is sufficiently large:
Take the count of the set of valid characters.
Take th... | Can machine learning decode the SHA256 hashes?
Most all the answers here are telling you why you can't do this but here's the direct answer to:
Regardless if this is "Possible", what algorithm would be the best approach?
Assuming the input is su |
5,246 | Can machine learning decode the SHA256 hashes? | Hashing functions are purposefully designed to be difficult to model, so (as pointed out already) this is likely to be very difficult. Nevertheless, any weakness in the hashing function will reduce its entropy, making it more predictable.
Regardless if this is "Possible", what algorithm would be the best approach?
A ... | Can machine learning decode the SHA256 hashes? | Hashing functions are purposefully designed to be difficult to model, so (as pointed out already) this is likely to be very difficult. Nevertheless, any weakness in the hashing function will reduce it | Can machine learning decode the SHA256 hashes?
Hashing functions are purposefully designed to be difficult to model, so (as pointed out already) this is likely to be very difficult. Nevertheless, any weakness in the hashing function will reduce its entropy, making it more predictable.
Regardless if this is "Possible",... | Can machine learning decode the SHA256 hashes?
Hashing functions are purposefully designed to be difficult to model, so (as pointed out already) this is likely to be very difficult. Nevertheless, any weakness in the hashing function will reduce it |
5,247 | Can machine learning decode the SHA256 hashes? | Lets say that your plaintext/input is exactly one block long (512bits=1block for SHA256). The input space for it is $2^{512}$ and hash space is $2^{256}$. For simplicity, lets take the first $2^{256}$ inputs into consideration.
Now you train a machine learning algorithm (Any algorithm of your choice), with a trainin... | Can machine learning decode the SHA256 hashes? | Lets say that your plaintext/input is exactly one block long (512bits=1block for SHA256). The input space for it is $2^{512}$ and hash space is $2^{256}$. For simplicity, lets take the first $2^{256}$ | Can machine learning decode the SHA256 hashes?
Lets say that your plaintext/input is exactly one block long (512bits=1block for SHA256). The input space for it is $2^{512}$ and hash space is $2^{256}$. For simplicity, lets take the first $2^{256}$ inputs into consideration.
Now you train a machine learning algorithm... | Can machine learning decode the SHA256 hashes?
Lets say that your plaintext/input is exactly one block long (512bits=1block for SHA256). The input space for it is $2^{512}$ and hash space is $2^{256}$. For simplicity, lets take the first $2^{256}$ |
5,248 | Can machine learning decode the SHA256 hashes? | The problem is that "machine learning" isn't intelligent. It just tries to find patterns. In SHA-256, there are no patterns. There is nothing to find. Machine learning hasn't got any chance that is better than brute force.
If you want to crack SHA-256 by computer, the only possibility is to create real intelligence, a... | Can machine learning decode the SHA256 hashes? | The problem is that "machine learning" isn't intelligent. It just tries to find patterns. In SHA-256, there are no patterns. There is nothing to find. Machine learning hasn't got any chance that is be | Can machine learning decode the SHA256 hashes?
The problem is that "machine learning" isn't intelligent. It just tries to find patterns. In SHA-256, there are no patterns. There is nothing to find. Machine learning hasn't got any chance that is better than brute force.
If you want to crack SHA-256 by computer, the onl... | Can machine learning decode the SHA256 hashes?
The problem is that "machine learning" isn't intelligent. It just tries to find patterns. In SHA-256, there are no patterns. There is nothing to find. Machine learning hasn't got any chance that is be |
5,249 | Expected number of ratio of girls vs boys birth | Start with no children
repeat step
{
Every couple who is still having children has a child. Half the couples have males and half the couples have females.
Those couples that have females stop having children
}
At each step you get an even number of males and females and the number of couples having children reduces by ... | Expected number of ratio of girls vs boys birth | Start with no children
repeat step
{
Every couple who is still having children has a child. Half the couples have males and half the couples have females.
Those couples that have females stop having c | Expected number of ratio of girls vs boys birth
Start with no children
repeat step
{
Every couple who is still having children has a child. Half the couples have males and half the couples have females.
Those couples that have females stop having children
}
At each step you get an even number of males and females and t... | Expected number of ratio of girls vs boys birth
Start with no children
repeat step
{
Every couple who is still having children has a child. Half the couples have males and half the couples have females.
Those couples that have females stop having c |
5,250 | Expected number of ratio of girls vs boys birth | Let $X$ be the number of boys in a family. As soon as they have a girl, they stop, so
\begin{array}{| l |l | }
\hline
X=0 & \text{if the first child was a girl}\\
X=1 & \text{if the first child was a boy and the second was a girl}\\
X=2 & \text{if the first two children were boys and the th... | Expected number of ratio of girls vs boys birth | Let $X$ be the number of boys in a family. As soon as they have a girl, they stop, so
\begin{array}{| l |l | }
\hline
X=0 & \text{if the first child was a girl}\\
X=1 & \te | Expected number of ratio of girls vs boys birth
Let $X$ be the number of boys in a family. As soon as they have a girl, they stop, so
\begin{array}{| l |l | }
\hline
X=0 & \text{if the first child was a girl}\\
X=1 & \text{if the first child was a boy and the second was a girl}\\
X=2 & \tex... | Expected number of ratio of girls vs boys birth
Let $X$ be the number of boys in a family. As soon as they have a girl, they stop, so
\begin{array}{| l |l | }
\hline
X=0 & \text{if the first child was a girl}\\
X=1 & \te |
5,251 | Expected number of ratio of girls vs boys birth | Summary
The simple model that all births independently have a 50% chance of being girls is unrealistic and, as it turns out, exceptional. As soon as we consider the consequences of variation in outcomes among the population, the answer is that the girl:boy ratio can be any value not exceeding 1:1. (In reality it like... | Expected number of ratio of girls vs boys birth | Summary
The simple model that all births independently have a 50% chance of being girls is unrealistic and, as it turns out, exceptional. As soon as we consider the consequences of variation in outco | Expected number of ratio of girls vs boys birth
Summary
The simple model that all births independently have a 50% chance of being girls is unrealistic and, as it turns out, exceptional. As soon as we consider the consequences of variation in outcomes among the population, the answer is that the girl:boy ratio can be a... | Expected number of ratio of girls vs boys birth
Summary
The simple model that all births independently have a 50% chance of being girls is unrealistic and, as it turns out, exceptional. As soon as we consider the consequences of variation in outco |
5,252 | Expected number of ratio of girls vs boys birth | The birth of each child is an independent event with P=0.5 for a boy and P=0.5 for a girl. The other details (such as the family decisions) only distract you from this fact. The answer, then, is that the ratio is 1:1.
To expound on this: imagine that instead of having children, you're flipping a fair coin (P(heads)=0.5... | Expected number of ratio of girls vs boys birth | The birth of each child is an independent event with P=0.5 for a boy and P=0.5 for a girl. The other details (such as the family decisions) only distract you from this fact. The answer, then, is that | Expected number of ratio of girls vs boys birth
The birth of each child is an independent event with P=0.5 for a boy and P=0.5 for a girl. The other details (such as the family decisions) only distract you from this fact. The answer, then, is that the ratio is 1:1.
To expound on this: imagine that instead of having chi... | Expected number of ratio of girls vs boys birth
The birth of each child is an independent event with P=0.5 for a boy and P=0.5 for a girl. The other details (such as the family decisions) only distract you from this fact. The answer, then, is that |
5,253 | Expected number of ratio of girls vs boys birth | Imagine tossing a fair coin until you observe a head. How many tails do you toss?
$P(0 \text{ tails}) = \frac{1}{2}, P(1 \text{ tail}) = (\frac{1}{2})^2, P(2 \text{ tails}) = (\frac{1}{2})^3, ...$
The expected number of tails is easily calculated* to be 1.
The number of heads is always 1.
* if this is not clear to you,... | Expected number of ratio of girls vs boys birth | Imagine tossing a fair coin until you observe a head. How many tails do you toss?
$P(0 \text{ tails}) = \frac{1}{2}, P(1 \text{ tail}) = (\frac{1}{2})^2, P(2 \text{ tails}) = (\frac{1}{2})^3, ...$
The | Expected number of ratio of girls vs boys birth
Imagine tossing a fair coin until you observe a head. How many tails do you toss?
$P(0 \text{ tails}) = \frac{1}{2}, P(1 \text{ tail}) = (\frac{1}{2})^2, P(2 \text{ tails}) = (\frac{1}{2})^3, ...$
The expected number of tails is easily calculated* to be 1.
The number of h... | Expected number of ratio of girls vs boys birth
Imagine tossing a fair coin until you observe a head. How many tails do you toss?
$P(0 \text{ tails}) = \frac{1}{2}, P(1 \text{ tail}) = (\frac{1}{2})^2, P(2 \text{ tails}) = (\frac{1}{2})^3, ...$
The |
5,254 | Expected number of ratio of girls vs boys birth | Couples with exactly one girl and no boys are the most common
The reason this all works out is because the probability of the one scenario in which there are more girls is much larger than the scenarios where there are more boys. And the scenarios where there are lots more boys have very low probabilities. The specific... | Expected number of ratio of girls vs boys birth | Couples with exactly one girl and no boys are the most common
The reason this all works out is because the probability of the one scenario in which there are more girls is much larger than the scenari | Expected number of ratio of girls vs boys birth
Couples with exactly one girl and no boys are the most common
The reason this all works out is because the probability of the one scenario in which there are more girls is much larger than the scenarios where there are more boys. And the scenarios where there are lots mor... | Expected number of ratio of girls vs boys birth
Couples with exactly one girl and no boys are the most common
The reason this all works out is because the probability of the one scenario in which there are more girls is much larger than the scenari |
5,255 | Expected number of ratio of girls vs boys birth | You can also use simulation:
p<-0
for (i in 1:10000){
a<-0
while(a != 1){ #Stops when having a girl
a<-as.numeric(rbinom(1, 1, 0.5)) #Simulation of a new birth with probability 0.5
p=p+1 #Number of births
}
}
(p-10000)/10000 #Ratio | Expected number of ratio of girls vs boys birth | You can also use simulation:
p<-0
for (i in 1:10000){
a<-0
while(a != 1){ #Stops when having a girl
a<-as.numeric(rbinom(1, 1, 0.5)) #Simulation of a new birth with probability 0.5
p=p | Expected number of ratio of girls vs boys birth
You can also use simulation:
p<-0
for (i in 1:10000){
a<-0
while(a != 1){ #Stops when having a girl
a<-as.numeric(rbinom(1, 1, 0.5)) #Simulation of a new birth with probability 0.5
p=p+1 #Number of births
}
}
(p-10000)/10000 #Ratio | Expected number of ratio of girls vs boys birth
You can also use simulation:
p<-0
for (i in 1:10000){
a<-0
while(a != 1){ #Stops when having a girl
a<-as.numeric(rbinom(1, 1, 0.5)) #Simulation of a new birth with probability 0.5
p=p |
5,256 | Expected number of ratio of girls vs boys birth | Mapping this out helped me better see how the ratio of the birth population (assumed to be 1:1) and the ratio of the population of children would both be 1:1.
While some families would have multiple boys but only one girl, which initially led me to think there would be more boys than girls, the number of those familie... | Expected number of ratio of girls vs boys birth | Mapping this out helped me better see how the ratio of the birth population (assumed to be 1:1) and the ratio of the population of children would both be 1:1.
While some families would have multiple | Expected number of ratio of girls vs boys birth
Mapping this out helped me better see how the ratio of the birth population (assumed to be 1:1) and the ratio of the population of children would both be 1:1.
While some families would have multiple boys but only one girl, which initially led me to think there would be m... | Expected number of ratio of girls vs boys birth
Mapping this out helped me better see how the ratio of the birth population (assumed to be 1:1) and the ratio of the population of children would both be 1:1.
While some families would have multiple |
5,257 | Expected number of ratio of girls vs boys birth | What you got was the simplest, and a correct answer. If the probability of a newborn child being a boy is p, and children of the wrong gender are not met by unfortunate accidents, then it doesn't matter if the parents make decisions about having more children based on the gender of the child. If the number of children ... | Expected number of ratio of girls vs boys birth | What you got was the simplest, and a correct answer. If the probability of a newborn child being a boy is p, and children of the wrong gender are not met by unfortunate accidents, then it doesn't matt | Expected number of ratio of girls vs boys birth
What you got was the simplest, and a correct answer. If the probability of a newborn child being a boy is p, and children of the wrong gender are not met by unfortunate accidents, then it doesn't matter if the parents make decisions about having more children based on the... | Expected number of ratio of girls vs boys birth
What you got was the simplest, and a correct answer. If the probability of a newborn child being a boy is p, and children of the wrong gender are not met by unfortunate accidents, then it doesn't matt |
5,258 | Expected number of ratio of girls vs boys birth | Let
$\text{$\Omega$={(G),(B,G),(B,B,G),$\dots$}}$
be the sample space and let
$\text{X: $\Omega\longrightarrow\mathbb{R}$; $\omega\mapsto\vert\omega\vert$-1}$
be the random variable that maps each outcome, $\omega$, onto the number of boys it involves. The expected value of boys, $\text{E(X)}$, comes then down to
$\t... | Expected number of ratio of girls vs boys birth | Let
$\text{$\Omega$={(G),(B,G),(B,B,G),$\dots$}}$
be the sample space and let
$\text{X: $\Omega\longrightarrow\mathbb{R}$; $\omega\mapsto\vert\omega\vert$-1}$
be the random variable that maps each out | Expected number of ratio of girls vs boys birth
Let
$\text{$\Omega$={(G),(B,G),(B,B,G),$\dots$}}$
be the sample space and let
$\text{X: $\Omega\longrightarrow\mathbb{R}$; $\omega\mapsto\vert\omega\vert$-1}$
be the random variable that maps each outcome, $\omega$, onto the number of boys it involves. The expected value ... | Expected number of ratio of girls vs boys birth
Let
$\text{$\Omega$={(G),(B,G),(B,B,G),$\dots$}}$
be the sample space and let
$\text{X: $\Omega\longrightarrow\mathbb{R}$; $\omega\mapsto\vert\omega\vert$-1}$
be the random variable that maps each out |
5,259 | Expected number of ratio of girls vs boys birth | It's a trick question. The ratio stays the same (1:1). The right answer is that it does not affect birth ratio, but it does affect the number of children per family with a limiting factor of an average of 2 births per family.
This is the kind of question you might find on a logic test. The answer is not about birth rat... | Expected number of ratio of girls vs boys birth | It's a trick question. The ratio stays the same (1:1). The right answer is that it does not affect birth ratio, but it does affect the number of children per family with a limiting factor of an averag | Expected number of ratio of girls vs boys birth
It's a trick question. The ratio stays the same (1:1). The right answer is that it does not affect birth ratio, but it does affect the number of children per family with a limiting factor of an average of 2 births per family.
This is the kind of question you might find on... | Expected number of ratio of girls vs boys birth
It's a trick question. The ratio stays the same (1:1). The right answer is that it does not affect birth ratio, but it does affect the number of children per family with a limiting factor of an averag |
5,260 | Expected number of ratio of girls vs boys birth | I am showing the code I wrote for a Monte Carlo simulation (500x1000 families) using `MATLAB' software. Please scrutinise the code so that I did not make a mistake.
The result is generated and plotted below. It shows the simulated girl birth probability has very good agreement with the underlying natural birth probabi... | Expected number of ratio of girls vs boys birth | I am showing the code I wrote for a Monte Carlo simulation (500x1000 families) using `MATLAB' software. Please scrutinise the code so that I did not make a mistake.
The result is generated and plotte | Expected number of ratio of girls vs boys birth
I am showing the code I wrote for a Monte Carlo simulation (500x1000 families) using `MATLAB' software. Please scrutinise the code so that I did not make a mistake.
The result is generated and plotted below. It shows the simulated girl birth probability has very good agr... | Expected number of ratio of girls vs boys birth
I am showing the code I wrote for a Monte Carlo simulation (500x1000 families) using `MATLAB' software. Please scrutinise the code so that I did not make a mistake.
The result is generated and plotte |
5,261 | Expected number of ratio of girls vs boys birth | Let the random variable denoting the $i^{th}$ child in the country be $X_i$ taking on values 1 and 0 if the child is a boy or girl respectively. Assume that the marginal probability that each birth is a boy or girl is $0.5$.
The expected number of boys in the country = $E[\sum_i X_i] = \sum_i E[X_i] = 0.5 n$ (where $n... | Expected number of ratio of girls vs boys birth | Let the random variable denoting the $i^{th}$ child in the country be $X_i$ taking on values 1 and 0 if the child is a boy or girl respectively. Assume that the marginal probability that each birth is | Expected number of ratio of girls vs boys birth
Let the random variable denoting the $i^{th}$ child in the country be $X_i$ taking on values 1 and 0 if the child is a boy or girl respectively. Assume that the marginal probability that each birth is a boy or girl is $0.5$.
The expected number of boys in the country = $... | Expected number of ratio of girls vs boys birth
Let the random variable denoting the $i^{th}$ child in the country be $X_i$ taking on values 1 and 0 if the child is a boy or girl respectively. Assume that the marginal probability that each birth is |
5,262 | Expected number of ratio of girls vs boys birth | I independently also programmed a simulation in matlab, prior to seeing what others have done. Strictly speaking it is not a MC because I only run the experiment once. But once is sufficient to obtain results. Here is what my simulation yields. I don't take a stand on the probability of births being p=0.5 as a primitiv... | Expected number of ratio of girls vs boys birth | I independently also programmed a simulation in matlab, prior to seeing what others have done. Strictly speaking it is not a MC because I only run the experiment once. But once is sufficient to obtain | Expected number of ratio of girls vs boys birth
I independently also programmed a simulation in matlab, prior to seeing what others have done. Strictly speaking it is not a MC because I only run the experiment once. But once is sufficient to obtain results. Here is what my simulation yields. I don't take a stand on the... | Expected number of ratio of girls vs boys birth
I independently also programmed a simulation in matlab, prior to seeing what others have done. Strictly speaking it is not a MC because I only run the experiment once. But once is sufficient to obtain |
5,263 | Expected number of ratio of girls vs boys birth | It depends on the number of families.
Let $X$ be the number of children in a family, it is geometric random variable with $p=0.5$, i.e.,
$$
P(X = x) = 0.5^x, x=1,2,3...
$$
which implies $E(X) = 2$
Suppose there are $N$ families in the country, the girl ratio is
$$
\frac{N}{ \sum X_i}
$$
Since $\sum X_i /N \rightarrow ... | Expected number of ratio of girls vs boys birth | It depends on the number of families.
Let $X$ be the number of children in a family, it is geometric random variable with $p=0.5$, i.e.,
$$
P(X = x) = 0.5^x, x=1,2,3...
$$
which implies $E(X) = 2$
Sup | Expected number of ratio of girls vs boys birth
It depends on the number of families.
Let $X$ be the number of children in a family, it is geometric random variable with $p=0.5$, i.e.,
$$
P(X = x) = 0.5^x, x=1,2,3...
$$
which implies $E(X) = 2$
Suppose there are $N$ families in the country, the girl ratio is
$$
\frac{... | Expected number of ratio of girls vs boys birth
It depends on the number of families.
Let $X$ be the number of children in a family, it is geometric random variable with $p=0.5$, i.e.,
$$
P(X = x) = 0.5^x, x=1,2,3...
$$
which implies $E(X) = 2$
Sup |
5,264 | Would a Bayesian admit that there is one fixed parameter value? | IMHO "yes"! Here is one of my favorite quotes by Greenland (2006: 767):
It is often said (incorrectly) that ‘parameters are treated as fixed
by the frequentist but as random by the Bayesian’. For frequentists
and Bayesians alike, the value of a parameter may have been fixed from
the start or may have been genera... | Would a Bayesian admit that there is one fixed parameter value? | IMHO "yes"! Here is one of my favorite quotes by Greenland (2006: 767):
It is often said (incorrectly) that ‘parameters are treated as fixed
by the frequentist but as random by the Bayesian’. For f | Would a Bayesian admit that there is one fixed parameter value?
IMHO "yes"! Here is one of my favorite quotes by Greenland (2006: 767):
It is often said (incorrectly) that ‘parameters are treated as fixed
by the frequentist but as random by the Bayesian’. For frequentists
and Bayesians alike, the value of a parame... | Would a Bayesian admit that there is one fixed parameter value?
IMHO "yes"! Here is one of my favorite quotes by Greenland (2006: 767):
It is often said (incorrectly) that ‘parameters are treated as fixed
by the frequentist but as random by the Bayesian’. For f |
5,265 | Would a Bayesian admit that there is one fixed parameter value? | The Bayesian conception of a probability is not necessarily subjective (c.f. Jaynes). The important distinction here is that the Bayesian attempts to determine his/her state of knowledge regarding the value of the parameter by combining a prior distribution for its plausible value with the likelihood which summarises ... | Would a Bayesian admit that there is one fixed parameter value? | The Bayesian conception of a probability is not necessarily subjective (c.f. Jaynes). The important distinction here is that the Bayesian attempts to determine his/her state of knowledge regarding th | Would a Bayesian admit that there is one fixed parameter value?
The Bayesian conception of a probability is not necessarily subjective (c.f. Jaynes). The important distinction here is that the Bayesian attempts to determine his/her state of knowledge regarding the value of the parameter by combining a prior distributi... | Would a Bayesian admit that there is one fixed parameter value?
The Bayesian conception of a probability is not necessarily subjective (c.f. Jaynes). The important distinction here is that the Bayesian attempts to determine his/her state of knowledge regarding th |
5,266 | Would a Bayesian admit that there is one fixed parameter value? | To your main point, in Bayesian Data Analysis (3rd ed., 93), Gelman also writes
From the perspective of Bayesian data analysis, we can often interpret classical point estimates as exact or approximate posterior summaries based on some implicit full probability model. In the limit of large sample size, in fact, we can ... | Would a Bayesian admit that there is one fixed parameter value? | To your main point, in Bayesian Data Analysis (3rd ed., 93), Gelman also writes
From the perspective of Bayesian data analysis, we can often interpret classical point estimates as exact or approximat | Would a Bayesian admit that there is one fixed parameter value?
To your main point, in Bayesian Data Analysis (3rd ed., 93), Gelman also writes
From the perspective of Bayesian data analysis, we can often interpret classical point estimates as exact or approximate posterior summaries based on some implicit full probab... | Would a Bayesian admit that there is one fixed parameter value?
To your main point, in Bayesian Data Analysis (3rd ed., 93), Gelman also writes
From the perspective of Bayesian data analysis, we can often interpret classical point estimates as exact or approximat |
5,267 | Would a Bayesian admit that there is one fixed parameter value? | Do you think that there is a single "true fixed parameter" for something like the contribution of milk drinking to a child's growth? Or for the decrease in a tumor's size based on the amount of chemical X you inject into a patient's body? Pick any model you're familiar with and ask yourself if you actually believe that... | Would a Bayesian admit that there is one fixed parameter value? | Do you think that there is a single "true fixed parameter" for something like the contribution of milk drinking to a child's growth? Or for the decrease in a tumor's size based on the amount of chemic | Would a Bayesian admit that there is one fixed parameter value?
Do you think that there is a single "true fixed parameter" for something like the contribution of milk drinking to a child's growth? Or for the decrease in a tumor's size based on the amount of chemical X you inject into a patient's body? Pick any model yo... | Would a Bayesian admit that there is one fixed parameter value?
Do you think that there is a single "true fixed parameter" for something like the contribution of milk drinking to a child's growth? Or for the decrease in a tumor's size based on the amount of chemic |
5,268 | Would a Bayesian admit that there is one fixed parameter value? | But do Bayesians theoretically acknowledge that there is one true
fixed parameter value out in the 'real world?'
In my opinion, the answer is yes. There is an unknown value $\theta_0$ of the parameter and the prior distribution describes our knowledge/uncertainty about it. In the Bayesian mathematical modelling, $\t... | Would a Bayesian admit that there is one fixed parameter value? | But do Bayesians theoretically acknowledge that there is one true
fixed parameter value out in the 'real world?'
In my opinion, the answer is yes. There is an unknown value $\theta_0$ of the parame | Would a Bayesian admit that there is one fixed parameter value?
But do Bayesians theoretically acknowledge that there is one true
fixed parameter value out in the 'real world?'
In my opinion, the answer is yes. There is an unknown value $\theta_0$ of the parameter and the prior distribution describes our knowledge/u... | Would a Bayesian admit that there is one fixed parameter value?
But do Bayesians theoretically acknowledge that there is one true
fixed parameter value out in the 'real world?'
In my opinion, the answer is yes. There is an unknown value $\theta_0$ of the parame |
5,269 | Would a Bayesian admit that there is one fixed parameter value? | If we go and couple Bayesianism with a deterministic universe (before you say anything with the word 'quantum' in it, humour me and recall that this is not physics.stackexchange) we get some interesting results.
Making our assumptions explicit:
We have a Bayesian agent being part of and observing a deterministic unive... | Would a Bayesian admit that there is one fixed parameter value? | If we go and couple Bayesianism with a deterministic universe (before you say anything with the word 'quantum' in it, humour me and recall that this is not physics.stackexchange) we get some interesti | Would a Bayesian admit that there is one fixed parameter value?
If we go and couple Bayesianism with a deterministic universe (before you say anything with the word 'quantum' in it, humour me and recall that this is not physics.stackexchange) we get some interesting results.
Making our assumptions explicit:
We have a ... | Would a Bayesian admit that there is one fixed parameter value?
If we go and couple Bayesianism with a deterministic universe (before you say anything with the word 'quantum' in it, humour me and recall that this is not physics.stackexchange) we get some interesti |
5,270 | Would a Bayesian admit that there is one fixed parameter value? | I am not sure it is a relevant question because it requires more definition than the math itself requires. Because the math itself does not require it, I am not sure asking which Bayesian interpretation is correct has a lot of meaning.
Imagine two parallel universes. They are identical in the sense that the sequence ... | Would a Bayesian admit that there is one fixed parameter value? | I am not sure it is a relevant question because it requires more definition than the math itself requires. Because the math itself does not require it, I am not sure asking which Bayesian interpretat | Would a Bayesian admit that there is one fixed parameter value?
I am not sure it is a relevant question because it requires more definition than the math itself requires. Because the math itself does not require it, I am not sure asking which Bayesian interpretation is correct has a lot of meaning.
Imagine two paralle... | Would a Bayesian admit that there is one fixed parameter value?
I am not sure it is a relevant question because it requires more definition than the math itself requires. Because the math itself does not require it, I am not sure asking which Bayesian interpretat |
5,271 | Would a Bayesian admit that there is one fixed parameter value? | There are improper priors, for example Jeffreys, which has a certain relation to Fishers Information matrix. Then it is not subjective. | Would a Bayesian admit that there is one fixed parameter value? | There are improper priors, for example Jeffreys, which has a certain relation to Fishers Information matrix. Then it is not subjective. | Would a Bayesian admit that there is one fixed parameter value?
There are improper priors, for example Jeffreys, which has a certain relation to Fishers Information matrix. Then it is not subjective. | Would a Bayesian admit that there is one fixed parameter value?
There are improper priors, for example Jeffreys, which has a certain relation to Fishers Information matrix. Then it is not subjective. |
5,272 | What are the cons of Bayesian analysis? | I'm going to give you an answer. Four drawbacks actually. Note that none of these are actually objections that should drive one all the way to frequentist analysis, but there are cons to going with a Bayesian framework:
Choice of prior. This is the usual carping for a reason, though in my case it's not the usual "prio... | What are the cons of Bayesian analysis? | I'm going to give you an answer. Four drawbacks actually. Note that none of these are actually objections that should drive one all the way to frequentist analysis, but there are cons to going with a | What are the cons of Bayesian analysis?
I'm going to give you an answer. Four drawbacks actually. Note that none of these are actually objections that should drive one all the way to frequentist analysis, but there are cons to going with a Bayesian framework:
Choice of prior. This is the usual carping for a reason, th... | What are the cons of Bayesian analysis?
I'm going to give you an answer. Four drawbacks actually. Note that none of these are actually objections that should drive one all the way to frequentist analysis, but there are cons to going with a |
5,273 | What are the cons of Bayesian analysis? | I am a Bayesian by inclination, but generally a frequentist in practice. The reason for this is usually that performing the full Bayesian analysis properly (rather than e.g. MAP solutions) for the types of problem I am interested in is tricky and computationally intensive. Often a full Bayesian analysis is required t... | What are the cons of Bayesian analysis? | I am a Bayesian by inclination, but generally a frequentist in practice. The reason for this is usually that performing the full Bayesian analysis properly (rather than e.g. MAP solutions) for the ty | What are the cons of Bayesian analysis?
I am a Bayesian by inclination, but generally a frequentist in practice. The reason for this is usually that performing the full Bayesian analysis properly (rather than e.g. MAP solutions) for the types of problem I am interested in is tricky and computationally intensive. Ofte... | What are the cons of Bayesian analysis?
I am a Bayesian by inclination, but generally a frequentist in practice. The reason for this is usually that performing the full Bayesian analysis properly (rather than e.g. MAP solutions) for the ty |
5,274 | What are the cons of Bayesian analysis? | From a purely practical point of view, I am not a fan of methods which require lots of computation (I am thinking of Gibbs sampler and MCMC, often used in the Bayesian framework, but this also applies to e.g. bootstrap techniques in frequentist analysis). The reason being that any kind of debugging (testing the impleme... | What are the cons of Bayesian analysis? | From a purely practical point of view, I am not a fan of methods which require lots of computation (I am thinking of Gibbs sampler and MCMC, often used in the Bayesian framework, but this also applies | What are the cons of Bayesian analysis?
From a purely practical point of view, I am not a fan of methods which require lots of computation (I am thinking of Gibbs sampler and MCMC, often used in the Bayesian framework, but this also applies to e.g. bootstrap techniques in frequentist analysis). The reason being that an... | What are the cons of Bayesian analysis?
From a purely practical point of view, I am not a fan of methods which require lots of computation (I am thinking of Gibbs sampler and MCMC, often used in the Bayesian framework, but this also applies |
5,275 | What are the cons of Bayesian analysis? | Sometimes there's a simple and natural "classical" solution to a problem, in which case a fancy Bayesian method (especially with MCMC) would be overkill.
Further, in variable selection type problems, it can be more straightforward and clear to consider something like a penalized likelihood; there may exist a prior on... | What are the cons of Bayesian analysis? | Sometimes there's a simple and natural "classical" solution to a problem, in which case a fancy Bayesian method (especially with MCMC) would be overkill.
Further, in variable selection type problems | What are the cons of Bayesian analysis?
Sometimes there's a simple and natural "classical" solution to a problem, in which case a fancy Bayesian method (especially with MCMC) would be overkill.
Further, in variable selection type problems, it can be more straightforward and clear to consider something like a penalize... | What are the cons of Bayesian analysis?
Sometimes there's a simple and natural "classical" solution to a problem, in which case a fancy Bayesian method (especially with MCMC) would be overkill.
Further, in variable selection type problems |
5,276 | What are the cons of Bayesian analysis? | I am relatively new to Bayesian methods, but one thing that that irks me is that, while I understand the rationale of priors (i.e. science is a cumulative endeavour, so for most questions there is some amount of previous experience/thinking that should inform your interpretation of the data), I dislike that the Bayesia... | What are the cons of Bayesian analysis? | I am relatively new to Bayesian methods, but one thing that that irks me is that, while I understand the rationale of priors (i.e. science is a cumulative endeavour, so for most questions there is som | What are the cons of Bayesian analysis?
I am relatively new to Bayesian methods, but one thing that that irks me is that, while I understand the rationale of priors (i.e. science is a cumulative endeavour, so for most questions there is some amount of previous experience/thinking that should inform your interpretation ... | What are the cons of Bayesian analysis?
I am relatively new to Bayesian methods, but one thing that that irks me is that, while I understand the rationale of priors (i.e. science is a cumulative endeavour, so for most questions there is som |
5,277 | What are the cons of Bayesian analysis? | Decision theory is the underlying theory on which statistics operates. The problem is to find a good (in some sense) procedure for producing decisions from data. However, there's rarely an unambiguous choice of procedure, in the sense of minimizing expected loss, so other criteria must be invoked to choose among them... | What are the cons of Bayesian analysis? | Decision theory is the underlying theory on which statistics operates. The problem is to find a good (in some sense) procedure for producing decisions from data. However, there's rarely an unambiguo | What are the cons of Bayesian analysis?
Decision theory is the underlying theory on which statistics operates. The problem is to find a good (in some sense) procedure for producing decisions from data. However, there's rarely an unambiguous choice of procedure, in the sense of minimizing expected loss, so other crite... | What are the cons of Bayesian analysis?
Decision theory is the underlying theory on which statistics operates. The problem is to find a good (in some sense) procedure for producing decisions from data. However, there's rarely an unambiguo |
5,278 | What are the cons of Bayesian analysis? | For some time I have wanted to educate myself more on Bayesian approaches to modeling to get past my cursory understanding (I have coded Gibbs samplers in graduate course work, but have never done anything real). Along the way though I have thought some of Brian Dennis' papers have been though-provoking and have wished... | What are the cons of Bayesian analysis? | For some time I have wanted to educate myself more on Bayesian approaches to modeling to get past my cursory understanding (I have coded Gibbs samplers in graduate course work, but have never done any | What are the cons of Bayesian analysis?
For some time I have wanted to educate myself more on Bayesian approaches to modeling to get past my cursory understanding (I have coded Gibbs samplers in graduate course work, but have never done anything real). Along the way though I have thought some of Brian Dennis' papers ha... | What are the cons of Bayesian analysis?
For some time I have wanted to educate myself more on Bayesian approaches to modeling to get past my cursory understanding (I have coded Gibbs samplers in graduate course work, but have never done any |
5,279 | What are the cons of Bayesian analysis? | What are the open problems in Bayesian Statistics from the ISBA quarterly newsletter list 5 problems with bayesian stats from various leaders in the field, #1 being, boringly enough, "Model selection and hypothesis testing". | What are the cons of Bayesian analysis? | What are the open problems in Bayesian Statistics from the ISBA quarterly newsletter list 5 problems with bayesian stats from various leaders in the field, #1 being, boringly enough, "Model selection | What are the cons of Bayesian analysis?
What are the open problems in Bayesian Statistics from the ISBA quarterly newsletter list 5 problems with bayesian stats from various leaders in the field, #1 being, boringly enough, "Model selection and hypothesis testing". | What are the cons of Bayesian analysis?
What are the open problems in Bayesian Statistics from the ISBA quarterly newsletter list 5 problems with bayesian stats from various leaders in the field, #1 being, boringly enough, "Model selection |
5,280 | Are CDFs more fundamental than PDFs? | Every probability distribution on (a subset of) $\mathbb R^n$ has a cumulative distribution function, and it uniquely defines the distribution. So, in this sense, the CDF is indeed as fundamental as the distribution itself.
A probability density function, however, exists only for (absolutely) continuous probability di... | Are CDFs more fundamental than PDFs? | Every probability distribution on (a subset of) $\mathbb R^n$ has a cumulative distribution function, and it uniquely defines the distribution. So, in this sense, the CDF is indeed as fundamental as | Are CDFs more fundamental than PDFs?
Every probability distribution on (a subset of) $\mathbb R^n$ has a cumulative distribution function, and it uniquely defines the distribution. So, in this sense, the CDF is indeed as fundamental as the distribution itself.
A probability density function, however, exists only for (... | Are CDFs more fundamental than PDFs?
Every probability distribution on (a subset of) $\mathbb R^n$ has a cumulative distribution function, and it uniquely defines the distribution. So, in this sense, the CDF is indeed as fundamental as |
5,281 | Are CDFs more fundamental than PDFs? | I believe your econometrics professor was thinking something along the following lines.
Consider the function $F$ with domiain $[0, 1]$ defined by
$$F(x) = \frac{1}{2}x \ \text{for} \ x < \frac{1}{2} $$
$$F(x) = \frac{1}{2}x + \frac{1}{2} \ \text{for} \ x \geq \frac{1}{2} $$
This is a discontinuous function, but a comp... | Are CDFs more fundamental than PDFs? | I believe your econometrics professor was thinking something along the following lines.
Consider the function $F$ with domiain $[0, 1]$ defined by
$$F(x) = \frac{1}{2}x \ \text{for} \ x < \frac{1}{2} | Are CDFs more fundamental than PDFs?
I believe your econometrics professor was thinking something along the following lines.
Consider the function $F$ with domiain $[0, 1]$ defined by
$$F(x) = \frac{1}{2}x \ \text{for} \ x < \frac{1}{2} $$
$$F(x) = \frac{1}{2}x + \frac{1}{2} \ \text{for} \ x \geq \frac{1}{2} $$
This is... | Are CDFs more fundamental than PDFs?
I believe your econometrics professor was thinking something along the following lines.
Consider the function $F$ with domiain $[0, 1]$ defined by
$$F(x) = \frac{1}{2}x \ \text{for} \ x < \frac{1}{2} |
5,282 | Are CDFs more fundamental than PDFs? | Ilmari gives a good answer from a theoretical perspective. However, one may also ask what purposes the density (pdf) and the distribution function (pdf) serve for practical computations. This could clarify for which situations one is more directly useful than the other.
For probability distributions on $\mathbb{R}$ the... | Are CDFs more fundamental than PDFs? | Ilmari gives a good answer from a theoretical perspective. However, one may also ask what purposes the density (pdf) and the distribution function (pdf) serve for practical computations. This could cl | Are CDFs more fundamental than PDFs?
Ilmari gives a good answer from a theoretical perspective. However, one may also ask what purposes the density (pdf) and the distribution function (pdf) serve for practical computations. This could clarify for which situations one is more directly useful than the other.
For probabil... | Are CDFs more fundamental than PDFs?
Ilmari gives a good answer from a theoretical perspective. However, one may also ask what purposes the density (pdf) and the distribution function (pdf) serve for practical computations. This could cl |
5,283 | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | The quoted passage is indeed incorrect. A correlation coefficient quantifies the degree of association throughout an entire population (or sample, in the case of the sample correlation coefficient). It does not divide the population into parts with one part showing an association and the other part not. It could be the... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | The quoted passage is indeed incorrect. A correlation coefficient quantifies the degree of association throughout an entire population (or sample, in the case of the sample correlation coefficient). I | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
The quoted passage is indeed incorrect. A correlation coefficient quantifies the degree of association throughout an entire population (or sample, in the case of the sample correlation coefficient). It does not divide the population into ... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
The quoted passage is indeed incorrect. A correlation coefficient quantifies the degree of association throughout an entire population (or sample, in the case of the sample correlation coefficient). I |
5,284 | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | No, 0.2 doesn't mean 1 in 5 people show correlation. I don't know how he could write this nonsense.
Here's the source of 0.2 number: "On the sources of the height–intelligence correlation: New insights from a bivariate ACE model with assortative mating", https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3044837/ Apparently... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | No, 0.2 doesn't mean 1 in 5 people show correlation. I don't know how he could write this nonsense.
Here's the source of 0.2 number: "On the sources of the height–intelligence correlation: New insigh | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
No, 0.2 doesn't mean 1 in 5 people show correlation. I don't know how he could write this nonsense.
Here's the source of 0.2 number: "On the sources of the height–intelligence correlation: New insights from a bivariate ACE model with ass... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
No, 0.2 doesn't mean 1 in 5 people show correlation. I don't know how he could write this nonsense.
Here's the source of 0.2 number: "On the sources of the height–intelligence correlation: New insigh |
5,285 | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | The irony in the statement is almost too thick to parse. Given the title of the text, I'm assuming some tongue-in-cheek was intended. However, your "gut" saying that this is wrong is probably on the right track, if intuition counts for anything. Unfortunately, a lot of scientific reporting eludes intuition when dealing... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | The irony in the statement is almost too thick to parse. Given the title of the text, I'm assuming some tongue-in-cheek was intended. However, your "gut" saying that this is wrong is probably on the r | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
The irony in the statement is almost too thick to parse. Given the title of the text, I'm assuming some tongue-in-cheek was intended. However, your "gut" saying that this is wrong is probably on the right track, if intuition counts for an... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
The irony in the statement is almost too thick to parse. Given the title of the text, I'm assuming some tongue-in-cheek was intended. However, your "gut" saying that this is wrong is probably on the r |
5,286 | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | It would be difficult to come up with an interpretation of this that is meaningful, let alone correct. Association is not a property of individual data points. If you had just the height and intelligence of one person, how could you possibly say whether height and intelligence are associated? I suppose if we had the me... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"? | It would be difficult to come up with an interpretation of this that is meaningful, let alone correct. Association is not a property of individual data points. If you had just the height and intellige | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
It would be difficult to come up with an interpretation of this that is meaningful, let alone correct. Association is not a property of individual data points. If you had just the height and intelligence of one person, how could you possi... | Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?
It would be difficult to come up with an interpretation of this that is meaningful, let alone correct. Association is not a property of individual data points. If you had just the height and intellige |
5,287 | What is residual standard error? | A fitted regression model uses the parameters to generate point estimate predictions which are the means of observed responses if you were to replicate the study with the same $X$ values an infinite number of times (and when the linear model is true). The difference between these predicted values and the ones used to f... | What is residual standard error? | A fitted regression model uses the parameters to generate point estimate predictions which are the means of observed responses if you were to replicate the study with the same $X$ values an infinite n | What is residual standard error?
A fitted regression model uses the parameters to generate point estimate predictions which are the means of observed responses if you were to replicate the study with the same $X$ values an infinite number of times (and when the linear model is true). The difference between these predic... | What is residual standard error?
A fitted regression model uses the parameters to generate point estimate predictions which are the means of observed responses if you were to replicate the study with the same $X$ values an infinite n |
5,288 | What is residual standard error? | Say we have the following ANOVA table (adapted from R's example(aov) command):
Df Sum Sq Mean Sq F value Pr(>F)
Model 1 37.0 37.00 0.483 0.525
Residuals 4 306.3 76.57
If you divide the sum of squares from any source of variation (model or residuals) by its respective degrees of... | What is residual standard error? | Say we have the following ANOVA table (adapted from R's example(aov) command):
Df Sum Sq Mean Sq F value Pr(>F)
Model 1 37.0 37.00 0.483 0.525
Residuals 4 306.3 76.57 | What is residual standard error?
Say we have the following ANOVA table (adapted from R's example(aov) command):
Df Sum Sq Mean Sq F value Pr(>F)
Model 1 37.0 37.00 0.483 0.525
Residuals 4 306.3 76.57
If you divide the sum of squares from any source of variation (model or residu... | What is residual standard error?
Say we have the following ANOVA table (adapted from R's example(aov) command):
Df Sum Sq Mean Sq F value Pr(>F)
Model 1 37.0 37.00 0.483 0.525
Residuals 4 306.3 76.57 |
5,289 | What is residual standard error? | Typically you will have a regression model looks like this:
$$
Y = \beta_{0} + \beta_{1}X + \epsilon
$$
where $ \epsilon $ is an error term independent of $ X $.
If $ \beta_{0} $ and $ \beta_{1} $ are known, we still cannot perfectly predict Y using X due to $ \epsilon $. Therefore, we use RSE as a judgement value o... | What is residual standard error? | Typically you will have a regression model looks like this:
$$
Y = \beta_{0} + \beta_{1}X + \epsilon
$$
where $ \epsilon $ is an error term independent of $ X $.
If $ \beta_{0} $ and $ \beta_{1} $ | What is residual standard error?
Typically you will have a regression model looks like this:
$$
Y = \beta_{0} + \beta_{1}X + \epsilon
$$
where $ \epsilon $ is an error term independent of $ X $.
If $ \beta_{0} $ and $ \beta_{1} $ are known, we still cannot perfectly predict Y using X due to $ \epsilon $. Therefore, ... | What is residual standard error?
Typically you will have a regression model looks like this:
$$
Y = \beta_{0} + \beta_{1}X + \epsilon
$$
where $ \epsilon $ is an error term independent of $ X $.
If $ \beta_{0} $ and $ \beta_{1} $ |
5,290 | What is residual standard error? | The residual standard error is $\sqrt{MSE}$. The $MSE$ is an unbiased estimator of $\sigma^2$, where $\sigma^2 = Var(y|x)$.
To make it more clear of the answer by @Silverfish and @Waldir Leoncio.
A summary of all definitions was shown below. Always got confused by these terms, put it here instead of making it as a comm... | What is residual standard error? | The residual standard error is $\sqrt{MSE}$. The $MSE$ is an unbiased estimator of $\sigma^2$, where $\sigma^2 = Var(y|x)$.
To make it more clear of the answer by @Silverfish and @Waldir Leoncio.
A su | What is residual standard error?
The residual standard error is $\sqrt{MSE}$. The $MSE$ is an unbiased estimator of $\sigma^2$, where $\sigma^2 = Var(y|x)$.
To make it more clear of the answer by @Silverfish and @Waldir Leoncio.
A summary of all definitions was shown below. Always got confused by these terms, put it he... | What is residual standard error?
The residual standard error is $\sqrt{MSE}$. The $MSE$ is an unbiased estimator of $\sigma^2$, where $\sigma^2 = Var(y|x)$.
To make it more clear of the answer by @Silverfish and @Waldir Leoncio.
A su |
5,291 | What is residual standard error? | As noted by @Amelio Vazquez-Reina and @little_monster, given a (simple linear) regression model:
$$
Y = \beta_0 + X \beta_1 + \epsilon
$$
where $\epsilon$ is a noise term with variance $\sigma^2$, i.e. $Var(\epsilon) = \sigma^2$, Residual Standard Error ($RSE$) is an estimate of $\sigma^2$ (the latter being usually unk... | What is residual standard error? | As noted by @Amelio Vazquez-Reina and @little_monster, given a (simple linear) regression model:
$$
Y = \beta_0 + X \beta_1 + \epsilon
$$
where $\epsilon$ is a noise term with variance $\sigma^2$, i.e | What is residual standard error?
As noted by @Amelio Vazquez-Reina and @little_monster, given a (simple linear) regression model:
$$
Y = \beta_0 + X \beta_1 + \epsilon
$$
where $\epsilon$ is a noise term with variance $\sigma^2$, i.e. $Var(\epsilon) = \sigma^2$, Residual Standard Error ($RSE$) is an estimate of $\sigma... | What is residual standard error?
As noted by @Amelio Vazquez-Reina and @little_monster, given a (simple linear) regression model:
$$
Y = \beta_0 + X \beta_1 + \epsilon
$$
where $\epsilon$ is a noise term with variance $\sigma^2$, i.e |
5,292 | What can we say about population mean from a sample size of 1? | Here is a brand-new article on this question for the Poisson case, taking a nice pedagogical approach:
Andersson. Per Gösta (2015). A Classroom Approach to the Construction of an Approximate Confidence Interval of a Poisson Mean Using One Observation. The American Statistician, 69(3), 160-164, DOI: 10.1080/00031305.201... | What can we say about population mean from a sample size of 1? | Here is a brand-new article on this question for the Poisson case, taking a nice pedagogical approach:
Andersson. Per Gösta (2015). A Classroom Approach to the Construction of an Approximate Confidenc | What can we say about population mean from a sample size of 1?
Here is a brand-new article on this question for the Poisson case, taking a nice pedagogical approach:
Andersson. Per Gösta (2015). A Classroom Approach to the Construction of an Approximate Confidence Interval of a Poisson Mean Using One Observation. The A... | What can we say about population mean from a sample size of 1?
Here is a brand-new article on this question for the Poisson case, taking a nice pedagogical approach:
Andersson. Per Gösta (2015). A Classroom Approach to the Construction of an Approximate Confidenc |
5,293 | What can we say about population mean from a sample size of 1? | If the population is known to be normal, a 95% confidence interval based on a single observation $x$ is given by $$x \pm 9.68 \left| x \right| $$
This is discussed in the article "An Effective Confidence Interval for the Mean With Samples of Size One and Two," by Wall, Boen, and Tweedie, The American Statistician, May ... | What can we say about population mean from a sample size of 1? | If the population is known to be normal, a 95% confidence interval based on a single observation $x$ is given by $$x \pm 9.68 \left| x \right| $$
This is discussed in the article "An Effective Confide | What can we say about population mean from a sample size of 1?
If the population is known to be normal, a 95% confidence interval based on a single observation $x$ is given by $$x \pm 9.68 \left| x \right| $$
This is discussed in the article "An Effective Confidence Interval for the Mean With Samples of Size One and Tw... | What can we say about population mean from a sample size of 1?
If the population is known to be normal, a 95% confidence interval based on a single observation $x$ is given by $$x \pm 9.68 \left| x \right| $$
This is discussed in the article "An Effective Confide |
5,294 | What can we say about population mean from a sample size of 1? | Sure there is. Use a Bayesian paradigm. Chances are you have at least some idea of what $\mu$ could possibly be - for instance, that it physically cannot be negative, or that it obviously cannot be larger than 100 (maybe you are measuring the height of your local high school football team members in feet). Put a prior ... | What can we say about population mean from a sample size of 1? | Sure there is. Use a Bayesian paradigm. Chances are you have at least some idea of what $\mu$ could possibly be - for instance, that it physically cannot be negative, or that it obviously cannot be la | What can we say about population mean from a sample size of 1?
Sure there is. Use a Bayesian paradigm. Chances are you have at least some idea of what $\mu$ could possibly be - for instance, that it physically cannot be negative, or that it obviously cannot be larger than 100 (maybe you are measuring the height of your... | What can we say about population mean from a sample size of 1?
Sure there is. Use a Bayesian paradigm. Chances are you have at least some idea of what $\mu$ could possibly be - for instance, that it physically cannot be negative, or that it obviously cannot be la |
5,295 | What can we say about population mean from a sample size of 1? | A small simulation exercise to illustrate whether the answer by @soakley works:
# Set the number of trials, M
M=10^6
# Set the true mean for each trial
mu=rep(0,M)
# Set the true standard deviation for each trial
sd=rep(1,M)
# Set counter to zero
count=0
for(i in 1:M){
# Control the random number generation so that th... | What can we say about population mean from a sample size of 1? | A small simulation exercise to illustrate whether the answer by @soakley works:
# Set the number of trials, M
M=10^6
# Set the true mean for each trial
mu=rep(0,M)
# Set the true standard deviation fo | What can we say about population mean from a sample size of 1?
A small simulation exercise to illustrate whether the answer by @soakley works:
# Set the number of trials, M
M=10^6
# Set the true mean for each trial
mu=rep(0,M)
# Set the true standard deviation for each trial
sd=rep(1,M)
# Set counter to zero
count=0
fo... | What can we say about population mean from a sample size of 1?
A small simulation exercise to illustrate whether the answer by @soakley works:
# Set the number of trials, M
M=10^6
# Set the true mean for each trial
mu=rep(0,M)
# Set the true standard deviation fo |
5,296 | What can we say about population mean from a sample size of 1? | See Edelman, D (1990) 'A confidence interval for the center of an unknown unimodal distribution based on a sample size one' The American Statistician, Vol 44, no 4.
Article covers the Normal and Nonparametric cases. | What can we say about population mean from a sample size of 1? | See Edelman, D (1990) 'A confidence interval for the center of an unknown unimodal distribution based on a sample size one' The American Statistician, Vol 44, no 4.
Article covers the Normal and Nonpa | What can we say about population mean from a sample size of 1?
See Edelman, D (1990) 'A confidence interval for the center of an unknown unimodal distribution based on a sample size one' The American Statistician, Vol 44, no 4.
Article covers the Normal and Nonparametric cases. | What can we say about population mean from a sample size of 1?
See Edelman, D (1990) 'A confidence interval for the center of an unknown unimodal distribution based on a sample size one' The American Statistician, Vol 44, no 4.
Article covers the Normal and Nonpa |
5,297 | What can we say about population mean from a sample size of 1? | Here is a simulation to demonstrate that @soakley's confidence interval works for a normally distributed random variable.
It takes $10^4$ values of $\mu$ in $[-10,10]$ and of $\sigma$ in $[0,10]$ and
for each of those pairs, it generates $10^6$ single observations $x$ and
sees what proportion of the corresponding con... | What can we say about population mean from a sample size of 1? | Here is a simulation to demonstrate that @soakley's confidence interval works for a normally distributed random variable.
It takes $10^4$ values of $\mu$ in $[-10,10]$ and of $\sigma$ in $[0,10]$ an | What can we say about population mean from a sample size of 1?
Here is a simulation to demonstrate that @soakley's confidence interval works for a normally distributed random variable.
It takes $10^4$ values of $\mu$ in $[-10,10]$ and of $\sigma$ in $[0,10]$ and
for each of those pairs, it generates $10^6$ single obs... | What can we say about population mean from a sample size of 1?
Here is a simulation to demonstrate that @soakley's confidence interval works for a normally distributed random variable.
It takes $10^4$ values of $\mu$ in $[-10,10]$ and of $\sigma$ in $[0,10]$ an |
5,298 | What is model identifiability? | For identifiability we are talking about a parameter $\theta$ (which could be a vector), which ranges over a parameter space $\Theta$, and a family of distributions (for simplicity, think PDFs) indexed by $\theta$ which we typically write something like $\{ f_{\theta}|\, \theta \in \Theta\}$. For instance, $\theta$ co... | What is model identifiability? | For identifiability we are talking about a parameter $\theta$ (which could be a vector), which ranges over a parameter space $\Theta$, and a family of distributions (for simplicity, think PDFs) indexe | What is model identifiability?
For identifiability we are talking about a parameter $\theta$ (which could be a vector), which ranges over a parameter space $\Theta$, and a family of distributions (for simplicity, think PDFs) indexed by $\theta$ which we typically write something like $\{ f_{\theta}|\, \theta \in \Theta... | What is model identifiability?
For identifiability we are talking about a parameter $\theta$ (which could be a vector), which ranges over a parameter space $\Theta$, and a family of distributions (for simplicity, think PDFs) indexe |
5,299 | What is model identifiability? | One way is to inspect the covariance matrix, $\Sigma$, of your parameter estimates. If two parameter estimates are perfectly (approximately) correlated with each other or one parameter estimate is a (approximately) linear combination of several others, then your model is not identified; the parameters that are function... | What is model identifiability? | One way is to inspect the covariance matrix, $\Sigma$, of your parameter estimates. If two parameter estimates are perfectly (approximately) correlated with each other or one parameter estimate is a ( | What is model identifiability?
One way is to inspect the covariance matrix, $\Sigma$, of your parameter estimates. If two parameter estimates are perfectly (approximately) correlated with each other or one parameter estimate is a (approximately) linear combination of several others, then your model is not identified; t... | What is model identifiability?
One way is to inspect the covariance matrix, $\Sigma$, of your parameter estimates. If two parameter estimates are perfectly (approximately) correlated with each other or one parameter estimate is a ( |
5,300 | What is the difference between errors and residuals? | Errors pertain to the true data generating process (DGP), whereas residuals are what is left over after having estimated your model. In truth, assumptions like normality, homoscedasticity, and independence apply to the errors of the DGP, not your model's residuals. (For example, having fit $p+1$ parameters in your mo... | What is the difference between errors and residuals? | Errors pertain to the true data generating process (DGP), whereas residuals are what is left over after having estimated your model. In truth, assumptions like normality, homoscedasticity, and indepe | What is the difference between errors and residuals?
Errors pertain to the true data generating process (DGP), whereas residuals are what is left over after having estimated your model. In truth, assumptions like normality, homoscedasticity, and independence apply to the errors of the DGP, not your model's residuals. ... | What is the difference between errors and residuals?
Errors pertain to the true data generating process (DGP), whereas residuals are what is left over after having estimated your model. In truth, assumptions like normality, homoscedasticity, and indepe |
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