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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3,701 | What is the difference between estimation and prediction? | "Prediction" and "estimation" indeed are sometimes used interchangeably in non-technical writing and they seem to function similarly, but there is a sharp distinction between them in the standard model of a statistical problem. An estimator uses data to guess at a parameter while a predictor uses the data to guess at ... | What is the difference between estimation and prediction? | "Prediction" and "estimation" indeed are sometimes used interchangeably in non-technical writing and they seem to function similarly, but there is a sharp distinction between them in the standard mode | What is the difference between estimation and prediction?
"Prediction" and "estimation" indeed are sometimes used interchangeably in non-technical writing and they seem to function similarly, but there is a sharp distinction between them in the standard model of a statistical problem. An estimator uses data to guess a... | What is the difference between estimation and prediction?
"Prediction" and "estimation" indeed are sometimes used interchangeably in non-technical writing and they seem to function similarly, but there is a sharp distinction between them in the standard mode |
3,702 | What is the difference between estimation and prediction? | Estimation is always for unknown parameter whereas prediction is for random variable. | What is the difference between estimation and prediction? | Estimation is always for unknown parameter whereas prediction is for random variable. | What is the difference between estimation and prediction?
Estimation is always for unknown parameter whereas prediction is for random variable. | What is the difference between estimation and prediction?
Estimation is always for unknown parameter whereas prediction is for random variable. |
3,703 | What is the difference between estimation and prediction? | There is no difference in the models. There is indeed a (slight) difference in the action conducted. Estimation is the calibration of your probabilistic model using data ("learning" in the AI terminology). Prediction is the "guessing" of a future observation. Assuming this "guessing" is based on past data- this might b... | What is the difference between estimation and prediction? | There is no difference in the models. There is indeed a (slight) difference in the action conducted. Estimation is the calibration of your probabilistic model using data ("learning" in the AI terminol | What is the difference between estimation and prediction?
There is no difference in the models. There is indeed a (slight) difference in the action conducted. Estimation is the calibration of your probabilistic model using data ("learning" in the AI terminology). Prediction is the "guessing" of a future observation. As... | What is the difference between estimation and prediction?
There is no difference in the models. There is indeed a (slight) difference in the action conducted. Estimation is the calibration of your probabilistic model using data ("learning" in the AI terminol |
3,704 | What is the difference between estimation and prediction? | Usually "estimation" is reserved for parameters and the "predicition" is for values. However, sometimes the distinction gets blurred, e.g. you may have seen something like "estimate the value tomorrow" instead of "predict the value tomorrow."
The value-at-risk (VaR) is an interesting case. VaR is not a parameter, but w... | What is the difference between estimation and prediction? | Usually "estimation" is reserved for parameters and the "predicition" is for values. However, sometimes the distinction gets blurred, e.g. you may have seen something like "estimate the value tomorrow | What is the difference between estimation and prediction?
Usually "estimation" is reserved for parameters and the "predicition" is for values. However, sometimes the distinction gets blurred, e.g. you may have seen something like "estimate the value tomorrow" instead of "predict the value tomorrow."
The value-at-risk (... | What is the difference between estimation and prediction?
Usually "estimation" is reserved for parameters and the "predicition" is for values. However, sometimes the distinction gets blurred, e.g. you may have seen something like "estimate the value tomorrow |
3,705 | What is the difference between estimation and prediction? | Prediction is the use of sample regression function to estimate a value for the dependent variable conditioned on some an unobserved values of the independent variable.
Estimation is the process or technique of calculating an unknown parameter or quantity of the population. | What is the difference between estimation and prediction? | Prediction is the use of sample regression function to estimate a value for the dependent variable conditioned on some an unobserved values of the independent variable.
Estimation is the process or te | What is the difference between estimation and prediction?
Prediction is the use of sample regression function to estimate a value for the dependent variable conditioned on some an unobserved values of the independent variable.
Estimation is the process or technique of calculating an unknown parameter or quantity of the... | What is the difference between estimation and prediction?
Prediction is the use of sample regression function to estimate a value for the dependent variable conditioned on some an unobserved values of the independent variable.
Estimation is the process or te |
3,706 | What is the difference between estimation and prediction? | I find below definitions more explanatory:
Estimation is the calculated approximation of a result. This result might be a forecast but not necessarily. For example, I can estimate that the number of cars on the Golden Gate Bridge at 5 PM yesterday was 900 by assuming the three lanes going toward Marin were at capacity,... | What is the difference between estimation and prediction? | I find below definitions more explanatory:
Estimation is the calculated approximation of a result. This result might be a forecast but not necessarily. For example, I can estimate that the number of c | What is the difference between estimation and prediction?
I find below definitions more explanatory:
Estimation is the calculated approximation of a result. This result might be a forecast but not necessarily. For example, I can estimate that the number of cars on the Golden Gate Bridge at 5 PM yesterday was 900 by ass... | What is the difference between estimation and prediction?
I find below definitions more explanatory:
Estimation is the calculated approximation of a result. This result might be a forecast but not necessarily. For example, I can estimate that the number of c |
3,707 | Binary classification with strongly unbalanced classes | Both hxd1011 and Frank are right (+1).
Essentially resampling and/or cost-sensitive learning are the two main ways of getting around the problem of imbalanced data; third is to use kernel methods that sometimes might be less effected by the class imbalance.
Let me stress that there is no silver-bullet solution. By def... | Binary classification with strongly unbalanced classes | Both hxd1011 and Frank are right (+1).
Essentially resampling and/or cost-sensitive learning are the two main ways of getting around the problem of imbalanced data; third is to use kernel methods tha | Binary classification with strongly unbalanced classes
Both hxd1011 and Frank are right (+1).
Essentially resampling and/or cost-sensitive learning are the two main ways of getting around the problem of imbalanced data; third is to use kernel methods that sometimes might be less effected by the class imbalance.
Let me... | Binary classification with strongly unbalanced classes
Both hxd1011 and Frank are right (+1).
Essentially resampling and/or cost-sensitive learning are the two main ways of getting around the problem of imbalanced data; third is to use kernel methods tha |
3,708 | Binary classification with strongly unbalanced classes | First, the evaluation metric for imbalanced data would not be accuracy. Suppose you are doing fraud detection, that 99.9% of your data is not fraud. We can easy make a dummy model that have 99.9% accuracy. (just predict all data non-fraud).
You want to change your evaluation metric from accuracy to something else, such... | Binary classification with strongly unbalanced classes | First, the evaluation metric for imbalanced data would not be accuracy. Suppose you are doing fraud detection, that 99.9% of your data is not fraud. We can easy make a dummy model that have 99.9% accu | Binary classification with strongly unbalanced classes
First, the evaluation metric for imbalanced data would not be accuracy. Suppose you are doing fraud detection, that 99.9% of your data is not fraud. We can easy make a dummy model that have 99.9% accuracy. (just predict all data non-fraud).
You want to change your ... | Binary classification with strongly unbalanced classes
First, the evaluation metric for imbalanced data would not be accuracy. Suppose you are doing fraud detection, that 99.9% of your data is not fraud. We can easy make a dummy model that have 99.9% accu |
3,709 | Binary classification with strongly unbalanced classes | Class imbalance issues can be addressed with either cost-sensitive learning or resampling. See advantages and disadvantages of cost-sensitive learning vs. sampling, copypasted below:
{1} gives a list of advantages and disadvantages of cost-sensitive learning vs. sampling:
2.2 Sampling
Oversampling and undersampling c... | Binary classification with strongly unbalanced classes | Class imbalance issues can be addressed with either cost-sensitive learning or resampling. See advantages and disadvantages of cost-sensitive learning vs. sampling, copypasted below:
{1} gives a list | Binary classification with strongly unbalanced classes
Class imbalance issues can be addressed with either cost-sensitive learning or resampling. See advantages and disadvantages of cost-sensitive learning vs. sampling, copypasted below:
{1} gives a list of advantages and disadvantages of cost-sensitive learning vs. s... | Binary classification with strongly unbalanced classes
Class imbalance issues can be addressed with either cost-sensitive learning or resampling. See advantages and disadvantages of cost-sensitive learning vs. sampling, copypasted below:
{1} gives a list |
3,710 | Binary classification with strongly unbalanced classes | Several answers to this query have already provided several different approaches, all valid. This suggestion is from a paper and associated software by Gary King, eminent political scientist at Harvard. He has co-authored a paper titled Logistic Regression in Rare Events Data which provides some fairly cogent solutions... | Binary classification with strongly unbalanced classes | Several answers to this query have already provided several different approaches, all valid. This suggestion is from a paper and associated software by Gary King, eminent political scientist at Harvar | Binary classification with strongly unbalanced classes
Several answers to this query have already provided several different approaches, all valid. This suggestion is from a paper and associated software by Gary King, eminent political scientist at Harvard. He has co-authored a paper titled Logistic Regression in Rare ... | Binary classification with strongly unbalanced classes
Several answers to this query have already provided several different approaches, all valid. This suggestion is from a paper and associated software by Gary King, eminent political scientist at Harvar |
3,711 | Binary classification with strongly unbalanced classes | I have to disagree with all of the answers. The original problem is not appropriate for classification at all but calls for an analysis of tendencies. See http://fharrell.com/post/classification
Miscasting the task as a classification task is what has caused so much work for everyone, and has caused invalid statistic... | Binary classification with strongly unbalanced classes | I have to disagree with all of the answers. The original problem is not appropriate for classification at all but calls for an analysis of tendencies. See http://fharrell.com/post/classification
Mis | Binary classification with strongly unbalanced classes
I have to disagree with all of the answers. The original problem is not appropriate for classification at all but calls for an analysis of tendencies. See http://fharrell.com/post/classification
Miscasting the task as a classification task is what has caused so m... | Binary classification with strongly unbalanced classes
I have to disagree with all of the answers. The original problem is not appropriate for classification at all but calls for an analysis of tendencies. See http://fharrell.com/post/classification
Mis |
3,712 | Binary classification with strongly unbalanced classes | Development of classifiers for datasets with imbalanced classes is a common problem in machine learning. Density-based methods can have significant merits over "traditional classifers" in such situation.
A density-based method estimates the unknown density $\hat{p}(x|y \in C)$, where $C$ is the most dominant class (In... | Binary classification with strongly unbalanced classes | Development of classifiers for datasets with imbalanced classes is a common problem in machine learning. Density-based methods can have significant merits over "traditional classifers" in such situati | Binary classification with strongly unbalanced classes
Development of classifiers for datasets with imbalanced classes is a common problem in machine learning. Density-based methods can have significant merits over "traditional classifers" in such situation.
A density-based method estimates the unknown density $\hat{p... | Binary classification with strongly unbalanced classes
Development of classifiers for datasets with imbalanced classes is a common problem in machine learning. Density-based methods can have significant merits over "traditional classifers" in such situati |
3,713 | Binary classification with strongly unbalanced classes | This is the sort of problem where Anomaly Detection is a useful approach. This is basically what rodrigo described in his answer, in which you determine the statistical profile of your training class, and set a probability threshold beyond which future measurements are determined not to belong to that class.
Here is a ... | Binary classification with strongly unbalanced classes | This is the sort of problem where Anomaly Detection is a useful approach. This is basically what rodrigo described in his answer, in which you determine the statistical profile of your training class, | Binary classification with strongly unbalanced classes
This is the sort of problem where Anomaly Detection is a useful approach. This is basically what rodrigo described in his answer, in which you determine the statistical profile of your training class, and set a probability threshold beyond which future measurements... | Binary classification with strongly unbalanced classes
This is the sort of problem where Anomaly Detection is a useful approach. This is basically what rodrigo described in his answer, in which you determine the statistical profile of your training class, |
3,714 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | (1) In contexts where the likelihood function is intractable (at least numerically), the use of the Bayesian approach, by means of Approximate Bayesian Computation (ABC), has gained ground over some frequentist competitors such as composite likelihoods (1, 2) or the empirical likelihood because it tends to be easier to... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | (1) In contexts where the likelihood function is intractable (at least numerically), the use of the Bayesian approach, by means of Approximate Bayesian Computation (ABC), has gained ground over some f | List of situations where a Bayesian approach is simpler, more practical, or more convenient
(1) In contexts where the likelihood function is intractable (at least numerically), the use of the Bayesian approach, by means of Approximate Bayesian Computation (ABC), has gained ground over some frequentist competitors such ... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
(1) In contexts where the likelihood function is intractable (at least numerically), the use of the Bayesian approach, by means of Approximate Bayesian Computation (ABC), has gained ground over some f |
3,715 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | As Bayesian software improves, the "easier to apply" issue becomes moot. Bayesian software is becoming packaged in easier and easier forms. A recent case in point is from an article titled, Bayesian estimation supersedes the t test. The following web site provides links to the article and software: http://www.indiana.e... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | As Bayesian software improves, the "easier to apply" issue becomes moot. Bayesian software is becoming packaged in easier and easier forms. A recent case in point is from an article titled, Bayesian e | List of situations where a Bayesian approach is simpler, more practical, or more convenient
As Bayesian software improves, the "easier to apply" issue becomes moot. Bayesian software is becoming packaged in easier and easier forms. A recent case in point is from an article titled, Bayesian estimation supersedes the t t... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
As Bayesian software improves, the "easier to apply" issue becomes moot. Bayesian software is becoming packaged in easier and easier forms. A recent case in point is from an article titled, Bayesian e |
3,716 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | I am trained in frequentist statistics (econometrics actually), but I have never had a confrontational stance towards the Bayesian approach, since my point of view is that the philosophical source of this "epic" battle was fundamentally misguided from the start (I have aired my views here). In fact I plan to also train... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | I am trained in frequentist statistics (econometrics actually), but I have never had a confrontational stance towards the Bayesian approach, since my point of view is that the philosophical source of | List of situations where a Bayesian approach is simpler, more practical, or more convenient
I am trained in frequentist statistics (econometrics actually), but I have never had a confrontational stance towards the Bayesian approach, since my point of view is that the philosophical source of this "epic" battle was funda... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
I am trained in frequentist statistics (econometrics actually), but I have never had a confrontational stance towards the Bayesian approach, since my point of view is that the philosophical source of |
3,717 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | This is a late reply, nevertheless I hope it adds something. I have been trained in telecommunication where most of the time we use the Bayesian approach.
Here is a simple example: Suppose you can transmit four possible signals of +5, +2.5, -2.5, and -5 volts. One of the signals from this set is transmitted, but the s... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | This is a late reply, nevertheless I hope it adds something. I have been trained in telecommunication where most of the time we use the Bayesian approach.
Here is a simple example: Suppose you can tr | List of situations where a Bayesian approach is simpler, more practical, or more convenient
This is a late reply, nevertheless I hope it adds something. I have been trained in telecommunication where most of the time we use the Bayesian approach.
Here is a simple example: Suppose you can transmit four possible signals... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
This is a late reply, nevertheless I hope it adds something. I have been trained in telecommunication where most of the time we use the Bayesian approach.
Here is a simple example: Suppose you can tr |
3,718 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | (2) Stress-strength models. The use of stress-strength models is popular in reliability. The basic idea consists of estimating the parameter $\theta=P(X<Y)$ where $X$ and $Y$ are random variables. Interestingly, the calculation of the profile likelihood of this parameter is quite difficult in general (even numerically ... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | (2) Stress-strength models. The use of stress-strength models is popular in reliability. The basic idea consists of estimating the parameter $\theta=P(X<Y)$ where $X$ and $Y$ are random variables. Int | List of situations where a Bayesian approach is simpler, more practical, or more convenient
(2) Stress-strength models. The use of stress-strength models is popular in reliability. The basic idea consists of estimating the parameter $\theta=P(X<Y)$ where $X$ and $Y$ are random variables. Interestingly, the calculation ... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
(2) Stress-strength models. The use of stress-strength models is popular in reliability. The basic idea consists of estimating the parameter $\theta=P(X<Y)$ where $X$ and $Y$ are random variables. Int |
3,719 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | So called 'Frequentist' statistical tests are typically equivalent to the in principle more complex Bayesian approach under certain assumptions. When these assumptions are applicable, then either approach will give the same result, so it is safe to use the easier to apply Frequentist test. The Bayesian approach is safe... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | So called 'Frequentist' statistical tests are typically equivalent to the in principle more complex Bayesian approach under certain assumptions. When these assumptions are applicable, then either appr | List of situations where a Bayesian approach is simpler, more practical, or more convenient
So called 'Frequentist' statistical tests are typically equivalent to the in principle more complex Bayesian approach under certain assumptions. When these assumptions are applicable, then either approach will give the same resu... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
So called 'Frequentist' statistical tests are typically equivalent to the in principle more complex Bayesian approach under certain assumptions. When these assumptions are applicable, then either appr |
3,720 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | (I'll try what I thought would be the most typical kind of answer.)
Let's say you have a situation where there are several variables and one response, and you know a good deal about how one of the variables ought to be related to the response, but not as much about the others.
In a situation like this, if you were t... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | (I'll try what I thought would be the most typical kind of answer.)
Let's say you have a situation where there are several variables and one response, and you know a good deal about how one of the va | List of situations where a Bayesian approach is simpler, more practical, or more convenient
(I'll try what I thought would be the most typical kind of answer.)
Let's say you have a situation where there are several variables and one response, and you know a good deal about how one of the variables ought to be related ... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
(I'll try what I thought would be the most typical kind of answer.)
Let's say you have a situation where there are several variables and one response, and you know a good deal about how one of the va |
3,721 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | Perhaps one of the most straightforward and common cases where the Bayesian approach is easier is the quantifying the uncertainty of parameters.
In this answer, I'm not referring to the interpretation of confidence intervals vs. credible intervals. For the moment, let's assume that a user is fine with using either met... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | Perhaps one of the most straightforward and common cases where the Bayesian approach is easier is the quantifying the uncertainty of parameters.
In this answer, I'm not referring to the interpretatio | List of situations where a Bayesian approach is simpler, more practical, or more convenient
Perhaps one of the most straightforward and common cases where the Bayesian approach is easier is the quantifying the uncertainty of parameters.
In this answer, I'm not referring to the interpretation of confidence intervals vs... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
Perhaps one of the most straightforward and common cases where the Bayesian approach is easier is the quantifying the uncertainty of parameters.
In this answer, I'm not referring to the interpretatio |
3,722 | List of situations where a Bayesian approach is simpler, more practical, or more convenient | An area of research in which the Bayesian methods are extremely straightforward and the Frequentist methods are extremely hard to follow is that of Optimal Design.
In a simple version of the problem, you would like to estimate a single regression coefficient of a logistic regression as efficiently as possible. You are... | List of situations where a Bayesian approach is simpler, more practical, or more convenient | An area of research in which the Bayesian methods are extremely straightforward and the Frequentist methods are extremely hard to follow is that of Optimal Design.
In a simple version of the problem, | List of situations where a Bayesian approach is simpler, more practical, or more convenient
An area of research in which the Bayesian methods are extremely straightforward and the Frequentist methods are extremely hard to follow is that of Optimal Design.
In a simple version of the problem, you would like to estimate ... | List of situations where a Bayesian approach is simpler, more practical, or more convenient
An area of research in which the Bayesian methods are extremely straightforward and the Frequentist methods are extremely hard to follow is that of Optimal Design.
In a simple version of the problem, |
3,723 | How to derive variance-covariance matrix of coefficients in linear regression | This is actually a cool question that challenges your basic understanding of a regression.
First take out any initial confusion about notation. We are looking at the regression:
$$y=b_0+b_1x+\hat{u}$$
where $b_0$ and $b_1$ are the estimators of the true $\beta_0$ and $\beta_1$, and $\hat{u}$ are the residuals of the r... | How to derive variance-covariance matrix of coefficients in linear regression | This is actually a cool question that challenges your basic understanding of a regression.
First take out any initial confusion about notation. We are looking at the regression:
$$y=b_0+b_1x+\hat{u}$ | How to derive variance-covariance matrix of coefficients in linear regression
This is actually a cool question that challenges your basic understanding of a regression.
First take out any initial confusion about notation. We are looking at the regression:
$$y=b_0+b_1x+\hat{u}$$
where $b_0$ and $b_1$ are the estimators... | How to derive variance-covariance matrix of coefficients in linear regression
This is actually a cool question that challenges your basic understanding of a regression.
First take out any initial confusion about notation. We are looking at the regression:
$$y=b_0+b_1x+\hat{u}$ |
3,724 | How to derive variance-covariance matrix of coefficients in linear regression | In your case we have
$$X'X=\begin{bmatrix}n & \sum X_i\\\sum X_i & \sum X_i^2\end{bmatrix}$$
Invert this matrix and you will get the desired result. | How to derive variance-covariance matrix of coefficients in linear regression | In your case we have
$$X'X=\begin{bmatrix}n & \sum X_i\\\sum X_i & \sum X_i^2\end{bmatrix}$$
Invert this matrix and you will get the desired result. | How to derive variance-covariance matrix of coefficients in linear regression
In your case we have
$$X'X=\begin{bmatrix}n & \sum X_i\\\sum X_i & \sum X_i^2\end{bmatrix}$$
Invert this matrix and you will get the desired result. | How to derive variance-covariance matrix of coefficients in linear regression
In your case we have
$$X'X=\begin{bmatrix}n & \sum X_i\\\sum X_i & \sum X_i^2\end{bmatrix}$$
Invert this matrix and you will get the desired result. |
3,725 | How to derive variance-covariance matrix of coefficients in linear regression | Maximum likelihood solution:
$ \mathcal{L}(\beta_0,\beta_1|\sigma,\epsilon_1,\ldots,\epsilon_n) =
\prod\limits_{i=1}^{n}\frac{1}{\sigma\sqrt{2\pi}}
\exp\!\left[-\frac{\epsilon_i^2}{2\sigma^2}\right] \mbox{, where }
\epsilon_i = \beta_0 + \beta_1 x_i - y_i$
$ \mathcal{LL}(\beta_0,\beta_1|\sigma,x_1,y_1,\ldots,x_... | How to derive variance-covariance matrix of coefficients in linear regression | Maximum likelihood solution:
$ \mathcal{L}(\beta_0,\beta_1|\sigma,\epsilon_1,\ldots,\epsilon_n) =
\prod\limits_{i=1}^{n}\frac{1}{\sigma\sqrt{2\pi}}
\exp\!\left[-\frac{\epsilon_i^2}{2\sigma^2}\rig | How to derive variance-covariance matrix of coefficients in linear regression
Maximum likelihood solution:
$ \mathcal{L}(\beta_0,\beta_1|\sigma,\epsilon_1,\ldots,\epsilon_n) =
\prod\limits_{i=1}^{n}\frac{1}{\sigma\sqrt{2\pi}}
\exp\!\left[-\frac{\epsilon_i^2}{2\sigma^2}\right] \mbox{, where }
\epsilon_i = \beta_0... | How to derive variance-covariance matrix of coefficients in linear regression
Maximum likelihood solution:
$ \mathcal{L}(\beta_0,\beta_1|\sigma,\epsilon_1,\ldots,\epsilon_n) =
\prod\limits_{i=1}^{n}\frac{1}{\sigma\sqrt{2\pi}}
\exp\!\left[-\frac{\epsilon_i^2}{2\sigma^2}\rig |
3,726 | How to derive variance-covariance matrix of coefficients in linear regression | It appears that $\beta_0 \beta_1$ are the predicted values (expected values). They make the switch between $E(b_0)=\beta_0$ and $E(b_1)=\beta_1$. | How to derive variance-covariance matrix of coefficients in linear regression | It appears that $\beta_0 \beta_1$ are the predicted values (expected values). They make the switch between $E(b_0)=\beta_0$ and $E(b_1)=\beta_1$. | How to derive variance-covariance matrix of coefficients in linear regression
It appears that $\beta_0 \beta_1$ are the predicted values (expected values). They make the switch between $E(b_0)=\beta_0$ and $E(b_1)=\beta_1$. | How to derive variance-covariance matrix of coefficients in linear regression
It appears that $\beta_0 \beta_1$ are the predicted values (expected values). They make the switch between $E(b_0)=\beta_0$ and $E(b_1)=\beta_1$. |
3,727 | How do I test that two continuous variables are independent? | (Answer partially updated in 2023.)
This is a very hard problem in general, though your variables are apparently only 1d so that helps. Of course, the first step (when possible) should be to plot the data and see if anything pops out at you; you're in 2d so this should be easy.
Here are a few approaches that work in $\... | How do I test that two continuous variables are independent? | (Answer partially updated in 2023.)
This is a very hard problem in general, though your variables are apparently only 1d so that helps. Of course, the first step (when possible) should be to plot the | How do I test that two continuous variables are independent?
(Answer partially updated in 2023.)
This is a very hard problem in general, though your variables are apparently only 1d so that helps. Of course, the first step (when possible) should be to plot the data and see if anything pops out at you; you're in 2d so t... | How do I test that two continuous variables are independent?
(Answer partially updated in 2023.)
This is a very hard problem in general, though your variables are apparently only 1d so that helps. Of course, the first step (when possible) should be to plot the |
3,728 | How do I test that two continuous variables are independent? | Hoeffding developed a general nonparametric test for the independence of two continuous variables using joint ranks to test $H_{0}: H(x,y) = F(x)G(y)$. This 1948 test is implemented in the R Hmisc package's hoeffd function. | How do I test that two continuous variables are independent? | Hoeffding developed a general nonparametric test for the independence of two continuous variables using joint ranks to test $H_{0}: H(x,y) = F(x)G(y)$. This 1948 test is implemented in the R Hmisc pa | How do I test that two continuous variables are independent?
Hoeffding developed a general nonparametric test for the independence of two continuous variables using joint ranks to test $H_{0}: H(x,y) = F(x)G(y)$. This 1948 test is implemented in the R Hmisc package's hoeffd function. | How do I test that two continuous variables are independent?
Hoeffding developed a general nonparametric test for the independence of two continuous variables using joint ranks to test $H_{0}: H(x,y) = F(x)G(y)$. This 1948 test is implemented in the R Hmisc pa |
3,729 | How do I test that two continuous variables are independent? | How about this paper:
http://arxiv.org/pdf/0803.4101.pdf
"Measuring and testing dependence by correlation of distances". Székely and Bakirov always have interesting stuff.
There is matlab code for the implementation:
http://www.mathworks.com/matlabcentral/fileexchange/39905-distance-correlation
If you find any other ... | How do I test that two continuous variables are independent? | How about this paper:
http://arxiv.org/pdf/0803.4101.pdf
"Measuring and testing dependence by correlation of distances". Székely and Bakirov always have interesting stuff.
There is matlab code for t | How do I test that two continuous variables are independent?
How about this paper:
http://arxiv.org/pdf/0803.4101.pdf
"Measuring and testing dependence by correlation of distances". Székely and Bakirov always have interesting stuff.
There is matlab code for the implementation:
http://www.mathworks.com/matlabcentral/f... | How do I test that two continuous variables are independent?
How about this paper:
http://arxiv.org/pdf/0803.4101.pdf
"Measuring and testing dependence by correlation of distances". Székely and Bakirov always have interesting stuff.
There is matlab code for t |
3,730 | How do I test that two continuous variables are independent? | The link between Distance Covariance and kernel tests (based on the Hilbert-Schmidt independence criterion) is given in the paper:
Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K., Equivalence of distance-based and RKHS-based statistics in hypothesis testing, Annals of Statistics, 41 (5), pp.2263-2702, ... | How do I test that two continuous variables are independent? | The link between Distance Covariance and kernel tests (based on the Hilbert-Schmidt independence criterion) is given in the paper:
Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K., Equ | How do I test that two continuous variables are independent?
The link between Distance Covariance and kernel tests (based on the Hilbert-Schmidt independence criterion) is given in the paper:
Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K., Equivalence of distance-based and RKHS-based statistics in hyp... | How do I test that two continuous variables are independent?
The link between Distance Covariance and kernel tests (based on the Hilbert-Schmidt independence criterion) is given in the paper:
Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K., Equ |
3,731 | How do I test that two continuous variables are independent? | Rarely (never?) in statistics can you demonstrate that your sample statistic = a point value. You can test against point values and either exclude them or not exclude them. But the nature of statistics is that it is about examining variable data. Because there is always variance then there will necessarily be no way to... | How do I test that two continuous variables are independent? | Rarely (never?) in statistics can you demonstrate that your sample statistic = a point value. You can test against point values and either exclude them or not exclude them. But the nature of statistic | How do I test that two continuous variables are independent?
Rarely (never?) in statistics can you demonstrate that your sample statistic = a point value. You can test against point values and either exclude them or not exclude them. But the nature of statistics is that it is about examining variable data. Because ther... | How do I test that two continuous variables are independent?
Rarely (never?) in statistics can you demonstrate that your sample statistic = a point value. You can test against point values and either exclude them or not exclude them. But the nature of statistic |
3,732 | How do I test that two continuous variables are independent? | 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.
It may be interesting ...
Garcia, J. E.; Gonzalez-Lope... | How do I test that two continuous variables are independent? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| How do I test that two continuous variables are independent?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | How do I test that two continuous variables are independent?
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.
|
3,733 | How do I test that two continuous variables are independent? | Yet another approach is Constrained Covariance: basically, for a "sufficiently rich" function class $G$, Constrained Covariance of two random variables $X$ and $Y$ is
$$ \text{CoCo}(X,Y)=\sup_{g_1,g_2\in G} \text{corr}(g_1(X),g_2(Y)) $$
(possibly related to another answer)
As for the computational aspect, please see Sa... | How do I test that two continuous variables are independent? | Yet another approach is Constrained Covariance: basically, for a "sufficiently rich" function class $G$, Constrained Covariance of two random variables $X$ and $Y$ is
$$ \text{CoCo}(X,Y)=\sup_{g_1,g_2 | How do I test that two continuous variables are independent?
Yet another approach is Constrained Covariance: basically, for a "sufficiently rich" function class $G$, Constrained Covariance of two random variables $X$ and $Y$ is
$$ \text{CoCo}(X,Y)=\sup_{g_1,g_2\in G} \text{corr}(g_1(X),g_2(Y)) $$
(possibly related to a... | How do I test that two continuous variables are independent?
Yet another approach is Constrained Covariance: basically, for a "sufficiently rich" function class $G$, Constrained Covariance of two random variables $X$ and $Y$ is
$$ \text{CoCo}(X,Y)=\sup_{g_1,g_2 |
3,734 | A more definitive discussion of variable selection | Andrew Gelman is definitely a respected name in the statistical world. His principles closely align with some of the causal modeling research that has been done by other "big names" in the field. But I think given your interest in clinical research, you should be consulting other sources.
I am using the word "causal" ... | A more definitive discussion of variable selection | Andrew Gelman is definitely a respected name in the statistical world. His principles closely align with some of the causal modeling research that has been done by other "big names" in the field. But | A more definitive discussion of variable selection
Andrew Gelman is definitely a respected name in the statistical world. His principles closely align with some of the causal modeling research that has been done by other "big names" in the field. But I think given your interest in clinical research, you should be consu... | A more definitive discussion of variable selection
Andrew Gelman is definitely a respected name in the statistical world. His principles closely align with some of the causal modeling research that has been done by other "big names" in the field. But |
3,735 | A more definitive discussion of variable selection | This magnificent question and @AdamO's comprehensive answer are a prime example of how CV regularly renews my faith in humanity. I'll aim here mainly to offer some ways to appreciate that answer (and the OP's question) in a broader context.
Firstly, I venture to assert that all reliable advice regarding statistical pra... | A more definitive discussion of variable selection | This magnificent question and @AdamO's comprehensive answer are a prime example of how CV regularly renews my faith in humanity. I'll aim here mainly to offer some ways to appreciate that answer (and | A more definitive discussion of variable selection
This magnificent question and @AdamO's comprehensive answer are a prime example of how CV regularly renews my faith in humanity. I'll aim here mainly to offer some ways to appreciate that answer (and the OP's question) in a broader context.
Firstly, I venture to assert... | A more definitive discussion of variable selection
This magnificent question and @AdamO's comprehensive answer are a prime example of how CV regularly renews my faith in humanity. I'll aim here mainly to offer some ways to appreciate that answer (and |
3,736 | Examples of Bayesian and frequentist approach giving different answers | This example is taken from here. (I even think I got this link from SO, but cannot find it anymore.)
A coin has been tossed $n=14$ times, coming up heads $k=10$ times. If it is to be tossed twice more, would you bet on two heads? Assume you do not get to see the result of the first toss before the second toss (and also... | Examples of Bayesian and frequentist approach giving different answers | This example is taken from here. (I even think I got this link from SO, but cannot find it anymore.)
A coin has been tossed $n=14$ times, coming up heads $k=10$ times. If it is to be tossed twice more | Examples of Bayesian and frequentist approach giving different answers
This example is taken from here. (I even think I got this link from SO, but cannot find it anymore.)
A coin has been tossed $n=14$ times, coming up heads $k=10$ times. If it is to be tossed twice more, would you bet on two heads? Assume you do not g... | Examples of Bayesian and frequentist approach giving different answers
This example is taken from here. (I even think I got this link from SO, but cannot find it anymore.)
A coin has been tossed $n=14$ times, coming up heads $k=10$ times. If it is to be tossed twice more |
3,737 | Examples of Bayesian and frequentist approach giving different answers | See my question here, which mentions a paper by Edwin Jaynes that gives an example of a correctly constructed frequentist confidence interval, where there is sufficient information in the sample to know for certain that the true value of the statistic lies nowhere in the confidence interval (and thus the confidence int... | Examples of Bayesian and frequentist approach giving different answers | See my question here, which mentions a paper by Edwin Jaynes that gives an example of a correctly constructed frequentist confidence interval, where there is sufficient information in the sample to kn | Examples of Bayesian and frequentist approach giving different answers
See my question here, which mentions a paper by Edwin Jaynes that gives an example of a correctly constructed frequentist confidence interval, where there is sufficient information in the sample to know for certain that the true value of the statist... | Examples of Bayesian and frequentist approach giving different answers
See my question here, which mentions a paper by Edwin Jaynes that gives an example of a correctly constructed frequentist confidence interval, where there is sufficient information in the sample to kn |
3,738 | Examples of Bayesian and frequentist approach giving different answers | I believe this paper provides a more purposeful sense of the trade-offs in actual applications between the two. Part of this might be due to my preference for intervals rather than tests.
Gustafson, P. and Greenland, S. (2009). Interval Estimation for Messy Observational Data. Statistical Science 24: 328–342.
With r... | Examples of Bayesian and frequentist approach giving different answers | I believe this paper provides a more purposeful sense of the trade-offs in actual applications between the two. Part of this might be due to my preference for intervals rather than tests.
Gustafson, | Examples of Bayesian and frequentist approach giving different answers
I believe this paper provides a more purposeful sense of the trade-offs in actual applications between the two. Part of this might be due to my preference for intervals rather than tests.
Gustafson, P. and Greenland, S. (2009). Interval Estimation... | Examples of Bayesian and frequentist approach giving different answers
I believe this paper provides a more purposeful sense of the trade-offs in actual applications between the two. Part of this might be due to my preference for intervals rather than tests.
Gustafson, |
3,739 | Examples of Bayesian and frequentist approach giving different answers | If someone were to pose a question that has both a frequentist and Bayesian answer, I suspect that someone else would be able to identify an ambiguity in the question, thus making it not "well formed".
In other words, if you need a frequentist answer, use frequentist methods. If you need a Bayesian answer, use Bayes... | Examples of Bayesian and frequentist approach giving different answers | If someone were to pose a question that has both a frequentist and Bayesian answer, I suspect that someone else would be able to identify an ambiguity in the question, thus making it not "well formed" | Examples of Bayesian and frequentist approach giving different answers
If someone were to pose a question that has both a frequentist and Bayesian answer, I suspect that someone else would be able to identify an ambiguity in the question, thus making it not "well formed".
In other words, if you need a frequentist ans... | Examples of Bayesian and frequentist approach giving different answers
If someone were to pose a question that has both a frequentist and Bayesian answer, I suspect that someone else would be able to identify an ambiguity in the question, thus making it not "well formed" |
3,740 | Examples of Bayesian and frequentist approach giving different answers | I recommend looking at Exercise 3.15 of the freely-available textbook Information Theory, Inference and Learning Algorithms by MacKay.
When spun on edge 250 times, a Belgian one-euro coin came up heads 140
times and tails 110. 'It looks very suspicious to me', said Barry
Blight, a statistics lecturer at the London... | Examples of Bayesian and frequentist approach giving different answers | I recommend looking at Exercise 3.15 of the freely-available textbook Information Theory, Inference and Learning Algorithms by MacKay.
When spun on edge 250 times, a Belgian one-euro coin came up hea | Examples of Bayesian and frequentist approach giving different answers
I recommend looking at Exercise 3.15 of the freely-available textbook Information Theory, Inference and Learning Algorithms by MacKay.
When spun on edge 250 times, a Belgian one-euro coin came up heads 140
times and tails 110. 'It looks very susp... | Examples of Bayesian and frequentist approach giving different answers
I recommend looking at Exercise 3.15 of the freely-available textbook Information Theory, Inference and Learning Algorithms by MacKay.
When spun on edge 250 times, a Belgian one-euro coin came up hea |
3,741 | Examples of Bayesian and frequentist approach giving different answers | An important area where the two approaches will yield conflicting assessments is the context of multiplicity. Since p-values involve the probability of getting more extreme results than the results observed if a null hypothesis is true, having more looks at the data will increase the p-value. For Bayes on the other h... | Examples of Bayesian and frequentist approach giving different answers | An important area where the two approaches will yield conflicting assessments is the context of multiplicity. Since p-values involve the probability of getting more extreme results than the results o | Examples of Bayesian and frequentist approach giving different answers
An important area where the two approaches will yield conflicting assessments is the context of multiplicity. Since p-values involve the probability of getting more extreme results than the results observed if a null hypothesis is true, having more... | Examples of Bayesian and frequentist approach giving different answers
An important area where the two approaches will yield conflicting assessments is the context of multiplicity. Since p-values involve the probability of getting more extreme results than the results o |
3,742 | Examples of Bayesian and frequentist approach giving different answers | The answer provided by Christoph Hanck compares a Bayesian prediction interval for a future experimental result with a frequentist point estimate of a population-level parameter. A more appropriate comparison would be to compare a Bayesian prediction interval with a frequentist prediction interval. In my examples bel... | Examples of Bayesian and frequentist approach giving different answers | The answer provided by Christoph Hanck compares a Bayesian prediction interval for a future experimental result with a frequentist point estimate of a population-level parameter. A more appropriate c | Examples of Bayesian and frequentist approach giving different answers
The answer provided by Christoph Hanck compares a Bayesian prediction interval for a future experimental result with a frequentist point estimate of a population-level parameter. A more appropriate comparison would be to compare a Bayesian predicti... | Examples of Bayesian and frequentist approach giving different answers
The answer provided by Christoph Hanck compares a Bayesian prediction interval for a future experimental result with a frequentist point estimate of a population-level parameter. A more appropriate c |
3,743 | Examples of Bayesian and frequentist approach giving different answers | A funny buth insightfull example is given by xkcd in https://xkcd.com/1132/:
It stands for a whole group of problems where we have a strong prior and Frequentism neglects the prior. The Frequentist compares how likely the result is in the light of the null hypothesis but she does not consider whether the hypothesis is... | Examples of Bayesian and frequentist approach giving different answers | A funny buth insightfull example is given by xkcd in https://xkcd.com/1132/:
It stands for a whole group of problems where we have a strong prior and Frequentism neglects the prior. The Frequentist c | Examples of Bayesian and frequentist approach giving different answers
A funny buth insightfull example is given by xkcd in https://xkcd.com/1132/:
It stands for a whole group of problems where we have a strong prior and Frequentism neglects the prior. The Frequentist compares how likely the result is in the light of ... | Examples of Bayesian and frequentist approach giving different answers
A funny buth insightfull example is given by xkcd in https://xkcd.com/1132/:
It stands for a whole group of problems where we have a strong prior and Frequentism neglects the prior. The Frequentist c |
3,744 | Examples of Bayesian and frequentist approach giving different answers | The answer provided by Christoph Hanck compares a Bayesian predictive probability to a frequentist point estimate. Below are frequentist p-values for making a prediction (Johnson 2021a) as compared to a Bayesian posterior predictive distribution and a discussion on willingness to bet. Recall the problem statement,
"A... | Examples of Bayesian and frequentist approach giving different answers | The answer provided by Christoph Hanck compares a Bayesian predictive probability to a frequentist point estimate. Below are frequentist p-values for making a prediction (Johnson 2021a) as compared t | Examples of Bayesian and frequentist approach giving different answers
The answer provided by Christoph Hanck compares a Bayesian predictive probability to a frequentist point estimate. Below are frequentist p-values for making a prediction (Johnson 2021a) as compared to a Bayesian posterior predictive distribution an... | Examples of Bayesian and frequentist approach giving different answers
The answer provided by Christoph Hanck compares a Bayesian predictive probability to a frequentist point estimate. Below are frequentist p-values for making a prediction (Johnson 2021a) as compared t |
3,745 | Examples of Bayesian and frequentist approach giving different answers | There are four sources of differences between Bayesian, Likelihoodist, Frequentist, and the various uncategorized miscellaneous methods, such as the method of moments, that I have been able to discover. The first has to with differences in defining the idea of an optimal solution. The second has to do with the deeper... | Examples of Bayesian and frequentist approach giving different answers | There are four sources of differences between Bayesian, Likelihoodist, Frequentist, and the various uncategorized miscellaneous methods, such as the method of moments, that I have been able to discove | Examples of Bayesian and frequentist approach giving different answers
There are four sources of differences between Bayesian, Likelihoodist, Frequentist, and the various uncategorized miscellaneous methods, such as the method of moments, that I have been able to discover. The first has to with differences in defining... | Examples of Bayesian and frequentist approach giving different answers
There are four sources of differences between Bayesian, Likelihoodist, Frequentist, and the various uncategorized miscellaneous methods, such as the method of moments, that I have been able to discove |
3,746 | Examples of Bayesian and frequentist approach giving different answers | A very obvious case where it makes a difference is when there is a relevant prior information, but we are trying to analyze a small dataset. An example that I found quite useful (and used in my thesis, full details of the analysis below are given there) is the TGN1412 first in human trial.
During that first-in-human tr... | Examples of Bayesian and frequentist approach giving different answers | A very obvious case where it makes a difference is when there is a relevant prior information, but we are trying to analyze a small dataset. An example that I found quite useful (and used in my thesis | Examples of Bayesian and frequentist approach giving different answers
A very obvious case where it makes a difference is when there is a relevant prior information, but we are trying to analyze a small dataset. An example that I found quite useful (and used in my thesis, full details of the analysis below are given th... | Examples of Bayesian and frequentist approach giving different answers
A very obvious case where it makes a difference is when there is a relevant prior information, but we are trying to analyze a small dataset. An example that I found quite useful (and used in my thesis |
3,747 | Correlations between continuous and categorical (nominal) variables | The reviewer should have told you why the Spearman $\rho$ is not appropriate. Here is one version of that: Let the data be $(Z_i, I_i)$ where $Z$ is the measured variable and $I$ is the gender indicator, say it is 0 (man), 1 (woman). Then Spearman's $\rho$ is calculated based on the ranks of $Z, I$ respectively. Sinc... | Correlations between continuous and categorical (nominal) variables | The reviewer should have told you why the Spearman $\rho$ is not appropriate. Here is one version of that: Let the data be $(Z_i, I_i)$ where $Z$ is the measured variable and $I$ is the gender indic | Correlations between continuous and categorical (nominal) variables
The reviewer should have told you why the Spearman $\rho$ is not appropriate. Here is one version of that: Let the data be $(Z_i, I_i)$ where $Z$ is the measured variable and $I$ is the gender indicator, say it is 0 (man), 1 (woman). Then Spearman's ... | Correlations between continuous and categorical (nominal) variables
The reviewer should have told you why the Spearman $\rho$ is not appropriate. Here is one version of that: Let the data be $(Z_i, I_i)$ where $Z$ is the measured variable and $I$ is the gender indic |
3,748 | Correlations between continuous and categorical (nominal) variables | I'm having the same issue now. I didn't see anyone reference this just yet, but I'm researching the Point-Biserial Correlation which is built off the Pearson correlation coefficient. It is mean for a continuous variable and a dichotomous variable.
Quick read:
https://statistics.laerd.com/spss-tutorials/point-biserial-... | Correlations between continuous and categorical (nominal) variables | I'm having the same issue now. I didn't see anyone reference this just yet, but I'm researching the Point-Biserial Correlation which is built off the Pearson correlation coefficient. It is mean for a | Correlations between continuous and categorical (nominal) variables
I'm having the same issue now. I didn't see anyone reference this just yet, but I'm researching the Point-Biserial Correlation which is built off the Pearson correlation coefficient. It is mean for a continuous variable and a dichotomous variable.
Quic... | Correlations between continuous and categorical (nominal) variables
I'm having the same issue now. I didn't see anyone reference this just yet, but I'm researching the Point-Biserial Correlation which is built off the Pearson correlation coefficient. It is mean for a |
3,749 | Correlations between continuous and categorical (nominal) variables | It would seem that the most appropriate comparison would be to compare the medians (as it is non-normal) and distribution between the binary categories. I would suggest the non-parametric Mann-Whitney test... | Correlations between continuous and categorical (nominal) variables | It would seem that the most appropriate comparison would be to compare the medians (as it is non-normal) and distribution between the binary categories. I would suggest the non-parametric Mann-Whitney | Correlations between continuous and categorical (nominal) variables
It would seem that the most appropriate comparison would be to compare the medians (as it is non-normal) and distribution between the binary categories. I would suggest the non-parametric Mann-Whitney test... | Correlations between continuous and categorical (nominal) variables
It would seem that the most appropriate comparison would be to compare the medians (as it is non-normal) and distribution between the binary categories. I would suggest the non-parametric Mann-Whitney |
3,750 | Correlations between continuous and categorical (nominal) variables | For the specified problem, measuring the Area Under the Curve of a Receiver Operator Characteristic curve might help.
I am not an expert in this so I try to keep it simple. Please comment on any error or wrong interpretation so I can change it.
$x$ is your continuous variable. $y$ is your categorical.
See how many True... | Correlations between continuous and categorical (nominal) variables | For the specified problem, measuring the Area Under the Curve of a Receiver Operator Characteristic curve might help.
I am not an expert in this so I try to keep it simple. Please comment on any error | Correlations between continuous and categorical (nominal) variables
For the specified problem, measuring the Area Under the Curve of a Receiver Operator Characteristic curve might help.
I am not an expert in this so I try to keep it simple. Please comment on any error or wrong interpretation so I can change it.
$x$ is ... | Correlations between continuous and categorical (nominal) variables
For the specified problem, measuring the Area Under the Curve of a Receiver Operator Characteristic curve might help.
I am not an expert in this so I try to keep it simple. Please comment on any error |
3,751 | Correlations between continuous and categorical (nominal) variables | I like to think of it in more practical terms. A simple use case for continuous vs. categorical comparison is when you want to analyze treatment vs. control in an experiment. If you show statistical significance between treatment and control that implies that the categorical value (Treatment vs. Control) does indeed af... | Correlations between continuous and categorical (nominal) variables | I like to think of it in more practical terms. A simple use case for continuous vs. categorical comparison is when you want to analyze treatment vs. control in an experiment. If you show statistical s | Correlations between continuous and categorical (nominal) variables
I like to think of it in more practical terms. A simple use case for continuous vs. categorical comparison is when you want to analyze treatment vs. control in an experiment. If you show statistical significance between treatment and control that impli... | Correlations between continuous and categorical (nominal) variables
I like to think of it in more practical terms. A simple use case for continuous vs. categorical comparison is when you want to analyze treatment vs. control in an experiment. If you show statistical s |
3,752 | Regression for an outcome (ratio or fraction) between 0 and 1 | You should choose "hidden option c", where c is beta regression. This is a type of regression model that is appropriate when the response variable is distributed as Beta. You can think of it as analogous to a generalized linear model. It's exactly what you are looking for. There is a package in R called betareg whi... | Regression for an outcome (ratio or fraction) between 0 and 1 | You should choose "hidden option c", where c is beta regression. This is a type of regression model that is appropriate when the response variable is distributed as Beta. You can think of it as anal | Regression for an outcome (ratio or fraction) between 0 and 1
You should choose "hidden option c", where c is beta regression. This is a type of regression model that is appropriate when the response variable is distributed as Beta. You can think of it as analogous to a generalized linear model. It's exactly what yo... | Regression for an outcome (ratio or fraction) between 0 and 1
You should choose "hidden option c", where c is beta regression. This is a type of regression model that is appropriate when the response variable is distributed as Beta. You can think of it as anal |
3,753 | Regression for an outcome (ratio or fraction) between 0 and 1 | Are these paired samples or two independent populations?
If independent populations, you might consider log(M) = log(B) + $X_i$*log(ratio). M is your measurement (a vector containing all values of A and B) and X is a vector $X_i$ = 1 if $M_i$ is a value of A, $X_i$ = 0 if $M_i$ is a value of B.
Your intercept of this... | Regression for an outcome (ratio or fraction) between 0 and 1 | Are these paired samples or two independent populations?
If independent populations, you might consider log(M) = log(B) + $X_i$*log(ratio). M is your measurement (a vector containing all values of A | Regression for an outcome (ratio or fraction) between 0 and 1
Are these paired samples or two independent populations?
If independent populations, you might consider log(M) = log(B) + $X_i$*log(ratio). M is your measurement (a vector containing all values of A and B) and X is a vector $X_i$ = 1 if $M_i$ is a value of ... | Regression for an outcome (ratio or fraction) between 0 and 1
Are these paired samples or two independent populations?
If independent populations, you might consider log(M) = log(B) + $X_i$*log(ratio). M is your measurement (a vector containing all values of A |
3,754 | Regression for an outcome (ratio or fraction) between 0 and 1 | Not true. The data for logistic regression is binary 0 or 1 but the model predicts p say the probability of success given the predictors $X_i$, $i=1,2,..,k$ where $k$ is the number of predictor variables in the model. Actually because of the logit function the linear model predicts the value of log($\frac{p}{1-p}$). ... | Regression for an outcome (ratio or fraction) between 0 and 1 | Not true. The data for logistic regression is binary 0 or 1 but the model predicts p say the probability of success given the predictors $X_i$, $i=1,2,..,k$ where $k$ is the number of predictor varia | Regression for an outcome (ratio or fraction) between 0 and 1
Not true. The data for logistic regression is binary 0 or 1 but the model predicts p say the probability of success given the predictors $X_i$, $i=1,2,..,k$ where $k$ is the number of predictor variables in the model. Actually because of the logit function... | Regression for an outcome (ratio or fraction) between 0 and 1
Not true. The data for logistic regression is binary 0 or 1 but the model predicts p say the probability of success given the predictors $X_i$, $i=1,2,..,k$ where $k$ is the number of predictor varia |
3,755 | Regression for an outcome (ratio or fraction) between 0 and 1 | 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.
We can use sample_weights in SVM-C or any other classi... | Regression for an outcome (ratio or fraction) between 0 and 1 | 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.
| Regression for an outcome (ratio or fraction) between 0 and 1
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.
... | Regression for an outcome (ratio or fraction) between 0 and 1
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.
|
3,756 | What does the inverse of covariance matrix say about data? (Intuitively) | It is a measure of precision just as $\Sigma$ is a measure of dispersion.
More elaborately, $\Sigma$ is a measure of how the variables are dispersed around the mean (the diagonal elements) and how they co-vary with other variables (the off-diagonal) elements. The more the dispersion the farther apart they are from the... | What does the inverse of covariance matrix say about data? (Intuitively) | It is a measure of precision just as $\Sigma$ is a measure of dispersion.
More elaborately, $\Sigma$ is a measure of how the variables are dispersed around the mean (the diagonal elements) and how th | What does the inverse of covariance matrix say about data? (Intuitively)
It is a measure of precision just as $\Sigma$ is a measure of dispersion.
More elaborately, $\Sigma$ is a measure of how the variables are dispersed around the mean (the diagonal elements) and how they co-vary with other variables (the off-diagon... | What does the inverse of covariance matrix say about data? (Intuitively)
It is a measure of precision just as $\Sigma$ is a measure of dispersion.
More elaborately, $\Sigma$ is a measure of how the variables are dispersed around the mean (the diagonal elements) and how th |
3,757 | What does the inverse of covariance matrix say about data? (Intuitively) | Using superscripts to denote the elements of the inverse, $1/\sigma^{ii}$ is the variance of the component of variable $i$ that is uncorrelated with the $p-1$ other variables, and $-\sigma^{ij}/\sqrt{\sigma^{ii}\sigma^{jj}}$ is the partial correlation of variables $i$ and $j$, controlling for the $p-2$ other variables. | What does the inverse of covariance matrix say about data? (Intuitively) | Using superscripts to denote the elements of the inverse, $1/\sigma^{ii}$ is the variance of the component of variable $i$ that is uncorrelated with the $p-1$ other variables, and $-\sigma^{ij}/\sqrt{ | What does the inverse of covariance matrix say about data? (Intuitively)
Using superscripts to denote the elements of the inverse, $1/\sigma^{ii}$ is the variance of the component of variable $i$ that is uncorrelated with the $p-1$ other variables, and $-\sigma^{ij}/\sqrt{\sigma^{ii}\sigma^{jj}}$ is the partial correla... | What does the inverse of covariance matrix say about data? (Intuitively)
Using superscripts to denote the elements of the inverse, $1/\sigma^{ii}$ is the variance of the component of variable $i$ that is uncorrelated with the $p-1$ other variables, and $-\sigma^{ij}/\sqrt{ |
3,758 | How can I determine which of two sequences of coin flips is real and which is fake? | This is a variant on a standard intro stats demonstration: for homework after the first class I have assigned my students the exercise of flipping a coin 100 times and recording the results, broadly hinting that they don't really have to flip a coin and assuring them it won't be graded. Most will eschew the physical p... | How can I determine which of two sequences of coin flips is real and which is fake? | This is a variant on a standard intro stats demonstration: for homework after the first class I have assigned my students the exercise of flipping a coin 100 times and recording the results, broadly h | How can I determine which of two sequences of coin flips is real and which is fake?
This is a variant on a standard intro stats demonstration: for homework after the first class I have assigned my students the exercise of flipping a coin 100 times and recording the results, broadly hinting that they don't really have t... | How can I determine which of two sequences of coin flips is real and which is fake?
This is a variant on a standard intro stats demonstration: for homework after the first class I have assigned my students the exercise of flipping a coin 100 times and recording the results, broadly h |
3,759 | How can I determine which of two sequences of coin flips is real and which is fake? | There are two very good answers as of writing this, and so let me add a needlessly complex yet interesting approach to this problem.
I think one way to operationalize the human generated vs truly random question is to ask if the flips are autocorrelated. The hypothesis here being that humans will attempt to appear ra... | How can I determine which of two sequences of coin flips is real and which is fake? | There are two very good answers as of writing this, and so let me add a needlessly complex yet interesting approach to this problem.
I think one way to operationalize the human generated vs truly ran | How can I determine which of two sequences of coin flips is real and which is fake?
There are two very good answers as of writing this, and so let me add a needlessly complex yet interesting approach to this problem.
I think one way to operationalize the human generated vs truly random question is to ask if the flips ... | How can I determine which of two sequences of coin flips is real and which is fake?
There are two very good answers as of writing this, and so let me add a needlessly complex yet interesting approach to this problem.
I think one way to operationalize the human generated vs truly ran |
3,760 | How can I determine which of two sequences of coin flips is real and which is fake? | This is a class activity I've first read about in the book Teaching Statistics. A Bag of Tricks, 2nd ed. by Andrew Gelman and Deborah Nolan (they recommend 100 flips, though). Their reasoning to detect the fabricated sequence is based on the combination of the longest run and the number of runs. For the following plot,... | How can I determine which of two sequences of coin flips is real and which is fake? | This is a class activity I've first read about in the book Teaching Statistics. A Bag of Tricks, 2nd ed. by Andrew Gelman and Deborah Nolan (they recommend 100 flips, though). Their reasoning to detec | How can I determine which of two sequences of coin flips is real and which is fake?
This is a class activity I've first read about in the book Teaching Statistics. A Bag of Tricks, 2nd ed. by Andrew Gelman and Deborah Nolan (they recommend 100 flips, though). Their reasoning to detect the fabricated sequence is based o... | How can I determine which of two sequences of coin flips is real and which is fake?
This is a class activity I've first read about in the book Teaching Statistics. A Bag of Tricks, 2nd ed. by Andrew Gelman and Deborah Nolan (they recommend 100 flips, though). Their reasoning to detec |
3,761 | How can I determine which of two sequences of coin flips is real and which is fake? | The runs test (NIST page) is a nonparametric test designed to identify unusual frequencies of runs. If we observe $n_1$ heads and $n_2$ tails, the expected value and variance of the number of runs are:
$$\mu = {2n_1n_2 \over n_1+n_2} + 1$$
$$\sigma^2 = {2n_1n_2(2n_1n_2 - n_1 - n_2) \over (n_1+n_2)^2(n_1+n_2+1)}$$
As ... | How can I determine which of two sequences of coin flips is real and which is fake? | The runs test (NIST page) is a nonparametric test designed to identify unusual frequencies of runs. If we observe $n_1$ heads and $n_2$ tails, the expected value and variance of the number of runs ar | How can I determine which of two sequences of coin flips is real and which is fake?
The runs test (NIST page) is a nonparametric test designed to identify unusual frequencies of runs. If we observe $n_1$ heads and $n_2$ tails, the expected value and variance of the number of runs are:
$$\mu = {2n_1n_2 \over n_1+n_2} ... | How can I determine which of two sequences of coin flips is real and which is fake?
The runs test (NIST page) is a nonparametric test designed to identify unusual frequencies of runs. If we observe $n_1$ heads and $n_2$ tails, the expected value and variance of the number of runs ar |
3,762 | How can I determine which of two sequences of coin flips is real and which is fake? | Here's an empirical approach, based on compression as a proxy for algorithmic complexity:
import bz2
import random
import statistics
s1 = "TTHHTHTTHTTTHTTTHTTTHTTHTHHTHHTHTHHTTTHHTHTHTTHTHHTTHTHHTHTTTHHTTHHTTHHHTHHTHTTHTHTTHHTHHHTTHTHTTTHHTTHTHTHTHTHTTHTHTHHHTTHTHTHHTHHHTHTHTTHTTHHTHTHTHTTHHTTHTHTTHHHTHTHTHTTHTTHHTTHT... | How can I determine which of two sequences of coin flips is real and which is fake? | Here's an empirical approach, based on compression as a proxy for algorithmic complexity:
import bz2
import random
import statistics
s1 = "TTHHTHTTHTTTHTTTHTTTHTTHTHHTHHTHTHHTTTHHTHTHTTHTHHTTHTHHTHTT | How can I determine which of two sequences of coin flips is real and which is fake?
Here's an empirical approach, based on compression as a proxy for algorithmic complexity:
import bz2
import random
import statistics
s1 = "TTHHTHTTHTTTHTTTHTTTHTTHTHHTHHTHTHHTTTHHTHTHTTHTHHTTHTHHTHTTTHHTTHHTTHHHTHHTHTTHTHTTHHTHHHTTHTHT... | How can I determine which of two sequences of coin flips is real and which is fake?
Here's an empirical approach, based on compression as a proxy for algorithmic complexity:
import bz2
import random
import statistics
s1 = "TTHHTHTTHTTTHTTTHTTTHTTHTHHTHHTHTHHTTTHHTHTHTTHTHHTTHTHHTHTT |
3,763 | How can I determine which of two sequences of coin flips is real and which is fake? | This is probably an overcomplicated way of looking at it, but for me it's fun, so I present to you...
Moran's I
Now, Moran's I was developed to look at spatial autocorrelation (basically autocorrelation with multiple dimensions), but it can be applied to the 1-dimensional case as well. Some of my interpretations might ... | How can I determine which of two sequences of coin flips is real and which is fake? | This is probably an overcomplicated way of looking at it, but for me it's fun, so I present to you...
Moran's I
Now, Moran's I was developed to look at spatial autocorrelation (basically autocorrelati | How can I determine which of two sequences of coin flips is real and which is fake?
This is probably an overcomplicated way of looking at it, but for me it's fun, so I present to you...
Moran's I
Now, Moran's I was developed to look at spatial autocorrelation (basically autocorrelation with multiple dimensions), but it... | How can I determine which of two sequences of coin flips is real and which is fake?
This is probably an overcomplicated way of looking at it, but for me it's fun, so I present to you...
Moran's I
Now, Moran's I was developed to look at spatial autocorrelation (basically autocorrelati |
3,764 | How can I determine which of two sequences of coin flips is real and which is fake? | When people try to generate random sequences, they tend to avoid repeating themselves more than random processes avoid repeating themselves. Thus, if we look at consecutive pairs of flips, we would expect a human-generated sequence to have too many HT and TH and too few HH and TT compared to a typical random sequence.
... | How can I determine which of two sequences of coin flips is real and which is fake? | When people try to generate random sequences, they tend to avoid repeating themselves more than random processes avoid repeating themselves. Thus, if we look at consecutive pairs of flips, we would ex | How can I determine which of two sequences of coin flips is real and which is fake?
When people try to generate random sequences, they tend to avoid repeating themselves more than random processes avoid repeating themselves. Thus, if we look at consecutive pairs of flips, we would expect a human-generated sequence to h... | How can I determine which of two sequences of coin flips is real and which is fake?
When people try to generate random sequences, they tend to avoid repeating themselves more than random processes avoid repeating themselves. Thus, if we look at consecutive pairs of flips, we would ex |
3,765 | How can I determine which of two sequences of coin flips is real and which is fake? | This answer is inspired by @user1717828's answer which transforms the sequence of coin flips into a random walk. I don't show the two given sequences as random walks here; see @user1717828's answer for that plot.
The random walk approach is interesting because it examines long-run features of the sequence rather than s... | How can I determine which of two sequences of coin flips is real and which is fake? | This answer is inspired by @user1717828's answer which transforms the sequence of coin flips into a random walk. I don't show the two given sequences as random walks here; see @user1717828's answer fo | How can I determine which of two sequences of coin flips is real and which is fake?
This answer is inspired by @user1717828's answer which transforms the sequence of coin flips into a random walk. I don't show the two given sequences as random walks here; see @user1717828's answer for that plot.
The random walk approac... | How can I determine which of two sequences of coin flips is real and which is fake?
This answer is inspired by @user1717828's answer which transforms the sequence of coin flips into a random walk. I don't show the two given sequences as random walks here; see @user1717828's answer fo |
3,766 | How can I determine which of two sequences of coin flips is real and which is fake? | In addition to statistical approaches, one visual approach is to plot the sequences as a "drunkards walk". Treat H as a step forwards and T as a step back and plot the sequences. One way in Python is:
import altair as alt
import pandas as pd
seq1 = "HTHHHTHTTHHTTTTTTTTHHHTTTHHTTTTHHTTHHHTTHTHTTTTTTHTHTTTTHHHHTHTHTTH... | How can I determine which of two sequences of coin flips is real and which is fake? | In addition to statistical approaches, one visual approach is to plot the sequences as a "drunkards walk". Treat H as a step forwards and T as a step back and plot the sequences. One way in Python i | How can I determine which of two sequences of coin flips is real and which is fake?
In addition to statistical approaches, one visual approach is to plot the sequences as a "drunkards walk". Treat H as a step forwards and T as a step back and plot the sequences. One way in Python is:
import altair as alt
import panda... | How can I determine which of two sequences of coin flips is real and which is fake?
In addition to statistical approaches, one visual approach is to plot the sequences as a "drunkards walk". Treat H as a step forwards and T as a step back and plot the sequences. One way in Python i |
3,767 | How can I determine which of two sequences of coin flips is real and which is fake? | Looking at the HH, HT, TH, TT frequencies is probably the most straightforward way to approach the two series presented, given people's tendency to apply HT and TH more frequently when trying to appear random. More generally, however, that approach will fail to detect non-randomness even in sequences with obvious patte... | How can I determine which of two sequences of coin flips is real and which is fake? | Looking at the HH, HT, TH, TT frequencies is probably the most straightforward way to approach the two series presented, given people's tendency to apply HT and TH more frequently when trying to appea | How can I determine which of two sequences of coin flips is real and which is fake?
Looking at the HH, HT, TH, TT frequencies is probably the most straightforward way to approach the two series presented, given people's tendency to apply HT and TH more frequently when trying to appear random. More generally, however, t... | How can I determine which of two sequences of coin flips is real and which is fake?
Looking at the HH, HT, TH, TT frequencies is probably the most straightforward way to approach the two series presented, given people's tendency to apply HT and TH more frequently when trying to appea |
3,768 | How can I determine which of two sequences of coin flips is real and which is fake? | This problem specifies that we have the following information:
We observed two coin flip sequences: sequence $S_1$ and sequence $S_2$.
Each of these sequences could have been generated by either mechanism $R$ corresponding to independent flips of a fair coin or some other mechanism $\bar{R}$.
Exactly one of these two ... | How can I determine which of two sequences of coin flips is real and which is fake? | This problem specifies that we have the following information:
We observed two coin flip sequences: sequence $S_1$ and sequence $S_2$.
Each of these sequences could have been generated by either mech | How can I determine which of two sequences of coin flips is real and which is fake?
This problem specifies that we have the following information:
We observed two coin flip sequences: sequence $S_1$ and sequence $S_2$.
Each of these sequences could have been generated by either mechanism $R$ corresponding to independe... | How can I determine which of two sequences of coin flips is real and which is fake?
This problem specifies that we have the following information:
We observed two coin flip sequences: sequence $S_1$ and sequence $S_2$.
Each of these sequences could have been generated by either mech |
3,769 | Why is the sum of two random variables a convolution? | Convolution calculations associated with distributions of random variables are all mathematical manifestations of the Law of Total Probability.
In the language of my post at What is meant by a “random variable”?,
A pair of random variables $(X,Y)$ consists of a box of tickets on each of which are written two numbers,... | Why is the sum of two random variables a convolution? | Convolution calculations associated with distributions of random variables are all mathematical manifestations of the Law of Total Probability.
In the language of my post at What is meant by a “rando | Why is the sum of two random variables a convolution?
Convolution calculations associated with distributions of random variables are all mathematical manifestations of the Law of Total Probability.
In the language of my post at What is meant by a “random variable”?,
A pair of random variables $(X,Y)$ consists of a bo... | Why is the sum of two random variables a convolution?
Convolution calculations associated with distributions of random variables are all mathematical manifestations of the Law of Total Probability.
In the language of my post at What is meant by a “rando |
3,770 | Why is the sum of two random variables a convolution? | Notation, upper and lower case
https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics
Random variables are usually written in upper case roman letters: $X$, $Y$, etc.
Particular realizations of a random variable are written in corresponding lower case letters. For example $x_1$, $x_2$, …, $x_n$ could be... | Why is the sum of two random variables a convolution? | Notation, upper and lower case
https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics
Random variables are usually written in upper case roman letters: $X$, $Y$, etc.
Particular realiz | Why is the sum of two random variables a convolution?
Notation, upper and lower case
https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics
Random variables are usually written in upper case roman letters: $X$, $Y$, etc.
Particular realizations of a random variable are written in corresponding lower cas... | Why is the sum of two random variables a convolution?
Notation, upper and lower case
https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics
Random variables are usually written in upper case roman letters: $X$, $Y$, etc.
Particular realiz |
3,771 | Why is the sum of two random variables a convolution? | Your confusion seems to arise from conflating random variables with their distributions.
To "unlearn" this confusion, it might help to take a couple of steps back, empty your mind for a moment, forget about any fancy formalisms like probability spaces and sigma-algebras (if it helps, pretend you're back in elementary s... | Why is the sum of two random variables a convolution? | Your confusion seems to arise from conflating random variables with their distributions.
To "unlearn" this confusion, it might help to take a couple of steps back, empty your mind for a moment, forget | Why is the sum of two random variables a convolution?
Your confusion seems to arise from conflating random variables with their distributions.
To "unlearn" this confusion, it might help to take a couple of steps back, empty your mind for a moment, forget about any fancy formalisms like probability spaces and sigma-alge... | Why is the sum of two random variables a convolution?
Your confusion seems to arise from conflating random variables with their distributions.
To "unlearn" this confusion, it might help to take a couple of steps back, empty your mind for a moment, forget |
3,772 | Why is the sum of two random variables a convolution? | Actually I don't think this is quite right, unless I'm misunderstanding you.
If $X$ and $Y$ are independent random variables, then the sum/convolution relationship you're referring to is as follows:
$$
p(X+Y) = p(X)*p(Y)
$$
That is, the probability density function (pdf) of the sum is equal to the convolution (denoted... | Why is the sum of two random variables a convolution? | Actually I don't think this is quite right, unless I'm misunderstanding you.
If $X$ and $Y$ are independent random variables, then the sum/convolution relationship you're referring to is as follows:
| Why is the sum of two random variables a convolution?
Actually I don't think this is quite right, unless I'm misunderstanding you.
If $X$ and $Y$ are independent random variables, then the sum/convolution relationship you're referring to is as follows:
$$
p(X+Y) = p(X)*p(Y)
$$
That is, the probability density function... | Why is the sum of two random variables a convolution?
Actually I don't think this is quite right, unless I'm misunderstanding you.
If $X$ and $Y$ are independent random variables, then the sum/convolution relationship you're referring to is as follows:
|
3,773 | Why is the sum of two random variables a convolution? | Start by considering the set of all possible distinct outcomes of a process or experiment. Let $X$ be a rule (as yet unspecified) for assigning a number to any given outcome $\omega$; let $Y$ be too. Then $S=X+Y$ states a new rule $S$ for assigning a number to any given outcome: add the number you get from following ru... | Why is the sum of two random variables a convolution? | Start by considering the set of all possible distinct outcomes of a process or experiment. Let $X$ be a rule (as yet unspecified) for assigning a number to any given outcome $\omega$; let $Y$ be too. | Why is the sum of two random variables a convolution?
Start by considering the set of all possible distinct outcomes of a process or experiment. Let $X$ be a rule (as yet unspecified) for assigning a number to any given outcome $\omega$; let $Y$ be too. Then $S=X+Y$ states a new rule $S$ for assigning a number to any g... | Why is the sum of two random variables a convolution?
Start by considering the set of all possible distinct outcomes of a process or experiment. Let $X$ be a rule (as yet unspecified) for assigning a number to any given outcome $\omega$; let $Y$ be too. |
3,774 | Why is the sum of two random variables a convolution? | In response to your "Notice", um, ... no.
Let $X$, $Y$, and $Z$ be random variables and let $Z = X+Y$. Then, once you choose $Z$ and $X$, you force $Y = Z - X$. You make these two choices, in this order, when you write
$$ P(Z = z) = \int P(X = x) P(Y = z - x) \mathrm{d}x \text{.} $$
But that's a convolution. | Why is the sum of two random variables a convolution? | In response to your "Notice", um, ... no.
Let $X$, $Y$, and $Z$ be random variables and let $Z = X+Y$. Then, once you choose $Z$ and $X$, you force $Y = Z - X$. You make these two choices, in this o | Why is the sum of two random variables a convolution?
In response to your "Notice", um, ... no.
Let $X$, $Y$, and $Z$ be random variables and let $Z = X+Y$. Then, once you choose $Z$ and $X$, you force $Y = Z - X$. You make these two choices, in this order, when you write
$$ P(Z = z) = \int P(X = x) P(Y = z - x) \ma... | Why is the sum of two random variables a convolution?
In response to your "Notice", um, ... no.
Let $X$, $Y$, and $Z$ be random variables and let $Z = X+Y$. Then, once you choose $Z$ and $X$, you force $Y = Z - X$. You make these two choices, in this o |
3,775 | Why is the sum of two random variables a convolution? | The reason is the same that products of power functions are related to convolutions. The convolution always appears naturally, if you combine to objects which have a range (e.g. the powers of two power functions or the range of the PDFs) and where the new range appears as the sum of the original ranges.
It is easiest t... | Why is the sum of two random variables a convolution? | The reason is the same that products of power functions are related to convolutions. The convolution always appears naturally, if you combine to objects which have a range (e.g. the powers of two powe | Why is the sum of two random variables a convolution?
The reason is the same that products of power functions are related to convolutions. The convolution always appears naturally, if you combine to objects which have a range (e.g. the powers of two power functions or the range of the PDFs) and where the new range appe... | Why is the sum of two random variables a convolution?
The reason is the same that products of power functions are related to convolutions. The convolution always appears naturally, if you combine to objects which have a range (e.g. the powers of two powe |
3,776 | Why is the sum of two random variables a convolution? | This question may be old, but I'd like to provide yet another perspective. It builds on a formula for a change in variable in a joint probability density. It can be found in Lecture Notes: Probability and Random Processes at KTH, 2017 Ed. (Koski, T., 2017, pp 67), which itself refers to a detailed proof in Analysens Gr... | Why is the sum of two random variables a convolution? | This question may be old, but I'd like to provide yet another perspective. It builds on a formula for a change in variable in a joint probability density. It can be found in Lecture Notes: Probability | Why is the sum of two random variables a convolution?
This question may be old, but I'd like to provide yet another perspective. It builds on a formula for a change in variable in a joint probability density. It can be found in Lecture Notes: Probability and Random Processes at KTH, 2017 Ed. (Koski, T., 2017, pp 67), w... | Why is the sum of two random variables a convolution?
This question may be old, but I'd like to provide yet another perspective. It builds on a formula for a change in variable in a joint probability density. It can be found in Lecture Notes: Probability |
3,777 | Why is the sum of two random variables a convolution? | Let us prove the supposition for the continuous case, and then explain and illustrate it using histograms built up from random numbers, and the sums formed by adding ordered pairs of numbers such that the discrete convolution, and both random variables are all of length $n$.
From Grinstead CM, Snell JL. Introduction to... | Why is the sum of two random variables a convolution? | Let us prove the supposition for the continuous case, and then explain and illustrate it using histograms built up from random numbers, and the sums formed by adding ordered pairs of numbers such that | Why is the sum of two random variables a convolution?
Let us prove the supposition for the continuous case, and then explain and illustrate it using histograms built up from random numbers, and the sums formed by adding ordered pairs of numbers such that the discrete convolution, and both random variables are all of le... | Why is the sum of two random variables a convolution?
Let us prove the supposition for the continuous case, and then explain and illustrate it using histograms built up from random numbers, and the sums formed by adding ordered pairs of numbers such that |
3,778 | Why is the sum of two random variables a convolution? | General expressions for the sums of n continuous random variables are found here:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0216422
"Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease"
For positive random variables, the sum can be simply written... | Why is the sum of two random variables a convolution? | General expressions for the sums of n continuous random variables are found here:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0216422
"Multi-stage models for the failure of comp | Why is the sum of two random variables a convolution?
General expressions for the sums of n continuous random variables are found here:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0216422
"Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease"
For po... | Why is the sum of two random variables a convolution?
General expressions for the sums of n continuous random variables are found here:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0216422
"Multi-stage models for the failure of comp |
3,779 | Is random forest a boosting algorithm? | Random Forest is a bagging algorithm rather than a boosting algorithm.
They are two opposite way to achieve a low error.
We know that error can be composited from bias and variance. A too complex model has low bias but large variance, while a too simple model has low variance but large bias, both leading a high error b... | Is random forest a boosting algorithm? | Random Forest is a bagging algorithm rather than a boosting algorithm.
They are two opposite way to achieve a low error.
We know that error can be composited from bias and variance. A too complex mode | Is random forest a boosting algorithm?
Random Forest is a bagging algorithm rather than a boosting algorithm.
They are two opposite way to achieve a low error.
We know that error can be composited from bias and variance. A too complex model has low bias but large variance, while a too simple model has low variance but ... | Is random forest a boosting algorithm?
Random Forest is a bagging algorithm rather than a boosting algorithm.
They are two opposite way to achieve a low error.
We know that error can be composited from bias and variance. A too complex mode |
3,780 | Is random forest a boosting algorithm? | A random forest is not considered a boosting type of algorithm.
As explained in your boosting link:
...most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier. When they are added, they are typically weighted in some way tha... | Is random forest a boosting algorithm? | A random forest is not considered a boosting type of algorithm.
As explained in your boosting link:
...most boosting algorithms consist of iteratively learning weak classifiers with respect to a dis | Is random forest a boosting algorithm?
A random forest is not considered a boosting type of algorithm.
As explained in your boosting link:
...most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier. When they are added, they... | Is random forest a boosting algorithm?
A random forest is not considered a boosting type of algorithm.
As explained in your boosting link:
...most boosting algorithms consist of iteratively learning weak classifiers with respect to a dis |
3,781 | Is random forest a boosting algorithm? | It is an extension of bagging. The procedure is as follows, you take a bootstrap sample of your data and then use this to grow a classification or regression tree (CART). This is done a predefined number of times and the prediction is then the aggregation of the individual trees predictions, it could be a majority vote... | Is random forest a boosting algorithm? | It is an extension of bagging. The procedure is as follows, you take a bootstrap sample of your data and then use this to grow a classification or regression tree (CART). This is done a predefined num | Is random forest a boosting algorithm?
It is an extension of bagging. The procedure is as follows, you take a bootstrap sample of your data and then use this to grow a classification or regression tree (CART). This is done a predefined number of times and the prediction is then the aggregation of the individual trees p... | Is random forest a boosting algorithm?
It is an extension of bagging. The procedure is as follows, you take a bootstrap sample of your data and then use this to grow a classification or regression tree (CART). This is done a predefined num |
3,782 | Is random forest a boosting algorithm? | I believe you are confusing boosting in particular with ensemble methods in general, of which there are many. Your "definition" of boosting is not the full definition, which is elaborated on in Pat's answer. If you would like to learn more about ensemble methods, I recommend you pick up the following book:
John Elder ... | Is random forest a boosting algorithm? | I believe you are confusing boosting in particular with ensemble methods in general, of which there are many. Your "definition" of boosting is not the full definition, which is elaborated on in Pat's | Is random forest a boosting algorithm?
I believe you are confusing boosting in particular with ensemble methods in general, of which there are many. Your "definition" of boosting is not the full definition, which is elaborated on in Pat's answer. If you would like to learn more about ensemble methods, I recommend you p... | Is random forest a boosting algorithm?
I believe you are confusing boosting in particular with ensemble methods in general, of which there are many. Your "definition" of boosting is not the full definition, which is elaborated on in Pat's |
3,783 | Is random forest a boosting algorithm? | Random forest is a bagging technique and not a boosting technique. In boosting as the name suggests, one is learning from other which in turn boosts the learning.
The trees in random forests are run in parallel. There is no interaction between these trees while building the trees. Once all the trees are built, then a ... | Is random forest a boosting algorithm? | Random forest is a bagging technique and not a boosting technique. In boosting as the name suggests, one is learning from other which in turn boosts the learning.
The trees in random forests are run | Is random forest a boosting algorithm?
Random forest is a bagging technique and not a boosting technique. In boosting as the name suggests, one is learning from other which in turn boosts the learning.
The trees in random forests are run in parallel. There is no interaction between these trees while building the trees... | Is random forest a boosting algorithm?
Random forest is a bagging technique and not a boosting technique. In boosting as the name suggests, one is learning from other which in turn boosts the learning.
The trees in random forests are run |
3,784 | Is random forest a boosting algorithm? | I'd like to point out that Random Forest is not just a bagging technique.
It's a bagging + random subset of the features.
Definition on Wikipedia suggests that
...The above procedure describes the original bagging algorithm for trees. Random forests differ in only one way from this general scheme: they use a modified ... | Is random forest a boosting algorithm? | I'd like to point out that Random Forest is not just a bagging technique.
It's a bagging + random subset of the features.
Definition on Wikipedia suggests that
...The above procedure describes the or | Is random forest a boosting algorithm?
I'd like to point out that Random Forest is not just a bagging technique.
It's a bagging + random subset of the features.
Definition on Wikipedia suggests that
...The above procedure describes the original bagging algorithm for trees. Random forests differ in only one way from th... | Is random forest a boosting algorithm?
I'd like to point out that Random Forest is not just a bagging technique.
It's a bagging + random subset of the features.
Definition on Wikipedia suggests that
...The above procedure describes the or |
3,785 | Cross-Entropy or Log Likelihood in Output layer | The negative log likelihood (eq.80) is also known as the multiclass cross-entropy (ref: Pattern Recognition and Machine Learning Section 4.3.4), as they are in fact two different interpretations of the same formula.
eq.57 is the negative log likelihood of the Bernoulli distribution, whereas eq.80 is the negative log li... | Cross-Entropy or Log Likelihood in Output layer | The negative log likelihood (eq.80) is also known as the multiclass cross-entropy (ref: Pattern Recognition and Machine Learning Section 4.3.4), as they are in fact two different interpretations of th | Cross-Entropy or Log Likelihood in Output layer
The negative log likelihood (eq.80) is also known as the multiclass cross-entropy (ref: Pattern Recognition and Machine Learning Section 4.3.4), as they are in fact two different interpretations of the same formula.
eq.57 is the negative log likelihood of the Bernoulli di... | Cross-Entropy or Log Likelihood in Output layer
The negative log likelihood (eq.80) is also known as the multiclass cross-entropy (ref: Pattern Recognition and Machine Learning Section 4.3.4), as they are in fact two different interpretations of th |
3,786 | Cross-Entropy or Log Likelihood in Output layer | Expanding on @dontloo's answer,
consider a classification task with $K$ classes.
Let's separately look at the output layer of a network and the cost
function. For our purpose here, the output layer is either sigmoid or
softmax and the cost function is either cross-entropy or log-likelihood.
Output Layers
In the case o... | Cross-Entropy or Log Likelihood in Output layer | Expanding on @dontloo's answer,
consider a classification task with $K$ classes.
Let's separately look at the output layer of a network and the cost
function. For our purpose here, the output layer i | Cross-Entropy or Log Likelihood in Output layer
Expanding on @dontloo's answer,
consider a classification task with $K$ classes.
Let's separately look at the output layer of a network and the cost
function. For our purpose here, the output layer is either sigmoid or
softmax and the cost function is either cross-entrop... | Cross-Entropy or Log Likelihood in Output layer
Expanding on @dontloo's answer,
consider a classification task with $K$ classes.
Let's separately look at the output layer of a network and the cost
function. For our purpose here, the output layer i |
3,787 | Cross-Entropy or Log Likelihood in Output layer | I think that @user650654 made a mistake in his formulation of the Cross Entropy and therefore his conclusion is incorrect. In the case of hard labels (i.e., using one-hot vectors for ground truth, where only one element of the vector is assigned 1 and all others are assigned 0 probability), the Cross Entropy loss and t... | Cross-Entropy or Log Likelihood in Output layer | I think that @user650654 made a mistake in his formulation of the Cross Entropy and therefore his conclusion is incorrect. In the case of hard labels (i.e., using one-hot vectors for ground truth, whe | Cross-Entropy or Log Likelihood in Output layer
I think that @user650654 made a mistake in his formulation of the Cross Entropy and therefore his conclusion is incorrect. In the case of hard labels (i.e., using one-hot vectors for ground truth, where only one element of the vector is assigned 1 and all others are assig... | Cross-Entropy or Log Likelihood in Output layer
I think that @user650654 made a mistake in his formulation of the Cross Entropy and therefore his conclusion is incorrect. In the case of hard labels (i.e., using one-hot vectors for ground truth, whe |
3,788 | Interpretation of log transformed predictor and/or response | Charlie provides a nice, correct explanation. The Statistical Computing site at UCLA has some further examples:
https://stats.oarc.ucla.edu/sas/faq/how-can-i-interpret-log-transformed-variables-in-terms-of-percent-change-in-linear-regression, and
https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faqhow-do-i-inter... | Interpretation of log transformed predictor and/or response | Charlie provides a nice, correct explanation. The Statistical Computing site at UCLA has some further examples:
https://stats.oarc.ucla.edu/sas/faq/how-can-i-interpret-log-transformed-variables-in-te | Interpretation of log transformed predictor and/or response
Charlie provides a nice, correct explanation. The Statistical Computing site at UCLA has some further examples:
https://stats.oarc.ucla.edu/sas/faq/how-can-i-interpret-log-transformed-variables-in-terms-of-percent-change-in-linear-regression, and
https://stat... | Interpretation of log transformed predictor and/or response
Charlie provides a nice, correct explanation. The Statistical Computing site at UCLA has some further examples:
https://stats.oarc.ucla.edu/sas/faq/how-can-i-interpret-log-transformed-variables-in-te |
3,789 | Interpretation of log transformed predictor and/or response | In the log-log- model, see that
$$\begin{equation*}\beta_1 = \frac{\partial \log(y)}{\partial \log(x)}.\end{equation*}$$
Recall that
$$\begin{equation*} \frac{\partial \log(y)}{\partial y} = \frac{1}{y} \end{equation*}$$
or
$$\begin{equation*} \partial \log(y) = \frac{\partial y}{y}. \end{equation*}$$
Multiplying this ... | Interpretation of log transformed predictor and/or response | In the log-log- model, see that
$$\begin{equation*}\beta_1 = \frac{\partial \log(y)}{\partial \log(x)}.\end{equation*}$$
Recall that
$$\begin{equation*} \frac{\partial \log(y)}{\partial y} = \frac{1}{ | Interpretation of log transformed predictor and/or response
In the log-log- model, see that
$$\begin{equation*}\beta_1 = \frac{\partial \log(y)}{\partial \log(x)}.\end{equation*}$$
Recall that
$$\begin{equation*} \frac{\partial \log(y)}{\partial y} = \frac{1}{y} \end{equation*}$$
or
$$\begin{equation*} \partial \log(y)... | Interpretation of log transformed predictor and/or response
In the log-log- model, see that
$$\begin{equation*}\beta_1 = \frac{\partial \log(y)}{\partial \log(x)}.\end{equation*}$$
Recall that
$$\begin{equation*} \frac{\partial \log(y)}{\partial y} = \frac{1}{ |
3,790 | Interpretation of log transformed predictor and/or response | The main purpose of linear regression is to estimate a mean difference of outcomes comparing adjacent levels of a regressor. There are many types of means. We are most familiar with the arithmetic mean.
$$AM(X) = \frac{\left( X_1 + X_2 + \ldots + X_n \right)}{n}$$
The AM is what is estimated using OLS and untransforme... | Interpretation of log transformed predictor and/or response | The main purpose of linear regression is to estimate a mean difference of outcomes comparing adjacent levels of a regressor. There are many types of means. We are most familiar with the arithmetic mea | Interpretation of log transformed predictor and/or response
The main purpose of linear regression is to estimate a mean difference of outcomes comparing adjacent levels of a regressor. There are many types of means. We are most familiar with the arithmetic mean.
$$AM(X) = \frac{\left( X_1 + X_2 + \ldots + X_n \right)}... | Interpretation of log transformed predictor and/or response
The main purpose of linear regression is to estimate a mean difference of outcomes comparing adjacent levels of a regressor. There are many types of means. We are most familiar with the arithmetic mea |
3,791 | Two-tailed tests... I'm just not convinced. What's the point? | Think of the data as the tip of the iceberg – all you can see above the water is the tip of the iceberg but in reality you are interested in learning something about the entire iceberg.
Statisticians, data scientists and others working with data are careful to not let what they see above the water line influence and bi... | Two-tailed tests... I'm just not convinced. What's the point? | Think of the data as the tip of the iceberg – all you can see above the water is the tip of the iceberg but in reality you are interested in learning something about the entire iceberg.
Statisticians, | Two-tailed tests... I'm just not convinced. What's the point?
Think of the data as the tip of the iceberg – all you can see above the water is the tip of the iceberg but in reality you are interested in learning something about the entire iceberg.
Statisticians, data scientists and others working with data are careful ... | Two-tailed tests... I'm just not convinced. What's the point?
Think of the data as the tip of the iceberg – all you can see above the water is the tip of the iceberg but in reality you are interested in learning something about the entire iceberg.
Statisticians, |
3,792 | Two-tailed tests... I'm just not convinced. What's the point? | I think when considering your question it helps if you try to keep the goal/selling points of null-hypothesis significance testing (NHST) in mind; it's just one paradigm (albeit a very popular one) for statistical inference, and the others have their own strengths as well (e.g., see here for a discussion of NHST relati... | Two-tailed tests... I'm just not convinced. What's the point? | I think when considering your question it helps if you try to keep the goal/selling points of null-hypothesis significance testing (NHST) in mind; it's just one paradigm (albeit a very popular one) fo | Two-tailed tests... I'm just not convinced. What's the point?
I think when considering your question it helps if you try to keep the goal/selling points of null-hypothesis significance testing (NHST) in mind; it's just one paradigm (albeit a very popular one) for statistical inference, and the others have their own str... | Two-tailed tests... I'm just not convinced. What's the point?
I think when considering your question it helps if you try to keep the goal/selling points of null-hypothesis significance testing (NHST) in mind; it's just one paradigm (albeit a very popular one) fo |
3,793 | Two-tailed tests... I'm just not convinced. What's the point? | Unfortunately, the motivating example of drug development is not a good one as it's not what we do to develop drugs. We use different, more stringent rules to stop the study if trends are on the side of harm. This is for the safety of the patients and also because the drug is unlikely to magically swing in the directio... | Two-tailed tests... I'm just not convinced. What's the point? | Unfortunately, the motivating example of drug development is not a good one as it's not what we do to develop drugs. We use different, more stringent rules to stop the study if trends are on the side | Two-tailed tests... I'm just not convinced. What's the point?
Unfortunately, the motivating example of drug development is not a good one as it's not what we do to develop drugs. We use different, more stringent rules to stop the study if trends are on the side of harm. This is for the safety of the patients and also b... | Two-tailed tests... I'm just not convinced. What's the point?
Unfortunately, the motivating example of drug development is not a good one as it's not what we do to develop drugs. We use different, more stringent rules to stop the study if trends are on the side |
3,794 | Two-tailed tests... I'm just not convinced. What's the point? | One way to approach it is to temporarily forget about hypothesis testing and think about confidence intervals instead. One-sided tests correspond to one-sided confidence intervals and two-sided tests correspond to two-sided confidence intervals.
Suppose that you want to estimate the mean of a population. Naturally, yo... | Two-tailed tests... I'm just not convinced. What's the point? | One way to approach it is to temporarily forget about hypothesis testing and think about confidence intervals instead. One-sided tests correspond to one-sided confidence intervals and two-sided tests | Two-tailed tests... I'm just not convinced. What's the point?
One way to approach it is to temporarily forget about hypothesis testing and think about confidence intervals instead. One-sided tests correspond to one-sided confidence intervals and two-sided tests correspond to two-sided confidence intervals.
Suppose tha... | Two-tailed tests... I'm just not convinced. What's the point?
One way to approach it is to temporarily forget about hypothesis testing and think about confidence intervals instead. One-sided tests correspond to one-sided confidence intervals and two-sided tests |
3,795 | Two-tailed tests... I'm just not convinced. What's the point? | After learning the absolute basics of hypothesis testing and getting
to the part about one vs two tailed tests... I understand the basic
math and increased detection ability of one tailed tests, etc... But I
just can't wrap around my head around one thing... What's the point?
I'm really failing to understand wh... | Two-tailed tests... I'm just not convinced. What's the point? | After learning the absolute basics of hypothesis testing and getting
to the part about one vs two tailed tests... I understand the basic
math and increased detection ability of one tailed tests, e | Two-tailed tests... I'm just not convinced. What's the point?
After learning the absolute basics of hypothesis testing and getting
to the part about one vs two tailed tests... I understand the basic
math and increased detection ability of one tailed tests, etc... But I
just can't wrap around my head around one th... | Two-tailed tests... I'm just not convinced. What's the point?
After learning the absolute basics of hypothesis testing and getting
to the part about one vs two tailed tests... I understand the basic
math and increased detection ability of one tailed tests, e |
3,796 | Two-tailed tests... I'm just not convinced. What's the point? | Well, all difference relies in the question you want to answer. If the question is: "Is one group of values bigger than the other?" you can use a one tailed test. To answer the question: "Are these groups of values different?" you use the two tailed test. Take into consideration that a set of data may be statistically ... | Two-tailed tests... I'm just not convinced. What's the point? | Well, all difference relies in the question you want to answer. If the question is: "Is one group of values bigger than the other?" you can use a one tailed test. To answer the question: "Are these gr | Two-tailed tests... I'm just not convinced. What's the point?
Well, all difference relies in the question you want to answer. If the question is: "Is one group of values bigger than the other?" you can use a one tailed test. To answer the question: "Are these groups of values different?" you use the two tailed test. Ta... | Two-tailed tests... I'm just not convinced. What's the point?
Well, all difference relies in the question you want to answer. If the question is: "Is one group of values bigger than the other?" you can use a one tailed test. To answer the question: "Are these gr |
3,797 | Two-tailed tests... I'm just not convinced. What's the point? | But how is this "doctored" result any less valid than if you had simply chosen the correct one-tailed test in the first place?
The alpha value is the probability that you will reject the null, given that the null is true. Suppose your null is that the sample mean is normally distributed with mean zero. If P(sample mea... | Two-tailed tests... I'm just not convinced. What's the point? | But how is this "doctored" result any less valid than if you had simply chosen the correct one-tailed test in the first place?
The alpha value is the probability that you will reject the null, given | Two-tailed tests... I'm just not convinced. What's the point?
But how is this "doctored" result any less valid than if you had simply chosen the correct one-tailed test in the first place?
The alpha value is the probability that you will reject the null, given that the null is true. Suppose your null is that the sampl... | Two-tailed tests... I'm just not convinced. What's the point?
But how is this "doctored" result any less valid than if you had simply chosen the correct one-tailed test in the first place?
The alpha value is the probability that you will reject the null, given |
3,798 | Two-tailed tests... I'm just not convinced. What's the point? | Regarding the 2nd point
Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed test was.
we have that, if the null is true, the first, two-tailed, test falsely rejects with probability $\alpha$, but t... | Two-tailed tests... I'm just not convinced. What's the point? | Regarding the 2nd point
Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed te | Two-tailed tests... I'm just not convinced. What's the point?
Regarding the 2nd point
Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed test was.
we have that, if the null is true, the first, two... | Two-tailed tests... I'm just not convinced. What's the point?
Regarding the 2nd point
Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed te |
3,799 | Two-tailed tests... I'm just not convinced. What's the point? | This is just one arbitrary way to look at it: What is a statistical test used for? Probably the most frequent reason to perform a test is because you want to convince people (i. e. editors, reviewers, readers, audience) that your results are "far enough off random" to be noteworthy. And somehow we concluded that $p < \... | Two-tailed tests... I'm just not convinced. What's the point? | This is just one arbitrary way to look at it: What is a statistical test used for? Probably the most frequent reason to perform a test is because you want to convince people (i. e. editors, reviewers, | Two-tailed tests... I'm just not convinced. What's the point?
This is just one arbitrary way to look at it: What is a statistical test used for? Probably the most frequent reason to perform a test is because you want to convince people (i. e. editors, reviewers, readers, audience) that your results are "far enough off ... | Two-tailed tests... I'm just not convinced. What's the point?
This is just one arbitrary way to look at it: What is a statistical test used for? Probably the most frequent reason to perform a test is because you want to convince people (i. e. editors, reviewers, |
3,800 | Two-tailed tests... I'm just not convinced. What's the point? | At first glance, neither of these statements make the assertion that a two-sided test is 'superior' to a one-sided study. There simply needs to be a logical connection from the research hypothesis being tested linked to the statistical inference being tested.
For instance:
... consider the consequences of missing an ... | Two-tailed tests... I'm just not convinced. What's the point? | At first glance, neither of these statements make the assertion that a two-sided test is 'superior' to a one-sided study. There simply needs to be a logical connection from the research hypothesis bei | Two-tailed tests... I'm just not convinced. What's the point?
At first glance, neither of these statements make the assertion that a two-sided test is 'superior' to a one-sided study. There simply needs to be a logical connection from the research hypothesis being tested linked to the statistical inference being tested... | Two-tailed tests... I'm just not convinced. What's the point?
At first glance, neither of these statements make the assertion that a two-sided test is 'superior' to a one-sided study. There simply needs to be a logical connection from the research hypothesis bei |
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