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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5,301 | What is the difference between errors and residuals? | An error is the difference between the observed value and the true value (very often unobserved, generated by the DGP).
A residual is the difference between the observed value and the predicted value (by the model). | What is the difference between errors and residuals? | An error is the difference between the observed value and the true value (very often unobserved, generated by the DGP).
A residual is the difference between the observed value and the predicted value | What is the difference between errors and residuals?
An error is the difference between the observed value and the true value (very often unobserved, generated by the DGP).
A residual is the difference between the observed value and the predicted value (by the model). | What is the difference between errors and residuals?
An error is the difference between the observed value and the true value (very often unobserved, generated by the DGP).
A residual is the difference between the observed value and the predicted value |
5,302 | What is the difference between errors and residuals? | Error term is a theoretical concept that can never be observed, but the residual is a real world value that is calculated for each time a regression is done | What is the difference between errors and residuals? | Error term is a theoretical concept that can never be observed, but the residual is a real world value that is calculated for each time a regression is done | What is the difference between errors and residuals?
Error term is a theoretical concept that can never be observed, but the residual is a real world value that is calculated for each time a regression is done | What is the difference between errors and residuals?
Error term is a theoretical concept that can never be observed, but the residual is a real world value that is calculated for each time a regression is done |
5,303 | What is the difference between errors and residuals? | Error of the data set is the differences between the observed values and the true / unobserved values. Residual is calculated after running the regression model and is the differences between the observed values and the estimated values. | What is the difference between errors and residuals? | Error of the data set is the differences between the observed values and the true / unobserved values. Residual is calculated after running the regression model and is the differences between the obse | What is the difference between errors and residuals?
Error of the data set is the differences between the observed values and the true / unobserved values. Residual is calculated after running the regression model and is the differences between the observed values and the estimated values. | What is the difference between errors and residuals?
Error of the data set is the differences between the observed values and the true / unobserved values. Residual is calculated after running the regression model and is the differences between the obse |
5,304 | What is the difference between errors and residuals? | Error term is an unknown value that could never be known unless the DGP is known. Therefore, theoretically, one can generate a variable x from say a Normal random variable and the error from a normal random variable. Then construct the variable $y$ as follow
$$
y_t=\beta x_t+e_t
$$
Here, $e_t$ stands for error term the... | What is the difference between errors and residuals? | Error term is an unknown value that could never be known unless the DGP is known. Therefore, theoretically, one can generate a variable x from say a Normal random variable and the error from a normal | What is the difference between errors and residuals?
Error term is an unknown value that could never be known unless the DGP is known. Therefore, theoretically, one can generate a variable x from say a Normal random variable and the error from a normal random variable. Then construct the variable $y$ as follow
$$
y_t=\... | What is the difference between errors and residuals?
Error term is an unknown value that could never be known unless the DGP is known. Therefore, theoretically, one can generate a variable x from say a Normal random variable and the error from a normal |
5,305 | Eliciting priors from experts | John Cook gives some interesting recommendations. Basically, get percentiles/quantiles (not means or obscure scale parameters!) from the experts, and fit them with the appropriate distribution.
http://www.johndcook.com/blog/2010/01/31/parameters-from-percentiles/ | Eliciting priors from experts | John Cook gives some interesting recommendations. Basically, get percentiles/quantiles (not means or obscure scale parameters!) from the experts, and fit them with the appropriate distribution.
http:/ | Eliciting priors from experts
John Cook gives some interesting recommendations. Basically, get percentiles/quantiles (not means or obscure scale parameters!) from the experts, and fit them with the appropriate distribution.
http://www.johndcook.com/blog/2010/01/31/parameters-from-percentiles/ | Eliciting priors from experts
John Cook gives some interesting recommendations. Basically, get percentiles/quantiles (not means or obscure scale parameters!) from the experts, and fit them with the appropriate distribution.
http:/ |
5,306 | Eliciting priors from experts | I am currently researching the trial roulette method for my masters thesis as an elicitation technique. This is a graphical method that allows an expert to represent her subjective probability distribution for an uncertain quantity.
Experts are given counters (or what one can think of as casino chips) representing equa... | Eliciting priors from experts | I am currently researching the trial roulette method for my masters thesis as an elicitation technique. This is a graphical method that allows an expert to represent her subjective probability distrib | Eliciting priors from experts
I am currently researching the trial roulette method for my masters thesis as an elicitation technique. This is a graphical method that allows an expert to represent her subjective probability distribution for an uncertain quantity.
Experts are given counters (or what one can think of as c... | Eliciting priors from experts
I am currently researching the trial roulette method for my masters thesis as an elicitation technique. This is a graphical method that allows an expert to represent her subjective probability distrib |
5,307 | Eliciting priors from experts | Eliciting priors is a tricky business.
Statistical Methods for Eliciting Probability Distributions and Eliciting Probability Distributions are quite good practical guides for prior elicitation. The process in both papers is outlined as follows:
background and preparation;
identifying and recruiting the expert(s);
mo... | Eliciting priors from experts | Eliciting priors is a tricky business.
Statistical Methods for Eliciting Probability Distributions and Eliciting Probability Distributions are quite good practical guides for prior elicitation. The | Eliciting priors from experts
Eliciting priors is a tricky business.
Statistical Methods for Eliciting Probability Distributions and Eliciting Probability Distributions are quite good practical guides for prior elicitation. The process in both papers is outlined as follows:
background and preparation;
identifying an... | Eliciting priors from experts
Eliciting priors is a tricky business.
Statistical Methods for Eliciting Probability Distributions and Eliciting Probability Distributions are quite good practical guides for prior elicitation. The |
5,308 | Eliciting priors from experts | I'd recommend letting the subject expert specify the mean or mode of the prior but I'd feel free to adjust what they give as a scale. Most people are not very good at quantifying variance.
And I would definitely not let the expert determine the distribution family, in particular the tail thickness. For example, supp... | Eliciting priors from experts | I'd recommend letting the subject expert specify the mean or mode of the prior but I'd feel free to adjust what they give as a scale. Most people are not very good at quantifying variance.
And I wo | Eliciting priors from experts
I'd recommend letting the subject expert specify the mean or mode of the prior but I'd feel free to adjust what they give as a scale. Most people are not very good at quantifying variance.
And I would definitely not let the expert determine the distribution family, in particular the tai... | Eliciting priors from experts
I'd recommend letting the subject expert specify the mean or mode of the prior but I'd feel free to adjust what they give as a scale. Most people are not very good at quantifying variance.
And I wo |
5,309 | Eliciting priors from experts | This interesting question is the subject of some research in ACERA. The lead researcher is Andrew Speirs-Bridge, and his work is eminently google-able :) | Eliciting priors from experts | This interesting question is the subject of some research in ACERA. The lead researcher is Andrew Speirs-Bridge, and his work is eminently google-able :) | Eliciting priors from experts
This interesting question is the subject of some research in ACERA. The lead researcher is Andrew Speirs-Bridge, and his work is eminently google-able :) | Eliciting priors from experts
This interesting question is the subject of some research in ACERA. The lead researcher is Andrew Speirs-Bridge, and his work is eminently google-able :) |
5,310 | Eliciting priors from experts | 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 is the most up-to-date reference, with clear inte... | Eliciting priors from experts | 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.
| Eliciting priors from experts
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 is the most up-to-d... | Eliciting priors from experts
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.
|
5,311 | Difference between GradientDescentOptimizer and AdamOptimizer (TensorFlow)? | The tf.train.AdamOptimizer uses Kingma and Ba's Adam algorithm to control the learning rate. Adam offers several advantages over the simple tf.train.GradientDescentOptimizer. Foremost is that it uses moving averages of the parameters (momentum); Bengio discusses the reasons for why this is beneficial in Section 3.1.1 o... | Difference between GradientDescentOptimizer and AdamOptimizer (TensorFlow)? | The tf.train.AdamOptimizer uses Kingma and Ba's Adam algorithm to control the learning rate. Adam offers several advantages over the simple tf.train.GradientDescentOptimizer. Foremost is that it uses | Difference between GradientDescentOptimizer and AdamOptimizer (TensorFlow)?
The tf.train.AdamOptimizer uses Kingma and Ba's Adam algorithm to control the learning rate. Adam offers several advantages over the simple tf.train.GradientDescentOptimizer. Foremost is that it uses moving averages of the parameters (momentum)... | Difference between GradientDescentOptimizer and AdamOptimizer (TensorFlow)?
The tf.train.AdamOptimizer uses Kingma and Ba's Adam algorithm to control the learning rate. Adam offers several advantages over the simple tf.train.GradientDescentOptimizer. Foremost is that it uses |
5,312 | Features for time series classification | Simple statistical features
Means in each of the $d$ dimensions
Standard deviations of the $d$ dimensions
Skewness, Kurtosis and Higher order moments of the $d$ dimensions
Maximum and Minimum values
Time serie analysis related features
The $d \times d-1$ Cross-Correlations between each dimension and the $d$ Auto-Co... | Features for time series classification | Simple statistical features
Means in each of the $d$ dimensions
Standard deviations of the $d$ dimensions
Skewness, Kurtosis and Higher order moments of the $d$ dimensions
Maximum and Minimum values | Features for time series classification
Simple statistical features
Means in each of the $d$ dimensions
Standard deviations of the $d$ dimensions
Skewness, Kurtosis and Higher order moments of the $d$ dimensions
Maximum and Minimum values
Time serie analysis related features
The $d \times d-1$ Cross-Correlations be... | Features for time series classification
Simple statistical features
Means in each of the $d$ dimensions
Standard deviations of the $d$ dimensions
Skewness, Kurtosis and Higher order moments of the $d$ dimensions
Maximum and Minimum values |
5,313 | Features for time series classification | As the other answers suggested, there is a huge number of time series characteristics that can be used as potential features. There are simple features such as the mean, time series related features such as the coefficients of an AR model or highly sophisticated features such as the test statistic of the augmented dick... | Features for time series classification | As the other answers suggested, there is a huge number of time series characteristics that can be used as potential features. There are simple features such as the mean, time series related features s | Features for time series classification
As the other answers suggested, there is a huge number of time series characteristics that can be used as potential features. There are simple features such as the mean, time series related features such as the coefficients of an AR model or highly sophisticated features such as ... | Features for time series classification
As the other answers suggested, there is a huge number of time series characteristics that can be used as potential features. There are simple features such as the mean, time series related features s |
5,314 | Features for time series classification | Emile, I think the features listed in your answer are pretty good starting points, though as always, I think some domain expertise (or at least a good long think) about your problem is equally important.
You may want to consider including features calculated from the derivatives (or integrals) of your signal. For examp... | Features for time series classification | Emile, I think the features listed in your answer are pretty good starting points, though as always, I think some domain expertise (or at least a good long think) about your problem is equally importa | Features for time series classification
Emile, I think the features listed in your answer are pretty good starting points, though as always, I think some domain expertise (or at least a good long think) about your problem is equally important.
You may want to consider including features calculated from the derivatives ... | Features for time series classification
Emile, I think the features listed in your answer are pretty good starting points, though as always, I think some domain expertise (or at least a good long think) about your problem is equally importa |
5,315 | Features for time series classification | I suggest you, instead of using classic approaches for extracting hand-engineered features, utilise autoencoders. Autoencoders plays an important role in the feature extraction of deep learning architecture.
The autoencoder tries to learn a function $f(X_T)≈X_T$. In other words, it is trying to learn an approximation t... | Features for time series classification | I suggest you, instead of using classic approaches for extracting hand-engineered features, utilise autoencoders. Autoencoders plays an important role in the feature extraction of deep learning archit | Features for time series classification
I suggest you, instead of using classic approaches for extracting hand-engineered features, utilise autoencoders. Autoencoders plays an important role in the feature extraction of deep learning architecture.
The autoencoder tries to learn a function $f(X_T)≈X_T$. In other words, ... | Features for time series classification
I suggest you, instead of using classic approaches for extracting hand-engineered features, utilise autoencoders. Autoencoders plays an important role in the feature extraction of deep learning archit |
5,316 | Features for time series classification | The linked paper will be somewhat enlightening, since it is interested in the more or less the same issue in another context.
Paper abstract (in the Internet Archive)
Paper PDF | Features for time series classification | The linked paper will be somewhat enlightening, since it is interested in the more or less the same issue in another context.
Paper abstract (in the Internet Archive)
Paper PDF | Features for time series classification
The linked paper will be somewhat enlightening, since it is interested in the more or less the same issue in another context.
Paper abstract (in the Internet Archive)
Paper PDF | Features for time series classification
The linked paper will be somewhat enlightening, since it is interested in the more or less the same issue in another context.
Paper abstract (in the Internet Archive)
Paper PDF |
5,317 | Features for time series classification | Depending on the length of your time series, the usual approach is to epoch the data into segments, e.g. 10 secs.
However, often prior to breaking the time-series into segments it is necessary to perform some preprocessing such as filtering and artifact rejection.
You can then compute a variety of features such as tho... | Features for time series classification | Depending on the length of your time series, the usual approach is to epoch the data into segments, e.g. 10 secs.
However, often prior to breaking the time-series into segments it is necessary to per | Features for time series classification
Depending on the length of your time series, the usual approach is to epoch the data into segments, e.g. 10 secs.
However, often prior to breaking the time-series into segments it is necessary to perform some preprocessing such as filtering and artifact rejection.
You can then c... | Features for time series classification
Depending on the length of your time series, the usual approach is to epoch the data into segments, e.g. 10 secs.
However, often prior to breaking the time-series into segments it is necessary to per |
5,318 | Features for time series classification | The TSFEL package provides this very comprehensive list of possible time series features. The source code shows how every feature is calculated in detail.
You can find a comprehensive list below:
* abs_energy(signal) Computes the absolute energy of the signal.
* auc(signal, fs) Computes the area under the curve of... | Features for time series classification | The TSFEL package provides this very comprehensive list of possible time series features. The source code shows how every feature is calculated in detail.
You can find a comprehensive list below:
* ab | Features for time series classification
The TSFEL package provides this very comprehensive list of possible time series features. The source code shows how every feature is calculated in detail.
You can find a comprehensive list below:
* abs_energy(signal) Computes the absolute energy of the signal.
* auc(signal, fs... | Features for time series classification
The TSFEL package provides this very comprehensive list of possible time series features. The source code shows how every feature is calculated in detail.
You can find a comprehensive list below:
* ab |
5,319 | Clarification on interpreting confidence intervals? | I think the fundamental problem is that frequentist statistics can only assign a probability to something that can have a long run frequency. Whether the true value of a parameter lies in a particular interval or not doesn't have a long run frequency, becuase we can only perform the experiment once, so you can't assig... | Clarification on interpreting confidence intervals? | I think the fundamental problem is that frequentist statistics can only assign a probability to something that can have a long run frequency. Whether the true value of a parameter lies in a particula | Clarification on interpreting confidence intervals?
I think the fundamental problem is that frequentist statistics can only assign a probability to something that can have a long run frequency. Whether the true value of a parameter lies in a particular interval or not doesn't have a long run frequency, becuase we can ... | Clarification on interpreting confidence intervals?
I think the fundamental problem is that frequentist statistics can only assign a probability to something that can have a long run frequency. Whether the true value of a parameter lies in a particula |
5,320 | Clarification on interpreting confidence intervals? | Major update, major new answer. Let me try to clearly address this point, because it's where the problem lies:
"If you argue that "after seeing the interval, the notion of probability no longer makes sense", then fine, let's work in an interpretation of probability in which it does make sense."
The rules of probabilit... | Clarification on interpreting confidence intervals? | Major update, major new answer. Let me try to clearly address this point, because it's where the problem lies:
"If you argue that "after seeing the interval, the notion of probability no longer makes | Clarification on interpreting confidence intervals?
Major update, major new answer. Let me try to clearly address this point, because it's where the problem lies:
"If you argue that "after seeing the interval, the notion of probability no longer makes sense", then fine, let's work in an interpretation of probability in... | Clarification on interpreting confidence intervals?
Major update, major new answer. Let me try to clearly address this point, because it's where the problem lies:
"If you argue that "after seeing the interval, the notion of probability no longer makes |
5,321 | Clarification on interpreting confidence intervals? | OK, now you're talking! I've voted to delete my previous answer because it doesn't make sense with this major-updated question.
In this new, updated question, with a computer that calculates 95% confidence intervals, under the orthodox frequentist interpretation, here are the answers to your questions:
No.
No.
Once ... | Clarification on interpreting confidence intervals? | OK, now you're talking! I've voted to delete my previous answer because it doesn't make sense with this major-updated question.
In this new, updated question, with a computer that calculates 95% conf | Clarification on interpreting confidence intervals?
OK, now you're talking! I've voted to delete my previous answer because it doesn't make sense with this major-updated question.
In this new, updated question, with a computer that calculates 95% confidence intervals, under the orthodox frequentist interpretation, her... | Clarification on interpreting confidence intervals?
OK, now you're talking! I've voted to delete my previous answer because it doesn't make sense with this major-updated question.
In this new, updated question, with a computer that calculates 95% conf |
5,322 | Clarification on interpreting confidence intervals? | I'll throw in my two cents (maybe redigesting some of the former answers). To a frequentist, the confidence interval itself is in essence a two-dimensional random variable: if you would redo the experiment a gazillion times, the confidence interval you would estimate (i.e.: calculate from your newly found data each tim... | Clarification on interpreting confidence intervals? | I'll throw in my two cents (maybe redigesting some of the former answers). To a frequentist, the confidence interval itself is in essence a two-dimensional random variable: if you would redo the exper | Clarification on interpreting confidence intervals?
I'll throw in my two cents (maybe redigesting some of the former answers). To a frequentist, the confidence interval itself is in essence a two-dimensional random variable: if you would redo the experiment a gazillion times, the confidence interval you would estimate ... | Clarification on interpreting confidence intervals?
I'll throw in my two cents (maybe redigesting some of the former answers). To a frequentist, the confidence interval itself is in essence a two-dimensional random variable: if you would redo the exper |
5,323 | Clarification on interpreting confidence intervals? | I don't think a frequentist can say there is any probability of the true (population) value of a statistic lying in the confidence interval for a particular sample. It either is, or it isn't, but there is no long run frequency for a particular event, just the population of events that you would get by repeated perform... | Clarification on interpreting confidence intervals? | I don't think a frequentist can say there is any probability of the true (population) value of a statistic lying in the confidence interval for a particular sample. It either is, or it isn't, but the | Clarification on interpreting confidence intervals?
I don't think a frequentist can say there is any probability of the true (population) value of a statistic lying in the confidence interval for a particular sample. It either is, or it isn't, but there is no long run frequency for a particular event, just the populat... | Clarification on interpreting confidence intervals?
I don't think a frequentist can say there is any probability of the true (population) value of a statistic lying in the confidence interval for a particular sample. It either is, or it isn't, but the |
5,324 | Clarification on interpreting confidence intervals? | The reason that the confidence interval doesn't specify "the probability that the true parameter lies in the interval" is because once the interval is specified, the paramater either lies in it or it doesn't. However, for a 95% confidence interval for example, you have a 95% chance of creating a confidence interval tha... | Clarification on interpreting confidence intervals? | The reason that the confidence interval doesn't specify "the probability that the true parameter lies in the interval" is because once the interval is specified, the paramater either lies in it or it | Clarification on interpreting confidence intervals?
The reason that the confidence interval doesn't specify "the probability that the true parameter lies in the interval" is because once the interval is specified, the paramater either lies in it or it doesn't. However, for a 95% confidence interval for example, you hav... | Clarification on interpreting confidence intervals?
The reason that the confidence interval doesn't specify "the probability that the true parameter lies in the interval" is because once the interval is specified, the paramater either lies in it or it |
5,325 | Clarification on interpreting confidence intervals? | The way you pose the problem is a little muddled. Take this statement: Let $E$ be the event that the true parameter falls in the interval $[a,b]$. This statement is meaningless from a frequentist perspective; the parameter is the parameter and it doesn't fall anywhere, it just is. P(E) is meaningless, P(E|C) is meaning... | Clarification on interpreting confidence intervals? | The way you pose the problem is a little muddled. Take this statement: Let $E$ be the event that the true parameter falls in the interval $[a,b]$. This statement is meaningless from a frequentist pers | Clarification on interpreting confidence intervals?
The way you pose the problem is a little muddled. Take this statement: Let $E$ be the event that the true parameter falls in the interval $[a,b]$. This statement is meaningless from a frequentist perspective; the parameter is the parameter and it doesn't fall anywhere... | Clarification on interpreting confidence intervals?
The way you pose the problem is a little muddled. Take this statement: Let $E$ be the event that the true parameter falls in the interval $[a,b]$. This statement is meaningless from a frequentist pers |
5,326 | Clarification on interpreting confidence intervals? | In frequentist statistics, the event $E$ is fixed -- the parameter either lies in $[a, b]$ or it doesn't. Thus, $E$ is independent of $C$ and $C'$ and so both $P(E|C) = P(E)$ and $P(E|C') = P(E)$.
(In your argument, you seem to think that $P(E|C) = 1$ and $P(E|C') = 0$, which is incorrect.) | Clarification on interpreting confidence intervals? | In frequentist statistics, the event $E$ is fixed -- the parameter either lies in $[a, b]$ or it doesn't. Thus, $E$ is independent of $C$ and $C'$ and so both $P(E|C) = P(E)$ and $P(E|C') = P(E)$.
(In | Clarification on interpreting confidence intervals?
In frequentist statistics, the event $E$ is fixed -- the parameter either lies in $[a, b]$ or it doesn't. Thus, $E$ is independent of $C$ and $C'$ and so both $P(E|C) = P(E)$ and $P(E|C') = P(E)$.
(In your argument, you seem to think that $P(E|C) = 1$ and $P(E|C') = 0... | Clarification on interpreting confidence intervals?
In frequentist statistics, the event $E$ is fixed -- the parameter either lies in $[a, b]$ or it doesn't. Thus, $E$ is independent of $C$ and $C'$ and so both $P(E|C) = P(E)$ and $P(E|C') = P(E)$.
(In |
5,327 | Clarification on interpreting confidence intervals? | There are so many long explanations here that I don't have time to read them. But I think the answer to the basic question can be short and sweet. It is the difference between a probability that is unconditional on the data. The probability of 1-alpha before collecting the dats is the probability that the well-defin... | Clarification on interpreting confidence intervals? | There are so many long explanations here that I don't have time to read them. But I think the answer to the basic question can be short and sweet. It is the difference between a probability that is | Clarification on interpreting confidence intervals?
There are so many long explanations here that I don't have time to read them. But I think the answer to the basic question can be short and sweet. It is the difference between a probability that is unconditional on the data. The probability of 1-alpha before collec... | Clarification on interpreting confidence intervals?
There are so many long explanations here that I don't have time to read them. But I think the answer to the basic question can be short and sweet. It is the difference between a probability that is |
5,328 | Clarification on interpreting confidence intervals? | If I say the probability the Knicks scored between xbar - 2sd(x) and xbar + 2sd(x) is about .95 in some given game in the past, that is a reasonable statement given some particular distributional assumption about the distribution of basketball scores. If I gather data about the scores given some sample of games and ca... | Clarification on interpreting confidence intervals? | If I say the probability the Knicks scored between xbar - 2sd(x) and xbar + 2sd(x) is about .95 in some given game in the past, that is a reasonable statement given some particular distributional ass | Clarification on interpreting confidence intervals?
If I say the probability the Knicks scored between xbar - 2sd(x) and xbar + 2sd(x) is about .95 in some given game in the past, that is a reasonable statement given some particular distributional assumption about the distribution of basketball scores. If I gather dat... | Clarification on interpreting confidence intervals?
If I say the probability the Knicks scored between xbar - 2sd(x) and xbar + 2sd(x) is about .95 in some given game in the past, that is a reasonable statement given some particular distributional ass |
5,329 | Clarification on interpreting confidence intervals? | Two observations about the many questions and responses that may help still.
Part of the confusion comes from glossing over some deeper math of probability theory, which, by the way, was not on a firm mathematical footing until about the 1940s. It gets into what constitutes sample spaces, probability spaces, etc.
Fir... | Clarification on interpreting confidence intervals? | Two observations about the many questions and responses that may help still.
Part of the confusion comes from glossing over some deeper math of probability theory, which, by the way, was not on a fir | Clarification on interpreting confidence intervals?
Two observations about the many questions and responses that may help still.
Part of the confusion comes from glossing over some deeper math of probability theory, which, by the way, was not on a firm mathematical footing until about the 1940s. It gets into what con... | Clarification on interpreting confidence intervals?
Two observations about the many questions and responses that may help still.
Part of the confusion comes from glossing over some deeper math of probability theory, which, by the way, was not on a fir |
5,330 | Clarification on interpreting confidence intervals? | The issue can be characterized as a confusion of prior and posterior probability
or maybe as the dissatisfaction of not knowing the joint distribution of certain random variables.
Conditioning
As an introductory example,
we consider a model for the experiment of drawing, without replacement,
two balls from an urn with ... | Clarification on interpreting confidence intervals? | The issue can be characterized as a confusion of prior and posterior probability
or maybe as the dissatisfaction of not knowing the joint distribution of certain random variables.
Conditioning
As an i | Clarification on interpreting confidence intervals?
The issue can be characterized as a confusion of prior and posterior probability
or maybe as the dissatisfaction of not knowing the joint distribution of certain random variables.
Conditioning
As an introductory example,
we consider a model for the experiment of drawi... | Clarification on interpreting confidence intervals?
The issue can be characterized as a confusion of prior and posterior probability
or maybe as the dissatisfaction of not knowing the joint distribution of certain random variables.
Conditioning
As an i |
5,331 | Clarification on interpreting confidence intervals? | Modeling
Correct procedure is:
(1) model the situation as a probability space $\mathcal{S} = (\Omega,\Sigma,P)$;
(2) define an event $E \in \Sigma$ of interest;
(3) determine its probability $P(E)$.
The event $E$ may be specified via random variables,
that is, functions on $\mathcal{S}$ (measurable functions, that is, ... | Clarification on interpreting confidence intervals? | Modeling
Correct procedure is:
(1) model the situation as a probability space $\mathcal{S} = (\Omega,\Sigma,P)$;
(2) define an event $E \in \Sigma$ of interest;
(3) determine its probability $P(E)$.
T | Clarification on interpreting confidence intervals?
Modeling
Correct procedure is:
(1) model the situation as a probability space $\mathcal{S} = (\Omega,\Sigma,P)$;
(2) define an event $E \in \Sigma$ of interest;
(3) determine its probability $P(E)$.
The event $E$ may be specified via random variables,
that is, functio... | Clarification on interpreting confidence intervals?
Modeling
Correct procedure is:
(1) model the situation as a probability space $\mathcal{S} = (\Omega,\Sigma,P)$;
(2) define an event $E \in \Sigma$ of interest;
(3) determine its probability $P(E)$.
T |
5,332 | Clarification on interpreting confidence intervals? | If we could say "the probability that the true parameter lies in this confidence interval" then we wouldn't take into account the size of the sample. No matter how large the sample is, as long as the the mean is the same, then the confidence interval would be equally wide. But when we say "if i repeat this 100 times, t... | Clarification on interpreting confidence intervals? | If we could say "the probability that the true parameter lies in this confidence interval" then we wouldn't take into account the size of the sample. No matter how large the sample is, as long as the | Clarification on interpreting confidence intervals?
If we could say "the probability that the true parameter lies in this confidence interval" then we wouldn't take into account the size of the sample. No matter how large the sample is, as long as the the mean is the same, then the confidence interval would be equally ... | Clarification on interpreting confidence intervals?
If we could say "the probability that the true parameter lies in this confidence interval" then we wouldn't take into account the size of the sample. No matter how large the sample is, as long as the |
5,333 | Importance of local response normalization in CNN | It seems that these kinds of layers have a minimal impact and are not used any more. Basically, their role have been outplayed by other regularization techniques (such as dropout and batch normalization), better initializations and training methods. This is what is written in the lecture notes for the Stanford Course C... | Importance of local response normalization in CNN | It seems that these kinds of layers have a minimal impact and are not used any more. Basically, their role have been outplayed by other regularization techniques (such as dropout and batch normalizati | Importance of local response normalization in CNN
It seems that these kinds of layers have a minimal impact and are not used any more. Basically, their role have been outplayed by other regularization techniques (such as dropout and batch normalization), better initializations and training methods. This is what is writ... | Importance of local response normalization in CNN
It seems that these kinds of layers have a minimal impact and are not used any more. Basically, their role have been outplayed by other regularization techniques (such as dropout and batch normalizati |
5,334 | Importance of local response normalization in CNN | Indeed, there seems no good explanation in a single place. The best is to read the articles from where it comes:
The original AlexNet article explains a bit in Section 3.3:
Krizhevsky, Sutskever, and Hinton, ImageNet Classification with Deep Convolutional Neural Networks, NIPS 2012. pdf
The exact way of doing this wa... | Importance of local response normalization in CNN | Indeed, there seems no good explanation in a single place. The best is to read the articles from where it comes:
The original AlexNet article explains a bit in Section 3.3:
Krizhevsky, Sutskever, and | Importance of local response normalization in CNN
Indeed, there seems no good explanation in a single place. The best is to read the articles from where it comes:
The original AlexNet article explains a bit in Section 3.3:
Krizhevsky, Sutskever, and Hinton, ImageNet Classification with Deep Convolutional Neural Networ... | Importance of local response normalization in CNN
Indeed, there seems no good explanation in a single place. The best is to read the articles from where it comes:
The original AlexNet article explains a bit in Section 3.3:
Krizhevsky, Sutskever, and |
5,335 | Importance of local response normalization in CNN | Here is my suggested answer, though I don't claim to be knowledgeable.
When performing gradient descent on a linear model, the error surface is quadratic, with the curvature determined by $XX_T$, where $X$ is your input. Now the ideal error surface for or gradient descent has the same curvature in all directions (... | Importance of local response normalization in CNN | Here is my suggested answer, though I don't claim to be knowledgeable.
When performing gradient descent on a linear model, the error surface is quadratic, with the curvature determined by $XX_T$, | Importance of local response normalization in CNN
Here is my suggested answer, though I don't claim to be knowledgeable.
When performing gradient descent on a linear model, the error surface is quadratic, with the curvature determined by $XX_T$, where $X$ is your input. Now the ideal error surface for or gradient ... | Importance of local response normalization in CNN
Here is my suggested answer, though I don't claim to be knowledgeable.
When performing gradient descent on a linear model, the error surface is quadratic, with the curvature determined by $XX_T$, |
5,336 | Importance of local response normalization in CNN | With this answer I would like to summarize contributions of other authors and provide a single place explanation of the LRN (or contrastive normalization) technique for those, who just want to get aware of what it is and how it works.
Motivation: 'This sort of response normalization (LRN) implements a form of lateral i... | Importance of local response normalization in CNN | With this answer I would like to summarize contributions of other authors and provide a single place explanation of the LRN (or contrastive normalization) technique for those, who just want to get awa | Importance of local response normalization in CNN
With this answer I would like to summarize contributions of other authors and provide a single place explanation of the LRN (or contrastive normalization) technique for those, who just want to get aware of what it is and how it works.
Motivation: 'This sort of response ... | Importance of local response normalization in CNN
With this answer I would like to summarize contributions of other authors and provide a single place explanation of the LRN (or contrastive normalization) technique for those, who just want to get awa |
5,337 | Importance of local response normalization in CNN | Local Response Normalization(LRN) type of layer turns out to be useful when using neurons with unbounded activations (e.g. rectified linear neurons), because it permits the detection of high-frequency features with a big neuron response, while damping responses that are uniformly large in a local neighborhood. It is a ... | Importance of local response normalization in CNN | Local Response Normalization(LRN) type of layer turns out to be useful when using neurons with unbounded activations (e.g. rectified linear neurons), because it permits the detection of high-frequency | Importance of local response normalization in CNN
Local Response Normalization(LRN) type of layer turns out to be useful when using neurons with unbounded activations (e.g. rectified linear neurons), because it permits the detection of high-frequency features with a big neuron response, while damping responses that are... | Importance of local response normalization in CNN
Local Response Normalization(LRN) type of layer turns out to be useful when using neurons with unbounded activations (e.g. rectified linear neurons), because it permits the detection of high-frequency |
5,338 | Importance of local response normalization in CNN | Local response normalization (LRN) is done pixel-wise for each channel $i$:
$$x_i = \frac{x_i}{ (k + ( \alpha \sum_j x_j^2 ))^\beta }$$
where $k, \alpha, \beta \in \mathbb{R}$ are constants. Note that you get L2 normalization if you set $\kappa = 0$, $\alpha=1$, $\beta=\frac{1}{2}$.
However, there is a much newer techn... | Importance of local response normalization in CNN | Local response normalization (LRN) is done pixel-wise for each channel $i$:
$$x_i = \frac{x_i}{ (k + ( \alpha \sum_j x_j^2 ))^\beta }$$
where $k, \alpha, \beta \in \mathbb{R}$ are constants. Note that | Importance of local response normalization in CNN
Local response normalization (LRN) is done pixel-wise for each channel $i$:
$$x_i = \frac{x_i}{ (k + ( \alpha \sum_j x_j^2 ))^\beta }$$
where $k, \alpha, \beta \in \mathbb{R}$ are constants. Note that you get L2 normalization if you set $\kappa = 0$, $\alpha=1$, $\beta=... | Importance of local response normalization in CNN
Local response normalization (LRN) is done pixel-wise for each channel $i$:
$$x_i = \frac{x_i}{ (k + ( \alpha \sum_j x_j^2 ))^\beta }$$
where $k, \alpha, \beta \in \mathbb{R}$ are constants. Note that |
5,339 | Importance of local response normalization in CNN | AlexNet also uses a competitive normalization step immediately after the ReLU step of layers C1 and C3, called local response normalization (LRN): the most strongly activated neurons inhibit other neurons located at the same position in neighboring feature maps (such competitive activation has been observed in biologic... | Importance of local response normalization in CNN | AlexNet also uses a competitive normalization step immediately after the ReLU step of layers C1 and C3, called local response normalization (LRN): the most strongly activated neurons inhibit other neu | Importance of local response normalization in CNN
AlexNet also uses a competitive normalization step immediately after the ReLU step of layers C1 and C3, called local response normalization (LRN): the most strongly activated neurons inhibit other neurons located at the same position in neighboring feature maps (such co... | Importance of local response normalization in CNN
AlexNet also uses a competitive normalization step immediately after the ReLU step of layers C1 and C3, called local response normalization (LRN): the most strongly activated neurons inhibit other neu |
5,340 | Confidence interval around binomial estimate of 0 or 1 | Do not use the normal approximation
Much has been written about this problem. A general advice is to never use the normal approximation (i.e., the asymptotic/Wald confidence interval), as it has terrible coverage properties. R code for illustrating this:
library(binom)
p = seq(0,1,.001)
coverage = binom.coverage(p, 25,... | Confidence interval around binomial estimate of 0 or 1 | Do not use the normal approximation
Much has been written about this problem. A general advice is to never use the normal approximation (i.e., the asymptotic/Wald confidence interval), as it has terri | Confidence interval around binomial estimate of 0 or 1
Do not use the normal approximation
Much has been written about this problem. A general advice is to never use the normal approximation (i.e., the asymptotic/Wald confidence interval), as it has terrible coverage properties. R code for illustrating this:
library(bi... | Confidence interval around binomial estimate of 0 or 1
Do not use the normal approximation
Much has been written about this problem. A general advice is to never use the normal approximation (i.e., the asymptotic/Wald confidence interval), as it has terri |
5,341 | Confidence interval around binomial estimate of 0 or 1 | Agresti (2007, pp.9-10) shows that when a proportion falls near 0 or 1, the confidence interval $p\pm z_{\alpha/2}\sqrt{p(1-p)/n}$ performs poorly. Instead, use a "duality with significance tests... [that] consists of all values of $\pi_0$ for the null hypothesis parameter that a judged plausible," where $\pi_0$ is the... | Confidence interval around binomial estimate of 0 or 1 | Agresti (2007, pp.9-10) shows that when a proportion falls near 0 or 1, the confidence interval $p\pm z_{\alpha/2}\sqrt{p(1-p)/n}$ performs poorly. Instead, use a "duality with significance tests... [ | Confidence interval around binomial estimate of 0 or 1
Agresti (2007, pp.9-10) shows that when a proportion falls near 0 or 1, the confidence interval $p\pm z_{\alpha/2}\sqrt{p(1-p)/n}$ performs poorly. Instead, use a "duality with significance tests... [that] consists of all values of $\pi_0$ for the null hypothesis p... | Confidence interval around binomial estimate of 0 or 1
Agresti (2007, pp.9-10) shows that when a proportion falls near 0 or 1, the confidence interval $p\pm z_{\alpha/2}\sqrt{p(1-p)/n}$ performs poorly. Instead, use a "duality with significance tests... [ |
5,342 | How do I test a nonlinear association? | ...the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?
One way of doing this would be to fit $y$ as a semi-parametrically estimated function of $x$ using, for example, a generalized additive model and testing whether or not that functional es... | How do I test a nonlinear association? | ...the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?
One way of doing this would be to fit $y$ as a semi-parametrically | How do I test a nonlinear association?
...the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?
One way of doing this would be to fit $y$ as a semi-parametrically estimated function of $x$ using, for example, a generalized additive model and te... | How do I test a nonlinear association?
...the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?
One way of doing this would be to fit $y$ as a semi-parametrically |
5,343 | How do I test a nonlinear association? | If the nonlinear relationship had been monotonic rank correlation (Spearman's rho) would be appropriate. In your example there is a clear small region where the curve changes from monotoncally increasing to montonically decreasing like a parabola would do at the point where the first derivative equals $0$.
I think if y... | How do I test a nonlinear association? | If the nonlinear relationship had been monotonic rank correlation (Spearman's rho) would be appropriate. In your example there is a clear small region where the curve changes from monotoncally increas | How do I test a nonlinear association?
If the nonlinear relationship had been monotonic rank correlation (Spearman's rho) would be appropriate. In your example there is a clear small region where the curve changes from monotoncally increasing to montonically decreasing like a parabola would do at the point where the fi... | How do I test a nonlinear association?
If the nonlinear relationship had been monotonic rank correlation (Spearman's rho) would be appropriate. In your example there is a clear small region where the curve changes from monotoncally increas |
5,344 | How do I test a nonlinear association? | You can test any kind of dependence by using distance correlation tests. See here for more informations about the distance correlation: Understanding distance correlation computations
And here the original paper: https://arxiv.org/pdf/0803.4101.pdf
In R this is implemented in the energy package with the dcor.test funct... | How do I test a nonlinear association? | You can test any kind of dependence by using distance correlation tests. See here for more informations about the distance correlation: Understanding distance correlation computations
And here the ori | How do I test a nonlinear association?
You can test any kind of dependence by using distance correlation tests. See here for more informations about the distance correlation: Understanding distance correlation computations
And here the original paper: https://arxiv.org/pdf/0803.4101.pdf
In R this is implemented in the ... | How do I test a nonlinear association?
You can test any kind of dependence by using distance correlation tests. See here for more informations about the distance correlation: Understanding distance correlation computations
And here the ori |
5,345 | How do I test a nonlinear association? | Someone correct me if my understanding is wrong here but one way to deal with non- linear variables is to use a linear approximation. So, for example, taking log of exponential distribution should allow you to treat the variable as normal distribution. It may then be used to solve the problem like any linear regression... | How do I test a nonlinear association? | Someone correct me if my understanding is wrong here but one way to deal with non- linear variables is to use a linear approximation. So, for example, taking log of exponential distribution should all | How do I test a nonlinear association?
Someone correct me if my understanding is wrong here but one way to deal with non- linear variables is to use a linear approximation. So, for example, taking log of exponential distribution should allow you to treat the variable as normal distribution. It may then be used to solve... | How do I test a nonlinear association?
Someone correct me if my understanding is wrong here but one way to deal with non- linear variables is to use a linear approximation. So, for example, taking log of exponential distribution should all |
5,346 | How do I test a nonlinear association? | I used to implement the general additive model to detect the non-linear relationship between two variables, but recently I've found out about the non-linear correlation implemented via nlcor package in R, you can implement this method in the same way as Pearson correlation, the correlation coefficient is between 0 and ... | How do I test a nonlinear association? | I used to implement the general additive model to detect the non-linear relationship between two variables, but recently I've found out about the non-linear correlation implemented via nlcor package i | How do I test a nonlinear association?
I used to implement the general additive model to detect the non-linear relationship between two variables, but recently I've found out about the non-linear correlation implemented via nlcor package in R, you can implement this method in the same way as Pearson correlation, the co... | How do I test a nonlinear association?
I used to implement the general additive model to detect the non-linear relationship between two variables, but recently I've found out about the non-linear correlation implemented via nlcor package i |
5,347 | Statistical test to tell whether two samples are pulled from the same population? | The tests that compare distributions are rule-out tests. They start with the null hypothesis that the 2 populations are identical, then try to reject that hypothesis. We can never prove the null to be true, just reject it, so these tests cannot really be used to show that 2 samples come from the same population (or i... | Statistical test to tell whether two samples are pulled from the same population? | The tests that compare distributions are rule-out tests. They start with the null hypothesis that the 2 populations are identical, then try to reject that hypothesis. We can never prove the null to | Statistical test to tell whether two samples are pulled from the same population?
The tests that compare distributions are rule-out tests. They start with the null hypothesis that the 2 populations are identical, then try to reject that hypothesis. We can never prove the null to be true, just reject it, so these test... | Statistical test to tell whether two samples are pulled from the same population?
The tests that compare distributions are rule-out tests. They start with the null hypothesis that the 2 populations are identical, then try to reject that hypothesis. We can never prove the null to |
5,348 | Statistical test to tell whether two samples are pulled from the same population? | http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
Assuming your sample values come from continuous distributions, I would suggest the Kolmogorov-Smirnov test. It can be used to test whether two samples come from different distributions (this is how I am interpreting your usage of population) based on their ... | Statistical test to tell whether two samples are pulled from the same population? | http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
Assuming your sample values come from continuous distributions, I would suggest the Kolmogorov-Smirnov test. It can be used to test whethe | Statistical test to tell whether two samples are pulled from the same population?
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
Assuming your sample values come from continuous distributions, I would suggest the Kolmogorov-Smirnov test. It can be used to test whether two samples come from different dist... | Statistical test to tell whether two samples are pulled from the same population?
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
Assuming your sample values come from continuous distributions, I would suggest the Kolmogorov-Smirnov test. It can be used to test whethe |
5,349 | Statistical test to tell whether two samples are pulled from the same population? | You can use a 'shift function' which checks whether the 2 distributions differ at at each decile. While its technically a test of whether they are from different populations rather than the same, if the distributions don't differ on any of the deciles then you can be reasonably sure they are from the same population, e... | Statistical test to tell whether two samples are pulled from the same population? | You can use a 'shift function' which checks whether the 2 distributions differ at at each decile. While its technically a test of whether they are from different populations rather than the same, if t | Statistical test to tell whether two samples are pulled from the same population?
You can use a 'shift function' which checks whether the 2 distributions differ at at each decile. While its technically a test of whether they are from different populations rather than the same, if the distributions don't differ on any o... | Statistical test to tell whether two samples are pulled from the same population?
You can use a 'shift function' which checks whether the 2 distributions differ at at each decile. While its technically a test of whether they are from different populations rather than the same, if t |
5,350 | Statistical test to tell whether two samples are pulled from the same population? | I recently had to do something similar (although in my case I needed to know if two distributions were significantly different).
Our samples were very large (several hundred to tens of thousands) so KS test said everything was different (even for distributions that appeared nearly identical upon inspection of their his... | Statistical test to tell whether two samples are pulled from the same population? | I recently had to do something similar (although in my case I needed to know if two distributions were significantly different).
Our samples were very large (several hundred to tens of thousands) so K | Statistical test to tell whether two samples are pulled from the same population?
I recently had to do something similar (although in my case I needed to know if two distributions were significantly different).
Our samples were very large (several hundred to tens of thousands) so KS test said everything was different (... | Statistical test to tell whether two samples are pulled from the same population?
I recently had to do something similar (although in my case I needed to know if two distributions were significantly different).
Our samples were very large (several hundred to tens of thousands) so K |
5,351 | Statistical test to tell whether two samples are pulled from the same population? | This question came up as the top related result when I was searching for a similar topic, namely, how to compare whether the means of two distributions had the same mean. My question is slightly different because two distributions could be different in ways other than mean (e.g. variance or skew or kurtosis or other "s... | Statistical test to tell whether two samples are pulled from the same population? | This question came up as the top related result when I was searching for a similar topic, namely, how to compare whether the means of two distributions had the same mean. My question is slightly diffe | Statistical test to tell whether two samples are pulled from the same population?
This question came up as the top related result when I was searching for a similar topic, namely, how to compare whether the means of two distributions had the same mean. My question is slightly different because two distributions could b... | Statistical test to tell whether two samples are pulled from the same population?
This question came up as the top related result when I was searching for a similar topic, namely, how to compare whether the means of two distributions had the same mean. My question is slightly diffe |
5,352 | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | Nice question (+1)!!
You will remember that for independent random variables $X$ and $Y$, $Var(X+Y) = Var(X) + Var(Y)$ and $Var(a\cdot X) = a^2 \cdot Var(X)$. So the variance of $\sum_{i=1}^n X_i$ is $\sum_{i=1}^n \sigma^2 = n\sigma^2$, and the variance of $\bar{X} = \frac{1}{n}\sum_{i=1}^n X_i$ is $n\sigma^2 / n^2 = \... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | Nice question (+1)!!
You will remember that for independent random variables $X$ and $Y$, $Var(X+Y) = Var(X) + Var(Y)$ and $Var(a\cdot X) = a^2 \cdot Var(X)$. So the variance of $\sum_{i=1}^n X_i$ is | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
Nice question (+1)!!
You will remember that for independent random variables $X$ and $Y$, $Var(X+Y) = Var(X) + Var(Y)$ and $Var(a\cdot X) = a^2 \cdot Var(X)$. So the variance of $\sum_{i=1}^n X_i$ is $\sum_{i=1}^n \sigma^2 = n\sigma^2$, and the variance of... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
Nice question (+1)!!
You will remember that for independent random variables $X$ and $Y$, $Var(X+Y) = Var(X) + Var(Y)$ and $Var(a\cdot X) = a^2 \cdot Var(X)$. So the variance of $\sum_{i=1}^n X_i$ is |
5,353 | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | There is a nice theory of what kind of distributions can be limiting distributions of sums of random variables. The nice resource is the following book by Petrov, which I personally enjoyed immensely.
It turns out, that if you are investigating limits of this type
$$\frac{1}{a_n}\sum_{i=1}^n(X_i-b_i), \quad (1)$$ where... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | There is a nice theory of what kind of distributions can be limiting distributions of sums of random variables. The nice resource is the following book by Petrov, which I personally enjoyed immensely. | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
There is a nice theory of what kind of distributions can be limiting distributions of sums of random variables. The nice resource is the following book by Petrov, which I personally enjoyed immensely.
It turns out, that if you are investigating limits of t... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
There is a nice theory of what kind of distributions can be limiting distributions of sums of random variables. The nice resource is the following book by Petrov, which I personally enjoyed immensely. |
5,354 | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | $s_n$ represents the sample standard deviation for the sample mean. $s_n$$^2$ is the sample variance for the sample mean and it equals $S_n^2/n$, where $S_n^2$ is the sample estimate of the population variance. Since $s_n =S_n/\sqrt{n}$ that explains how $\sqrt n$ appears in the first formula. Note there would be a $\... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | $s_n$ represents the sample standard deviation for the sample mean. $s_n$$^2$ is the sample variance for the sample mean and it equals $S_n^2/n$, where $S_n^2$ is the sample estimate of the population | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
$s_n$ represents the sample standard deviation for the sample mean. $s_n$$^2$ is the sample variance for the sample mean and it equals $S_n^2/n$, where $S_n^2$ is the sample estimate of the population variance. Since $s_n =S_n/\sqrt{n}$ that explains how $... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
$s_n$ represents the sample standard deviation for the sample mean. $s_n$$^2$ is the sample variance for the sample mean and it equals $S_n^2/n$, where $S_n^2$ is the sample estimate of the population |
5,355 | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | Intuitively, if $Z_n \to \mathcal N(0, \sigma^2)$ for some $\sigma^2$ we should expect that $\mbox{Var}(Z_n)$ is roughly equal to $\sigma^2$; it seems like a pretty reasonable expectation, though I don't think it is necessary in general. The reason for the $\sqrt n$ in the first expression is that the variance of $\bar... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)? | Intuitively, if $Z_n \to \mathcal N(0, \sigma^2)$ for some $\sigma^2$ we should expect that $\mbox{Var}(Z_n)$ is roughly equal to $\sigma^2$; it seems like a pretty reasonable expectation, though I do | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
Intuitively, if $Z_n \to \mathcal N(0, \sigma^2)$ for some $\sigma^2$ we should expect that $\mbox{Var}(Z_n)$ is roughly equal to $\sigma^2$; it seems like a pretty reasonable expectation, though I don't think it is necessary in general. The reason for the... | Where does $\sqrt{n}$ come from in central limit theorem (CLT)?
Intuitively, if $Z_n \to \mathcal N(0, \sigma^2)$ for some $\sigma^2$ we should expect that $\mbox{Var}(Z_n)$ is roughly equal to $\sigma^2$; it seems like a pretty reasonable expectation, though I do |
5,356 | How to interpret and report eta squared / partial eta squared in statistically significant and non-significant analyses? | Effect sizes for group mean differences
In general, I find standardised group mean differences (e.g., Cohen's d) a more meaningful effect size measure within the context of group differences. Measures like eta square are influenced by whether group samples sizes are equal, whereas Cohen's d is not. I also think that t... | How to interpret and report eta squared / partial eta squared in statistically significant and non- | Effect sizes for group mean differences
In general, I find standardised group mean differences (e.g., Cohen's d) a more meaningful effect size measure within the context of group differences. Measure | How to interpret and report eta squared / partial eta squared in statistically significant and non-significant analyses?
Effect sizes for group mean differences
In general, I find standardised group mean differences (e.g., Cohen's d) a more meaningful effect size measure within the context of group differences. Measu... | How to interpret and report eta squared / partial eta squared in statistically significant and non-
Effect sizes for group mean differences
In general, I find standardised group mean differences (e.g., Cohen's d) a more meaningful effect size measure within the context of group differences. Measure |
5,357 | Can simple linear regression be done without using plots and linear algebra? | Yes your onto it. You have to keep playing around with the 2333 until you find the right one which minimizes the error. But there's a mathematical way to find the "right" one. Let's call that number $\beta$. $E$, the sum of the squared errors (SSE) is a function of $\beta$ since for each choice of $\beta$ can calculate... | Can simple linear regression be done without using plots and linear algebra? | Yes your onto it. You have to keep playing around with the 2333 until you find the right one which minimizes the error. But there's a mathematical way to find the "right" one. Let's call that number $ | Can simple linear regression be done without using plots and linear algebra?
Yes your onto it. You have to keep playing around with the 2333 until you find the right one which minimizes the error. But there's a mathematical way to find the "right" one. Let's call that number $\beta$. $E$, the sum of the squared errors ... | Can simple linear regression be done without using plots and linear algebra?
Yes your onto it. You have to keep playing around with the 2333 until you find the right one which minimizes the error. But there's a mathematical way to find the "right" one. Let's call that number $ |
5,358 | Can simple linear regression be done without using plots and linear algebra? | Your understanding is close, but needs some extension: Simple linear regression is trying to find the formula that once you give X to it, would provide you with the closest estimation of Y based on a linear relation between X and Y.
Your example of house prices, when extended a bit, shows why you end up with scatter pl... | Can simple linear regression be done without using plots and linear algebra? | Your understanding is close, but needs some extension: Simple linear regression is trying to find the formula that once you give X to it, would provide you with the closest estimation of Y based on a | Can simple linear regression be done without using plots and linear algebra?
Your understanding is close, but needs some extension: Simple linear regression is trying to find the formula that once you give X to it, would provide you with the closest estimation of Y based on a linear relation between X and Y.
Your examp... | Can simple linear regression be done without using plots and linear algebra?
Your understanding is close, but needs some extension: Simple linear regression is trying to find the formula that once you give X to it, would provide you with the closest estimation of Y based on a |
5,359 | Can simple linear regression be done without using plots and linear algebra? | First of all, my compliments. It is difficult for everyone to struggle with statistics (I am a physician, so you can guess how hard it is for me)...
I can propose not a visual explanation to linear regression, but something very close: a tactile explanation to linear regression.
Imagine you are entering a room from a d... | Can simple linear regression be done without using plots and linear algebra? | First of all, my compliments. It is difficult for everyone to struggle with statistics (I am a physician, so you can guess how hard it is for me)...
I can propose not a visual explanation to linear re | Can simple linear regression be done without using plots and linear algebra?
First of all, my compliments. It is difficult for everyone to struggle with statistics (I am a physician, so you can guess how hard it is for me)...
I can propose not a visual explanation to linear regression, but something very close: a tacti... | Can simple linear regression be done without using plots and linear algebra?
First of all, my compliments. It is difficult for everyone to struggle with statistics (I am a physician, so you can guess how hard it is for me)...
I can propose not a visual explanation to linear re |
5,360 | Can simple linear regression be done without using plots and linear algebra? | The reason why plots are universally used to introduce simple regression - a response predicted by a single predictor - is that they aid understanding.
However, I believe I can give something of the flavor that might aid in understanding what's going on. In this I'll mostly focus on trying to convey some of the unders... | Can simple linear regression be done without using plots and linear algebra? | The reason why plots are universally used to introduce simple regression - a response predicted by a single predictor - is that they aid understanding.
However, I believe I can give something of the | Can simple linear regression be done without using plots and linear algebra?
The reason why plots are universally used to introduce simple regression - a response predicted by a single predictor - is that they aid understanding.
However, I believe I can give something of the flavor that might aid in understanding what... | Can simple linear regression be done without using plots and linear algebra?
The reason why plots are universally used to introduce simple regression - a response predicted by a single predictor - is that they aid understanding.
However, I believe I can give something of the |
5,361 | Can simple linear regression be done without using plots and linear algebra? | Nice example that can help for your question was provided by Andrew Gelman and David K. Park (2012). Let's stick to your example of predicting the price of house $Y$ given it's area $X$. For this we use simple linear regression model
$$ Y = \beta_0 + \beta_1 X + \varepsilon $$
For sake of simplicity, let's forget about... | Can simple linear regression be done without using plots and linear algebra? | Nice example that can help for your question was provided by Andrew Gelman and David K. Park (2012). Let's stick to your example of predicting the price of house $Y$ given it's area $X$. For this we u | Can simple linear regression be done without using plots and linear algebra?
Nice example that can help for your question was provided by Andrew Gelman and David K. Park (2012). Let's stick to your example of predicting the price of house $Y$ given it's area $X$. For this we use simple linear regression model
$$ Y = \b... | Can simple linear regression be done without using plots and linear algebra?
Nice example that can help for your question was provided by Andrew Gelman and David K. Park (2012). Let's stick to your example of predicting the price of house $Y$ given it's area $X$. For this we u |
5,362 | Can simple linear regression be done without using plots and linear algebra? | The short answer is, yes. What line goes best through the middle of all points that comprise the entirety or just the surface of an airplane or javelin? Draw it; in your head or on a picture. You are looking for and at that solitary line from which every point (of interest, whether you plot them or not) that would c... | Can simple linear regression be done without using plots and linear algebra? | The short answer is, yes. What line goes best through the middle of all points that comprise the entirety or just the surface of an airplane or javelin? Draw it; in your head or on a picture. You a | Can simple linear regression be done without using plots and linear algebra?
The short answer is, yes. What line goes best through the middle of all points that comprise the entirety or just the surface of an airplane or javelin? Draw it; in your head or on a picture. You are looking for and at that solitary line fr... | Can simple linear regression be done without using plots and linear algebra?
The short answer is, yes. What line goes best through the middle of all points that comprise the entirety or just the surface of an airplane or javelin? Draw it; in your head or on a picture. You a |
5,363 | Can simple linear regression be done without using plots and linear algebra? | Have you encountered the sort of toaster you often get in hotels. You put bread on a conveyor belt at one end and it comes out as toast at the other.
Unfortunately, in the toaster at this cheap hotel, the heaters have all got moved to random heights and distances from the entrance to the toaster. You cannot move the he... | Can simple linear regression be done without using plots and linear algebra? | Have you encountered the sort of toaster you often get in hotels. You put bread on a conveyor belt at one end and it comes out as toast at the other.
Unfortunately, in the toaster at this cheap hotel, | Can simple linear regression be done without using plots and linear algebra?
Have you encountered the sort of toaster you often get in hotels. You put bread on a conveyor belt at one end and it comes out as toast at the other.
Unfortunately, in the toaster at this cheap hotel, the heaters have all got moved to random h... | Can simple linear regression be done without using plots and linear algebra?
Have you encountered the sort of toaster you often get in hotels. You put bread on a conveyor belt at one end and it comes out as toast at the other.
Unfortunately, in the toaster at this cheap hotel, |
5,364 | Can simple linear regression be done without using plots and linear algebra? | My favorite explanation of linear regression is geometric, but not visual. It treats the data set as a single point in a high-dimensional space, rather than breaking it up into a cloud of points in two-dimensional space.
The area $a$ and price $p$ of a house are a pair of numbers, which you can think of as the coordina... | Can simple linear regression be done without using plots and linear algebra? | My favorite explanation of linear regression is geometric, but not visual. It treats the data set as a single point in a high-dimensional space, rather than breaking it up into a cloud of points in tw | Can simple linear regression be done without using plots and linear algebra?
My favorite explanation of linear regression is geometric, but not visual. It treats the data set as a single point in a high-dimensional space, rather than breaking it up into a cloud of points in two-dimensional space.
The area $a$ and price... | Can simple linear regression be done without using plots and linear algebra?
My favorite explanation of linear regression is geometric, but not visual. It treats the data set as a single point in a high-dimensional space, rather than breaking it up into a cloud of points in tw |
5,365 | Can simple linear regression be done without using plots and linear algebra? | @Chris Rackauckas and @EDM's answers are spot on. There are many ways to approach simple linear regression that don't require plotting or visual explanations of ordinary least squares estimation, and they give very solid explanations of what actually happens when you're running OLS.
I might add that using scatterplots... | Can simple linear regression be done without using plots and linear algebra? | @Chris Rackauckas and @EDM's answers are spot on. There are many ways to approach simple linear regression that don't require plotting or visual explanations of ordinary least squares estimation, and | Can simple linear regression be done without using plots and linear algebra?
@Chris Rackauckas and @EDM's answers are spot on. There are many ways to approach simple linear regression that don't require plotting or visual explanations of ordinary least squares estimation, and they give very solid explanations of what a... | Can simple linear regression be done without using plots and linear algebra?
@Chris Rackauckas and @EDM's answers are spot on. There are many ways to approach simple linear regression that don't require plotting or visual explanations of ordinary least squares estimation, and |
5,366 | Can simple linear regression be done without using plots and linear algebra? | Google for Anscombe Quartet.
It shows 4 sets of data which on inspecting numerically do not show much difference.
However, on creating a visual scatter plot, the differences become dramatically
visible.
It gives a pretty clear view why you should always plot your data, regression or no regression :-) | Can simple linear regression be done without using plots and linear algebra? | Google for Anscombe Quartet.
It shows 4 sets of data which on inspecting numerically do not show much difference.
However, on creating a visual scatter plot, the differences become dramatically
visib | Can simple linear regression be done without using plots and linear algebra?
Google for Anscombe Quartet.
It shows 4 sets of data which on inspecting numerically do not show much difference.
However, on creating a visual scatter plot, the differences become dramatically
visible.
It gives a pretty clear view why you sh... | Can simple linear regression be done without using plots and linear algebra?
Google for Anscombe Quartet.
It shows 4 sets of data which on inspecting numerically do not show much difference.
However, on creating a visual scatter plot, the differences become dramatically
visib |
5,367 | Can simple linear regression be done without using plots and linear algebra? | We want to have a solution that minimizes the difference between the predicted and actual values.
We assume that the $y=bx+a$ i.e. there is a linear relationship.
We don't care whether the difference between predicted and actual $y$ is positive or negative assume that distribution of errors of $y$ posses certain prope... | Can simple linear regression be done without using plots and linear algebra? | We want to have a solution that minimizes the difference between the predicted and actual values.
We assume that the $y=bx+a$ i.e. there is a linear relationship.
We don't care whether the difference | Can simple linear regression be done without using plots and linear algebra?
We want to have a solution that minimizes the difference between the predicted and actual values.
We assume that the $y=bx+a$ i.e. there is a linear relationship.
We don't care whether the difference between predicted and actual $y$ is positi... | Can simple linear regression be done without using plots and linear algebra?
We want to have a solution that minimizes the difference between the predicted and actual values.
We assume that the $y=bx+a$ i.e. there is a linear relationship.
We don't care whether the difference |
5,368 | Can simple linear regression be done without using plots and linear algebra? | I'm coming late to this conversation but I just want to add something that I think might aid understanding.
The computation for finding the OLS estimator relies on math from linear algebra involving matrices. It's my understanding there are a few different ways to do this. A = QR shows how to create an orthonormal matr... | Can simple linear regression be done without using plots and linear algebra? | I'm coming late to this conversation but I just want to add something that I think might aid understanding.
The computation for finding the OLS estimator relies on math from linear algebra involving m | Can simple linear regression be done without using plots and linear algebra?
I'm coming late to this conversation but I just want to add something that I think might aid understanding.
The computation for finding the OLS estimator relies on math from linear algebra involving matrices. It's my understanding there are a ... | Can simple linear regression be done without using plots and linear algebra?
I'm coming late to this conversation but I just want to add something that I think might aid understanding.
The computation for finding the OLS estimator relies on math from linear algebra involving m |
5,369 | What is the relationship between the mean squared error and the residual sum of squares function? | Actually it's mentioned in the Regression section of Mean squared error in Wikipedia:
In regression analysis, the term mean squared error is sometimes used
to refer to the unbiased estimate of error variance: the residual sum
of squares divided by the number of degrees of freedom.
You can also find some informati... | What is the relationship between the mean squared error and the residual sum of squares function? | Actually it's mentioned in the Regression section of Mean squared error in Wikipedia:
In regression analysis, the term mean squared error is sometimes used
to refer to the unbiased estimate of erro | What is the relationship between the mean squared error and the residual sum of squares function?
Actually it's mentioned in the Regression section of Mean squared error in Wikipedia:
In regression analysis, the term mean squared error is sometimes used
to refer to the unbiased estimate of error variance: the residu... | What is the relationship between the mean squared error and the residual sum of squares function?
Actually it's mentioned in the Regression section of Mean squared error in Wikipedia:
In regression analysis, the term mean squared error is sometimes used
to refer to the unbiased estimate of erro |
5,370 | What is the relationship between the mean squared error and the residual sum of squares function? | But be aware that Sum of Squared Errors (SSE) and Residue Sum of Squares (RSS) sometimes are used interchangeably, thus confusing the readers. For instance, check this URL out.
Strictly speaking from statistic point of views, Errors and Residues are completely different concepts. Errors mainly refer to difference betwe... | What is the relationship between the mean squared error and the residual sum of squares function? | But be aware that Sum of Squared Errors (SSE) and Residue Sum of Squares (RSS) sometimes are used interchangeably, thus confusing the readers. For instance, check this URL out.
Strictly speaking from | What is the relationship between the mean squared error and the residual sum of squares function?
But be aware that Sum of Squared Errors (SSE) and Residue Sum of Squares (RSS) sometimes are used interchangeably, thus confusing the readers. For instance, check this URL out.
Strictly speaking from statistic point of vie... | What is the relationship between the mean squared error and the residual sum of squares function?
But be aware that Sum of Squared Errors (SSE) and Residue Sum of Squares (RSS) sometimes are used interchangeably, thus confusing the readers. For instance, check this URL out.
Strictly speaking from |
5,371 | What is the relationship between the mean squared error and the residual sum of squares function? | I don´t think this is correct here if we consider MSE to be the sqaure of RMSE. For instance, you have a series of sampled data on predictions and observations, now you try to do a linear regresion: Observation (O)= a + b X Prediction (P). In this case, the MSE is the sum of squared difference between O and P and divid... | What is the relationship between the mean squared error and the residual sum of squares function? | I don´t think this is correct here if we consider MSE to be the sqaure of RMSE. For instance, you have a series of sampled data on predictions and observations, now you try to do a linear regresion: O | What is the relationship between the mean squared error and the residual sum of squares function?
I don´t think this is correct here if we consider MSE to be the sqaure of RMSE. For instance, you have a series of sampled data on predictions and observations, now you try to do a linear regresion: Observation (O)= a + b ... | What is the relationship between the mean squared error and the residual sum of squares function?
I don´t think this is correct here if we consider MSE to be the sqaure of RMSE. For instance, you have a series of sampled data on predictions and observations, now you try to do a linear regresion: O |
5,372 | Is regression with L1 regularization the same as Lasso, and with L2 regularization the same as ridge regression? And how to write "Lasso"? | Yes.
Yes.
LASSO is actually an acronym (least absolute shrinkage and selection operator), so it ought to be capitalized, but modern writing is the lexical equivalent of Mad Max. On the other hand, Amoeba writes that even the statisticians who coined the term LASSO now use the lower-case rendering (Hastie, Tibshirani an... | Is regression with L1 regularization the same as Lasso, and with L2 regularization the same as ridge | Yes.
Yes.
LASSO is actually an acronym (least absolute shrinkage and selection operator), so it ought to be capitalized, but modern writing is the lexical equivalent of Mad Max. On the other hand, Amo | Is regression with L1 regularization the same as Lasso, and with L2 regularization the same as ridge regression? And how to write "Lasso"?
Yes.
Yes.
LASSO is actually an acronym (least absolute shrinkage and selection operator), so it ought to be capitalized, but modern writing is the lexical equivalent of Mad Max. On ... | Is regression with L1 regularization the same as Lasso, and with L2 regularization the same as ridge
Yes.
Yes.
LASSO is actually an acronym (least absolute shrinkage and selection operator), so it ought to be capitalized, but modern writing is the lexical equivalent of Mad Max. On the other hand, Amo |
5,373 | Logistic regression model does not converge | glm() uses an iterative re-weighted least squares algorithm. The algorithm hit the maximum number of allowed iterations before signalling convergence. The default, documented in ?glm.control is 25. You pass control parameters as a list in the glm call:
delay.model <- glm(BigDelay ~ ArrDelay, data=flights, family=binomi... | Logistic regression model does not converge | glm() uses an iterative re-weighted least squares algorithm. The algorithm hit the maximum number of allowed iterations before signalling convergence. The default, documented in ?glm.control is 25. Yo | Logistic regression model does not converge
glm() uses an iterative re-weighted least squares algorithm. The algorithm hit the maximum number of allowed iterations before signalling convergence. The default, documented in ?glm.control is 25. You pass control parameters as a list in the glm call:
delay.model <- glm(BigD... | Logistic regression model does not converge
glm() uses an iterative re-weighted least squares algorithm. The algorithm hit the maximum number of allowed iterations before signalling convergence. The default, documented in ?glm.control is 25. Yo |
5,374 | Logistic regression model does not converge | You could try to check if Firth's bias reduction works with your dataset. It is a penalized likelihood approach that can be useful for datasets which produce divergences using the standard glm package. Sometimes it can be used instead of eliminating that variable which produces complete/almost complete separation.
For ... | Logistic regression model does not converge | You could try to check if Firth's bias reduction works with your dataset. It is a penalized likelihood approach that can be useful for datasets which produce divergences using the standard glm package | Logistic regression model does not converge
You could try to check if Firth's bias reduction works with your dataset. It is a penalized likelihood approach that can be useful for datasets which produce divergences using the standard glm package. Sometimes it can be used instead of eliminating that variable which produc... | Logistic regression model does not converge
You could try to check if Firth's bias reduction works with your dataset. It is a penalized likelihood approach that can be useful for datasets which produce divergences using the standard glm package |
5,375 | scale a number between a range [duplicate] | Your scaling will need to take into account the possible range of the original number. There is a difference if your 200 could have been in the range [200,201] or in [0,200] or in [0,10000].
So let
$r_{\text{min}}$ denote the minimum of the range of your measurement
$r_{\text{max}}$ denote the maximum of the range of... | scale a number between a range [duplicate] | Your scaling will need to take into account the possible range of the original number. There is a difference if your 200 could have been in the range [200,201] or in [0,200] or in [0,10000].
So let
| scale a number between a range [duplicate]
Your scaling will need to take into account the possible range of the original number. There is a difference if your 200 could have been in the range [200,201] or in [0,200] or in [0,10000].
So let
$r_{\text{min}}$ denote the minimum of the range of your measurement
$r_{\tex... | scale a number between a range [duplicate]
Your scaling will need to take into account the possible range of the original number. There is a difference if your 200 could have been in the range [200,201] or in [0,200] or in [0,10000].
So let
|
5,376 | scale a number between a range [duplicate] | In general, to scale your variable $x$ into a range $[a,b]$ you can use:
$$
x_{normalized} = (b-a)\frac{x - min(x)}{max(x) - min(x)} + a
$$ | scale a number between a range [duplicate] | In general, to scale your variable $x$ into a range $[a,b]$ you can use:
$$
x_{normalized} = (b-a)\frac{x - min(x)}{max(x) - min(x)} + a
$$ | scale a number between a range [duplicate]
In general, to scale your variable $x$ into a range $[a,b]$ you can use:
$$
x_{normalized} = (b-a)\frac{x - min(x)}{max(x) - min(x)} + a
$$ | scale a number between a range [duplicate]
In general, to scale your variable $x$ into a range $[a,b]$ you can use:
$$
x_{normalized} = (b-a)\frac{x - min(x)}{max(x) - min(x)} + a
$$ |
5,377 | Why don't linear regression assumptions matter in machine learning? | It’s because statistics puts an emphasis on model inference, while machine learning puts an emphasis on accurate predictions.
We like normal residuals in linear regression because then the usual $\hat{\beta}=(X^TX)^{-1}X^Ty$ is a maximum likelihood estimator.
We like uncorrelated predictors because then we get tighter ... | Why don't linear regression assumptions matter in machine learning? | It’s because statistics puts an emphasis on model inference, while machine learning puts an emphasis on accurate predictions.
We like normal residuals in linear regression because then the usual $\hat | Why don't linear regression assumptions matter in machine learning?
It’s because statistics puts an emphasis on model inference, while machine learning puts an emphasis on accurate predictions.
We like normal residuals in linear regression because then the usual $\hat{\beta}=(X^TX)^{-1}X^Ty$ is a maximum likelihood est... | Why don't linear regression assumptions matter in machine learning?
It’s because statistics puts an emphasis on model inference, while machine learning puts an emphasis on accurate predictions.
We like normal residuals in linear regression because then the usual $\hat |
5,378 | Why don't linear regression assumptions matter in machine learning? | The typical linear regression assumptions are required mostly to make sure your inferences are right.
For instance, suppose you want to check if a certain predictor is associated with your target variable. In a linear regression setting, you would calculate the p-value associated to the coefficient of that predictor. I... | Why don't linear regression assumptions matter in machine learning? | The typical linear regression assumptions are required mostly to make sure your inferences are right.
For instance, suppose you want to check if a certain predictor is associated with your target vari | Why don't linear regression assumptions matter in machine learning?
The typical linear regression assumptions are required mostly to make sure your inferences are right.
For instance, suppose you want to check if a certain predictor is associated with your target variable. In a linear regression setting, you would calc... | Why don't linear regression assumptions matter in machine learning?
The typical linear regression assumptions are required mostly to make sure your inferences are right.
For instance, suppose you want to check if a certain predictor is associated with your target vari |
5,379 | Why don't linear regression assumptions matter in machine learning? | A linear regression is a statistical procedure that can be interpreted from both perspectives. Instead I will tackle the question of comparing linear regression (and its assumptions) to other methods.
A linear regression takes the form
$$ Y_i = X_i'\beta + \varepsilon_i$$
Texbooks usually ask you to check (i) Exogeneit... | Why don't linear regression assumptions matter in machine learning? | A linear regression is a statistical procedure that can be interpreted from both perspectives. Instead I will tackle the question of comparing linear regression (and its assumptions) to other methods. | Why don't linear regression assumptions matter in machine learning?
A linear regression is a statistical procedure that can be interpreted from both perspectives. Instead I will tackle the question of comparing linear regression (and its assumptions) to other methods.
A linear regression takes the form
$$ Y_i = X_i'\be... | Why don't linear regression assumptions matter in machine learning?
A linear regression is a statistical procedure that can be interpreted from both perspectives. Instead I will tackle the question of comparing linear regression (and its assumptions) to other methods. |
5,380 | Why don't linear regression assumptions matter in machine learning? | Assumptions do matter for regression whether it is used for inference (as is most common in statistics) or prediction (as is most common in machine learning). However, the sets of assumptions are not the same; successful prediction requires less restrictive assumptions than sensible inference does. The post "T-consiste... | Why don't linear regression assumptions matter in machine learning? | Assumptions do matter for regression whether it is used for inference (as is most common in statistics) or prediction (as is most common in machine learning). However, the sets of assumptions are not | Why don't linear regression assumptions matter in machine learning?
Assumptions do matter for regression whether it is used for inference (as is most common in statistics) or prediction (as is most common in machine learning). However, the sets of assumptions are not the same; successful prediction requires less restri... | Why don't linear regression assumptions matter in machine learning?
Assumptions do matter for regression whether it is used for inference (as is most common in statistics) or prediction (as is most common in machine learning). However, the sets of assumptions are not |
5,381 | Why don't linear regression assumptions matter in machine learning? | Even ignoring inference, the normality assumption matters for machine learning. In predictive modeling, the conditional distributions of the target variable are important. Gross non-normality indicates alternative models and/or methods are needed.
My post just focuses on the assumption of normality of the dependent (or... | Why don't linear regression assumptions matter in machine learning? | Even ignoring inference, the normality assumption matters for machine learning. In predictive modeling, the conditional distributions of the target variable are important. Gross non-normality indicate | Why don't linear regression assumptions matter in machine learning?
Even ignoring inference, the normality assumption matters for machine learning. In predictive modeling, the conditional distributions of the target variable are important. Gross non-normality indicates alternative models and/or methods are needed.
My p... | Why don't linear regression assumptions matter in machine learning?
Even ignoring inference, the normality assumption matters for machine learning. In predictive modeling, the conditional distributions of the target variable are important. Gross non-normality indicate |
5,382 | Why don't linear regression assumptions matter in machine learning? | The real answer is because most people peddling machine learning are deceptive con artists.
The curse of dimensionality precludes most complex regressions that have any sort of chaotic relationship, since you are trying to build a surface of best fit over an N-1 dimensional space. See Page 41 of David Kristjanson Duven... | Why don't linear regression assumptions matter in machine learning? | The real answer is because most people peddling machine learning are deceptive con artists.
The curse of dimensionality precludes most complex regressions that have any sort of chaotic relationship, s | Why don't linear regression assumptions matter in machine learning?
The real answer is because most people peddling machine learning are deceptive con artists.
The curse of dimensionality precludes most complex regressions that have any sort of chaotic relationship, since you are trying to build a surface of best fit o... | Why don't linear regression assumptions matter in machine learning?
The real answer is because most people peddling machine learning are deceptive con artists.
The curse of dimensionality precludes most complex regressions that have any sort of chaotic relationship, s |
5,383 | Why do people use p-values instead of computing probability of the model given data? | Computing the probability that the hypothesis is correct doesn't fit well within the frequentist definition of a probability (a long run frequency), which was adopted to avoid the supposed subjectivity of the Bayesian definition of a probability. The truth of a particular hypothesis is not a random variable, it is eit... | Why do people use p-values instead of computing probability of the model given data? | Computing the probability that the hypothesis is correct doesn't fit well within the frequentist definition of a probability (a long run frequency), which was adopted to avoid the supposed subjectivit | Why do people use p-values instead of computing probability of the model given data?
Computing the probability that the hypothesis is correct doesn't fit well within the frequentist definition of a probability (a long run frequency), which was adopted to avoid the supposed subjectivity of the Bayesian definition of a p... | Why do people use p-values instead of computing probability of the model given data?
Computing the probability that the hypothesis is correct doesn't fit well within the frequentist definition of a probability (a long run frequency), which was adopted to avoid the supposed subjectivit |
5,384 | Why do people use p-values instead of computing probability of the model given data? | Nothing like answering a really old question, but here goes....
p-values are almost valid hypothesis tests. This is a slightly adapted exerpt taken from Jaynes's 2003 probability theory book (Repetitive experiments: probability and frequency). Suppose we have a null hypothesis $H_0$ that we wish to test. We have dat... | Why do people use p-values instead of computing probability of the model given data? | Nothing like answering a really old question, but here goes....
p-values are almost valid hypothesis tests. This is a slightly adapted exerpt taken from Jaynes's 2003 probability theory book (Repetit | Why do people use p-values instead of computing probability of the model given data?
Nothing like answering a really old question, but here goes....
p-values are almost valid hypothesis tests. This is a slightly adapted exerpt taken from Jaynes's 2003 probability theory book (Repetitive experiments: probability and fr... | Why do people use p-values instead of computing probability of the model given data?
Nothing like answering a really old question, but here goes....
p-values are almost valid hypothesis tests. This is a slightly adapted exerpt taken from Jaynes's 2003 probability theory book (Repetit |
5,385 | Why do people use p-values instead of computing probability of the model given data? | Your question is a great example of frequentist reasoning and is, actually quite natural. I've used this example in my classes to demonstrate the nature of hypothesis tests. I ask for a volunteer to predict the results of a coin flip. No matter what the result, I record a "correct" guess. We do this repeatedly unti... | Why do people use p-values instead of computing probability of the model given data? | Your question is a great example of frequentist reasoning and is, actually quite natural. I've used this example in my classes to demonstrate the nature of hypothesis tests. I ask for a volunteer to | Why do people use p-values instead of computing probability of the model given data?
Your question is a great example of frequentist reasoning and is, actually quite natural. I've used this example in my classes to demonstrate the nature of hypothesis tests. I ask for a volunteer to predict the results of a coin flip... | Why do people use p-values instead of computing probability of the model given data?
Your question is a great example of frequentist reasoning and is, actually quite natural. I've used this example in my classes to demonstrate the nature of hypothesis tests. I ask for a volunteer to |
5,386 | Why do people use p-values instead of computing probability of the model given data? | As a former academic who moved into practice, I'll take a shot. People use p-values because they are useful. You can't see it in textbooky examples of coin flips. Sure they're not really solid foundationally, but maybe that is not as necessary as we like to think when we're thinking academically.
In the world of data, ... | Why do people use p-values instead of computing probability of the model given data? | As a former academic who moved into practice, I'll take a shot. People use p-values because they are useful. You can't see it in textbooky examples of coin flips. Sure they're not really solid foundat | Why do people use p-values instead of computing probability of the model given data?
As a former academic who moved into practice, I'll take a shot. People use p-values because they are useful. You can't see it in textbooky examples of coin flips. Sure they're not really solid foundationally, but maybe that is not as n... | Why do people use p-values instead of computing probability of the model given data?
As a former academic who moved into practice, I'll take a shot. People use p-values because they are useful. You can't see it in textbooky examples of coin flips. Sure they're not really solid foundat |
5,387 | Why do people use p-values instead of computing probability of the model given data? | "Roughly speaking p-value gives a probability of the observed outcome of an experiment given the hypothesis (model)."
but it doesn't. Not even roughly - this fudges an essential distinction.
The model is not specified, as Raskolnikov points out, but let's assume you mean a binomial model (independent coin tosses, fixe... | Why do people use p-values instead of computing probability of the model given data? | "Roughly speaking p-value gives a probability of the observed outcome of an experiment given the hypothesis (model)."
but it doesn't. Not even roughly - this fudges an essential distinction.
The mode | Why do people use p-values instead of computing probability of the model given data?
"Roughly speaking p-value gives a probability of the observed outcome of an experiment given the hypothesis (model)."
but it doesn't. Not even roughly - this fudges an essential distinction.
The model is not specified, as Raskolnikov ... | Why do people use p-values instead of computing probability of the model given data?
"Roughly speaking p-value gives a probability of the observed outcome of an experiment given the hypothesis (model)."
but it doesn't. Not even roughly - this fudges an essential distinction.
The mode |
5,388 | Why do people use p-values instead of computing probability of the model given data? | A side note to the other excellent answers: on occasion there are times we don't. For example, up until very recently, they were outright banned at the journal Epidemiology - now they are merely "strongly discouraged" and the editorial board devoted a tremendous amount of space to a discussion of them here: http://jour... | Why do people use p-values instead of computing probability of the model given data? | A side note to the other excellent answers: on occasion there are times we don't. For example, up until very recently, they were outright banned at the journal Epidemiology - now they are merely "stro | Why do people use p-values instead of computing probability of the model given data?
A side note to the other excellent answers: on occasion there are times we don't. For example, up until very recently, they were outright banned at the journal Epidemiology - now they are merely "strongly discouraged" and the editorial... | Why do people use p-values instead of computing probability of the model given data?
A side note to the other excellent answers: on occasion there are times we don't. For example, up until very recently, they were outright banned at the journal Epidemiology - now they are merely "stro |
5,389 | Why do people use p-values instead of computing probability of the model given data? | I will only add a few remarks; I agree with you that the overuse of $p$-values is harmful.
Some people in applied stats misinterpret $p$-values, notably understanding them as the probability that the null
hypotheses is true; cf these papers: P Values are not Error Probabilities and Why We Don’t Really Know What "Stat... | Why do people use p-values instead of computing probability of the model given data? | I will only add a few remarks; I agree with you that the overuse of $p$-values is harmful.
Some people in applied stats misinterpret $p$-values, notably understanding them as the probability that the | Why do people use p-values instead of computing probability of the model given data?
I will only add a few remarks; I agree with you that the overuse of $p$-values is harmful.
Some people in applied stats misinterpret $p$-values, notably understanding them as the probability that the null
hypotheses is true; cf these... | Why do people use p-values instead of computing probability of the model given data?
I will only add a few remarks; I agree with you that the overuse of $p$-values is harmful.
Some people in applied stats misinterpret $p$-values, notably understanding them as the probability that the |
5,390 | Why do people use p-values instead of computing probability of the model given data? | Define probability. I mean it. Before we progress any further, we need to settle on terms.
An intuitive definition of probability is a measure of uncertainty. We are uncertain whether the next coin toss will come up heads or tails. That is uncertainty in the data $D$. We are also uncertain whether the coin is fair or n... | Why do people use p-values instead of computing probability of the model given data? | Define probability. I mean it. Before we progress any further, we need to settle on terms.
An intuitive definition of probability is a measure of uncertainty. We are uncertain whether the next coin to | Why do people use p-values instead of computing probability of the model given data?
Define probability. I mean it. Before we progress any further, we need to settle on terms.
An intuitive definition of probability is a measure of uncertainty. We are uncertain whether the next coin toss will come up heads or tails. Tha... | Why do people use p-values instead of computing probability of the model given data?
Define probability. I mean it. Before we progress any further, we need to settle on terms.
An intuitive definition of probability is a measure of uncertainty. We are uncertain whether the next coin to |
5,391 | Why do people use p-values instead of computing probability of the model given data? | But if we want to estimate the probability of the model, why don't we calculate the probability of the model given the experiment?
Because we don't know how. There's infinite number of model possible, and their probability space is not defined.
Here's a practical example. Let's say I want to forecast US GDP. I get the... | Why do people use p-values instead of computing probability of the model given data? | But if we want to estimate the probability of the model, why don't we calculate the probability of the model given the experiment?
Because we don't know how. There's infinite number of model possible | Why do people use p-values instead of computing probability of the model given data?
But if we want to estimate the probability of the model, why don't we calculate the probability of the model given the experiment?
Because we don't know how. There's infinite number of model possible, and their probability space is no... | Why do people use p-values instead of computing probability of the model given data?
But if we want to estimate the probability of the model, why don't we calculate the probability of the model given the experiment?
Because we don't know how. There's infinite number of model possible |
5,392 | Why do people use p-values instead of computing probability of the model given data? | IMHO, confidence intervals are a better method of expressing results. This is especially true when comparing results to be included in meta analysis and for "not significant" answers. This avoids the all too common misrepresentation of not significant results as significantly insignificant. I don't know in which "camp"... | Why do people use p-values instead of computing probability of the model given data? | IMHO, confidence intervals are a better method of expressing results. This is especially true when comparing results to be included in meta analysis and for "not significant" answers. This avoids the | Why do people use p-values instead of computing probability of the model given data?
IMHO, confidence intervals are a better method of expressing results. This is especially true when comparing results to be included in meta analysis and for "not significant" answers. This avoids the all too common misrepresentation of... | Why do people use p-values instead of computing probability of the model given data?
IMHO, confidence intervals are a better method of expressing results. This is especially true when comparing results to be included in meta analysis and for "not significant" answers. This avoids the |
5,393 | How do I avoid overlapping labels in an R plot? [closed] | Check out the new package ggrepel.
ggrepel provides geoms for ggplot2 to repel overlapping text labels. It works both for geom_text and geom_label.
Figure is taken from this blog post. | How do I avoid overlapping labels in an R plot? [closed] | Check out the new package ggrepel.
ggrepel provides geoms for ggplot2 to repel overlapping text labels. It works both for geom_text and geom_label.
Figure is taken from this blog post. | How do I avoid overlapping labels in an R plot? [closed]
Check out the new package ggrepel.
ggrepel provides geoms for ggplot2 to repel overlapping text labels. It works both for geom_text and geom_label.
Figure is taken from this blog post. | How do I avoid overlapping labels in an R plot? [closed]
Check out the new package ggrepel.
ggrepel provides geoms for ggplot2 to repel overlapping text labels. It works both for geom_text and geom_label.
Figure is taken from this blog post. |
5,394 | How do I avoid overlapping labels in an R plot? [closed] | The directlabels package does that. From its web page:
This package is an attempt to make direct labeling a reality in
everyday statistical practice by making available a body of useful
functions that make direct labeling of common plots easy to do with
high-level plotting systems such as lattice and ggplot2.
I... | How do I avoid overlapping labels in an R plot? [closed] | The directlabels package does that. From its web page:
This package is an attempt to make direct labeling a reality in
everyday statistical practice by making available a body of useful
functions | How do I avoid overlapping labels in an R plot? [closed]
The directlabels package does that. From its web page:
This package is an attempt to make direct labeling a reality in
everyday statistical practice by making available a body of useful
functions that make direct labeling of common plots easy to do with
hi... | How do I avoid overlapping labels in an R plot? [closed]
The directlabels package does that. From its web page:
This package is an attempt to make direct labeling a reality in
everyday statistical practice by making available a body of useful
functions |
5,395 | How do I avoid overlapping labels in an R plot? [closed] | I'd suggest you take a look at the wordcloud package. I know this package focuses not exactly on the points but on the labels themselves, and also the style seems to be rather fixed. But still, the results I got from using it were pretty stunning. Also note that the package version in question was released about the ti... | How do I avoid overlapping labels in an R plot? [closed] | I'd suggest you take a look at the wordcloud package. I know this package focuses not exactly on the points but on the labels themselves, and also the style seems to be rather fixed. But still, the re | How do I avoid overlapping labels in an R plot? [closed]
I'd suggest you take a look at the wordcloud package. I know this package focuses not exactly on the points but on the labels themselves, and also the style seems to be rather fixed. But still, the results I got from using it were pretty stunning. Also note that ... | How do I avoid overlapping labels in an R plot? [closed]
I'd suggest you take a look at the wordcloud package. I know this package focuses not exactly on the points but on the labels themselves, and also the style seems to be rather fixed. But still, the re |
5,396 | How do I avoid overlapping labels in an R plot? [closed] | I ran into a similar problem with several of the plots I have been working with and wrote a basic package that uses force field simulation to adjust object locations. The advantage over some of the above-cited solutions is the dynamic adjustment for relative object proximity in 2D. While much improvement is possible, ... | How do I avoid overlapping labels in an R plot? [closed] | I ran into a similar problem with several of the plots I have been working with and wrote a basic package that uses force field simulation to adjust object locations. The advantage over some of the ab | How do I avoid overlapping labels in an R plot? [closed]
I ran into a similar problem with several of the plots I have been working with and wrote a basic package that uses force field simulation to adjust object locations. The advantage over some of the above-cited solutions is the dynamic adjustment for relative obje... | How do I avoid overlapping labels in an R plot? [closed]
I ran into a similar problem with several of the plots I have been working with and wrote a basic package that uses force field simulation to adjust object locations. The advantage over some of the ab |
5,397 | How do I avoid overlapping labels in an R plot? [closed] | In the event that you simply cannot get the labels to work correctly as produced by R, keep in mind you can always save the graphs in a vector format (like .pdf) and pull them into an editing program like InkScape or Adobe Illustrator. | How do I avoid overlapping labels in an R plot? [closed] | In the event that you simply cannot get the labels to work correctly as produced by R, keep in mind you can always save the graphs in a vector format (like .pdf) and pull them into an editing program | How do I avoid overlapping labels in an R plot? [closed]
In the event that you simply cannot get the labels to work correctly as produced by R, keep in mind you can always save the graphs in a vector format (like .pdf) and pull them into an editing program like InkScape or Adobe Illustrator. | How do I avoid overlapping labels in an R plot? [closed]
In the event that you simply cannot get the labels to work correctly as produced by R, keep in mind you can always save the graphs in a vector format (like .pdf) and pull them into an editing program |
5,398 | How do I avoid overlapping labels in an R plot? [closed] | A couple of additional tools to look at in R:
The spread.labels function in the plotrix package
thigmophobe.labels in the plotrix package
the spread.labs function in the TeachingDemos package
the TkIdentify function in the TeachingDemos package
These won't do everything for you, but one of them may be part of a solu... | How do I avoid overlapping labels in an R plot? [closed] | A couple of additional tools to look at in R:
The spread.labels function in the plotrix package
thigmophobe.labels in the plotrix package
the spread.labs function in the TeachingDemos package
the Tk | How do I avoid overlapping labels in an R plot? [closed]
A couple of additional tools to look at in R:
The spread.labels function in the plotrix package
thigmophobe.labels in the plotrix package
the spread.labs function in the TeachingDemos package
the TkIdentify function in the TeachingDemos package
These won't do ... | How do I avoid overlapping labels in an R plot? [closed]
A couple of additional tools to look at in R:
The spread.labels function in the plotrix package
thigmophobe.labels in the plotrix package
the spread.labs function in the TeachingDemos package
the Tk |
5,399 | AIC guidelines in model selection | AIC and BIC hold the same interpretation in terms of model comparison. That is, the larger difference in either AIC or BIC indicates stronger evidence for one model over the other (the lower the better). It's just the the AIC doesn't penalize the number of parameters as strongly as BIC. There is also a correction to th... | AIC guidelines in model selection | AIC and BIC hold the same interpretation in terms of model comparison. That is, the larger difference in either AIC or BIC indicates stronger evidence for one model over the other (the lower the bette | AIC guidelines in model selection
AIC and BIC hold the same interpretation in terms of model comparison. That is, the larger difference in either AIC or BIC indicates stronger evidence for one model over the other (the lower the better). It's just the the AIC doesn't penalize the number of parameters as strongly as BIC... | AIC guidelines in model selection
AIC and BIC hold the same interpretation in terms of model comparison. That is, the larger difference in either AIC or BIC indicates stronger evidence for one model over the other (the lower the bette |
5,400 | AIC guidelines in model selection | You are talking about two different things and you are mixing them up. In the first case you have two models (1 and 2) and you obtained their AIC like $AIC_1$ and $AIC_2$. IF you want to compare these two models based on their AIC's, then model with lower AIC would be the preferred one i.e. if $AIC_1< AIC_2$ then you ... | AIC guidelines in model selection | You are talking about two different things and you are mixing them up. In the first case you have two models (1 and 2) and you obtained their AIC like $AIC_1$ and $AIC_2$. IF you want to compare these | AIC guidelines in model selection
You are talking about two different things and you are mixing them up. In the first case you have two models (1 and 2) and you obtained their AIC like $AIC_1$ and $AIC_2$. IF you want to compare these two models based on their AIC's, then model with lower AIC would be the preferred one... | AIC guidelines in model selection
You are talking about two different things and you are mixing them up. In the first case you have two models (1 and 2) and you obtained their AIC like $AIC_1$ and $AIC_2$. IF you want to compare these |
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