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 |
|---|---|---|---|---|---|---|
55,901 | Why does the Null Hypothesis have to be "equals to" and not "greater than or equal to"? | The reason for using $H_0: \mu = 12$ is that, among the set of values that correspond to $\mu \geq 12$, $\mu = 12$ is the most conservative (also called least favorable) configuration.
Let us be more precise what conservative means here. Say we set certain value of the observed statistic $\hat{\mu}$ at which we are wil... | Why does the Null Hypothesis have to be "equals to" and not "greater than or equal to"? | The reason for using $H_0: \mu = 12$ is that, among the set of values that correspond to $\mu \geq 12$, $\mu = 12$ is the most conservative (also called least favorable) configuration.
Let us be more | Why does the Null Hypothesis have to be "equals to" and not "greater than or equal to"?
The reason for using $H_0: \mu = 12$ is that, among the set of values that correspond to $\mu \geq 12$, $\mu = 12$ is the most conservative (also called least favorable) configuration.
Let us be more precise what conservative means ... | Why does the Null Hypothesis have to be "equals to" and not "greater than or equal to"?
The reason for using $H_0: \mu = 12$ is that, among the set of values that correspond to $\mu \geq 12$, $\mu = 12$ is the most conservative (also called least favorable) configuration.
Let us be more |
55,902 | "Proof?" of Bias/Variance trade-off | First write the statement mathematically: define $\mathcal{F}$ as a function space, $\hat{f}_{n,\mathcal{F}} = \arg\min_{\hat{f}\in\mathcal{F}}\sum_{i=1}^n (y_i - \hat{f}(x_i))^2$ as the optimal regression in $\mathcal{F}$, $Bias^2(\hat{f}_{n,\mathcal{F}}(x_0)) = [E(\hat{f}_{n,\mathcal{F}}(x_0)) - f(x_0)]^2$ and $Varia... | "Proof?" of Bias/Variance trade-off | First write the statement mathematically: define $\mathcal{F}$ as a function space, $\hat{f}_{n,\mathcal{F}} = \arg\min_{\hat{f}\in\mathcal{F}}\sum_{i=1}^n (y_i - \hat{f}(x_i))^2$ as the optimal regre | "Proof?" of Bias/Variance trade-off
First write the statement mathematically: define $\mathcal{F}$ as a function space, $\hat{f}_{n,\mathcal{F}} = \arg\min_{\hat{f}\in\mathcal{F}}\sum_{i=1}^n (y_i - \hat{f}(x_i))^2$ as the optimal regression in $\mathcal{F}$, $Bias^2(\hat{f}_{n,\mathcal{F}}(x_0)) = [E(\hat{f}_{n,\mathc... | "Proof?" of Bias/Variance trade-off
First write the statement mathematically: define $\mathcal{F}$ as a function space, $\hat{f}_{n,\mathcal{F}} = \arg\min_{\hat{f}\in\mathcal{F}}\sum_{i=1}^n (y_i - \hat{f}(x_i))^2$ as the optimal regre |
55,903 | "Proof?" of Bias/Variance trade-off | The reason is that there is sort of a proof. The initial important paper is, "Stein, C. (1956). "Inadmissibility of the usual estimator for the mean of a multivariate distribution". Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. 1. pp. 197–206."
What is important about it is th... | "Proof?" of Bias/Variance trade-off | The reason is that there is sort of a proof. The initial important paper is, "Stein, C. (1956). "Inadmissibility of the usual estimator for the mean of a multivariate distribution". Proceedings of th | "Proof?" of Bias/Variance trade-off
The reason is that there is sort of a proof. The initial important paper is, "Stein, C. (1956). "Inadmissibility of the usual estimator for the mean of a multivariate distribution". Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. 1. pp. 197–20... | "Proof?" of Bias/Variance trade-off
The reason is that there is sort of a proof. The initial important paper is, "Stein, C. (1956). "Inadmissibility of the usual estimator for the mean of a multivariate distribution". Proceedings of th |
55,904 | "Proof?" of Bias/Variance trade-off | One argument could be like this - In any setting where there is uncertainty about the true value of the parameter, error is inevitable. We dont have an algorithm or known way of deriving the value of the parameter right? This would automatically mean that the Quadratic risk would have to be greater than zero. This mean... | "Proof?" of Bias/Variance trade-off | One argument could be like this - In any setting where there is uncertainty about the true value of the parameter, error is inevitable. We dont have an algorithm or known way of deriving the value of | "Proof?" of Bias/Variance trade-off
One argument could be like this - In any setting where there is uncertainty about the true value of the parameter, error is inevitable. We dont have an algorithm or known way of deriving the value of the parameter right? This would automatically mean that the Quadratic risk would hav... | "Proof?" of Bias/Variance trade-off
One argument could be like this - In any setting where there is uncertainty about the true value of the parameter, error is inevitable. We dont have an algorithm or known way of deriving the value of |
55,905 | How to derive 2x2 cell counts from contingency table margins and the odds ratio | Write $\rho$ for the odds ratio, $\beta=\Pr(E)$, $\gamma=\Pr(O)$. Four independent equations are
$$\cases{a+b=\beta \\ a+c=\gamma \\ a+b+c+d=1 \\ ad = \rho bc.}$$
Adding the first two shows
$$b+c = \beta + \gamma - 2a. \tag{1}$$
Multiplying the first two equations and using $(1)$ yields
$$bc = \beta\gamma - (\beta+\... | How to derive 2x2 cell counts from contingency table margins and the odds ratio | Write $\rho$ for the odds ratio, $\beta=\Pr(E)$, $\gamma=\Pr(O)$. Four independent equations are
$$\cases{a+b=\beta \\ a+c=\gamma \\ a+b+c+d=1 \\ ad = \rho bc.}$$
Adding the first two shows
$$b+c = | How to derive 2x2 cell counts from contingency table margins and the odds ratio
Write $\rho$ for the odds ratio, $\beta=\Pr(E)$, $\gamma=\Pr(O)$. Four independent equations are
$$\cases{a+b=\beta \\ a+c=\gamma \\ a+b+c+d=1 \\ ad = \rho bc.}$$
Adding the first two shows
$$b+c = \beta + \gamma - 2a. \tag{1}$$
Multiplyi... | How to derive 2x2 cell counts from contingency table margins and the odds ratio
Write $\rho$ for the odds ratio, $\beta=\Pr(E)$, $\gamma=\Pr(O)$. Four independent equations are
$$\cases{a+b=\beta \\ a+c=\gamma \\ a+b+c+d=1 \\ ad = \rho bc.}$$
Adding the first two shows
$$b+c = |
55,906 | Inequality involving joint cumulative and marginal distributions | Hint for the right hand side:
$F_X(x) = P(X < x) \ge P(X < x \wedge Y < y) = F_{X, Y}(x, y)$.
Hint for the left hand side:
The following figure shows the $XY$ plane, with the horizontal and vertical lines intersecting at $(x, y)$.
The region $C$ is the area where $X < x \wedge Y < y$ - you need to integrate over it ... | Inequality involving joint cumulative and marginal distributions | Hint for the right hand side:
$F_X(x) = P(X < x) \ge P(X < x \wedge Y < y) = F_{X, Y}(x, y)$.
Hint for the left hand side:
The following figure shows the $XY$ plane, with the horizontal and vertical | Inequality involving joint cumulative and marginal distributions
Hint for the right hand side:
$F_X(x) = P(X < x) \ge P(X < x \wedge Y < y) = F_{X, Y}(x, y)$.
Hint for the left hand side:
The following figure shows the $XY$ plane, with the horizontal and vertical lines intersecting at $(x, y)$.
The region $C$ is the... | Inequality involving joint cumulative and marginal distributions
Hint for the right hand side:
$F_X(x) = P(X < x) \ge P(X < x \wedge Y < y) = F_{X, Y}(x, y)$.
Hint for the left hand side:
The following figure shows the $XY$ plane, with the horizontal and vertical |
55,907 | Inequality involving joint cumulative and marginal distributions | It is just the elementary inequality $$P(A)+P(B)-1\le P(A\cap B)\le \sqrt{P(A)P(B)}$$ for events $A=\{X\le x\}$ and $B=\{Y\le y\}$. There is no need to go into distributions.
Let $I_A$ be the indicator of $A$, i.e. $I_A=1$ if $A$ occurs and $I_A=0$ if $A$ does not occur.
Then by Cauchy-Schwarz inequality,
$$\left(E\lef... | Inequality involving joint cumulative and marginal distributions | It is just the elementary inequality $$P(A)+P(B)-1\le P(A\cap B)\le \sqrt{P(A)P(B)}$$ for events $A=\{X\le x\}$ and $B=\{Y\le y\}$. There is no need to go into distributions.
Let $I_A$ be the indicato | Inequality involving joint cumulative and marginal distributions
It is just the elementary inequality $$P(A)+P(B)-1\le P(A\cap B)\le \sqrt{P(A)P(B)}$$ for events $A=\{X\le x\}$ and $B=\{Y\le y\}$. There is no need to go into distributions.
Let $I_A$ be the indicator of $A$, i.e. $I_A=1$ if $A$ occurs and $I_A=0$ if $A$... | Inequality involving joint cumulative and marginal distributions
It is just the elementary inequality $$P(A)+P(B)-1\le P(A\cap B)\le \sqrt{P(A)P(B)}$$ for events $A=\{X\le x\}$ and $B=\{Y\le y\}$. There is no need to go into distributions.
Let $I_A$ be the indicato |
55,908 | Error bars in logarithmic scale | The error bar appears to be shorter because the same range requires less space higher up on the graph (where the divisions are closer together). Divisions on the logarithm scale come together as $\frac{1}{y}$ (the gradient of the logarithm) which will decrease the apparent length of the error bars (which in your case i... | Error bars in logarithmic scale | The error bar appears to be shorter because the same range requires less space higher up on the graph (where the divisions are closer together). Divisions on the logarithm scale come together as $\fra | Error bars in logarithmic scale
The error bar appears to be shorter because the same range requires less space higher up on the graph (where the divisions are closer together). Divisions on the logarithm scale come together as $\frac{1}{y}$ (the gradient of the logarithm) which will decrease the apparent length of the ... | Error bars in logarithmic scale
The error bar appears to be shorter because the same range requires less space higher up on the graph (where the divisions are closer together). Divisions on the logarithm scale come together as $\fra |
55,909 | Error bars in logarithmic scale | If you start with $x$ counts and you want to display $ x \pm \sqrt{x}$ then your error bar is of length $2\sqrt{x}$.
If instead your count is $kx$ counts and you want to display $ kx \pm \sqrt{kx}$ then your error bar is of length $2\sqrt{kx}$.
So your error bar on the larger count is longer than the original error ... | Error bars in logarithmic scale | If you start with $x$ counts and you want to display $ x \pm \sqrt{x}$ then your error bar is of length $2\sqrt{x}$.
If instead your count is $kx$ counts and you want to display $ kx \pm \sqrt{kx}$ | Error bars in logarithmic scale
If you start with $x$ counts and you want to display $ x \pm \sqrt{x}$ then your error bar is of length $2\sqrt{x}$.
If instead your count is $kx$ counts and you want to display $ kx \pm \sqrt{kx}$ then your error bar is of length $2\sqrt{kx}$.
So your error bar on the larger count is... | Error bars in logarithmic scale
If you start with $x$ counts and you want to display $ x \pm \sqrt{x}$ then your error bar is of length $2\sqrt{x}$.
If instead your count is $kx$ counts and you want to display $ kx \pm \sqrt{kx}$ |
55,910 | How do errors in variables affect the R2? | Yes, it's possible, but it requires a dearth of simpifying assumptions, not always likely to hold in practice. Let's assume the following model
$$y=\alpha+\beta x^*+\epsilon$$
As usual, we assume $E[x^*\epsilon]=0$. Since you didn't mention measurement error for $y$, I won't include it. However, we do have measurement ... | How do errors in variables affect the R2? | Yes, it's possible, but it requires a dearth of simpifying assumptions, not always likely to hold in practice. Let's assume the following model
$$y=\alpha+\beta x^*+\epsilon$$
As usual, we assume $E[x | How do errors in variables affect the R2?
Yes, it's possible, but it requires a dearth of simpifying assumptions, not always likely to hold in practice. Let's assume the following model
$$y=\alpha+\beta x^*+\epsilon$$
As usual, we assume $E[x^*\epsilon]=0$. Since you didn't mention measurement error for $y$, I won't in... | How do errors in variables affect the R2?
Yes, it's possible, but it requires a dearth of simpifying assumptions, not always likely to hold in practice. Let's assume the following model
$$y=\alpha+\beta x^*+\epsilon$$
As usual, we assume $E[x |
55,911 | Why do Deep Learning libraries force the cost function to output a scalar? | All machine learning is about minimizing cost of some model. The most elementary thing when you try to find minimum value is ability to compare two values. You can do it only with scalar values. For example, given two vectors [0,2], [2,2] how would you compare those tuples? You have to define some norm function. Euclid... | Why do Deep Learning libraries force the cost function to output a scalar? | All machine learning is about minimizing cost of some model. The most elementary thing when you try to find minimum value is ability to compare two values. You can do it only with scalar values. For e | Why do Deep Learning libraries force the cost function to output a scalar?
All machine learning is about minimizing cost of some model. The most elementary thing when you try to find minimum value is ability to compare two values. You can do it only with scalar values. For example, given two vectors [0,2], [2,2] how wo... | Why do Deep Learning libraries force the cost function to output a scalar?
All machine learning is about minimizing cost of some model. The most elementary thing when you try to find minimum value is ability to compare two values. You can do it only with scalar values. For e |
55,912 | Why do Deep Learning libraries force the cost function to output a scalar? | 3 output neurons
The loss function in most applications is chosen such that it calculates a combined loss for these three neurons (e.g. cross entropy loss). This defines the tradeoff between better matching of the target value of neuron 1 at the expense of worse matching of their respective target values of the other... | Why do Deep Learning libraries force the cost function to output a scalar? | 3 output neurons
The loss function in most applications is chosen such that it calculates a combined loss for these three neurons (e.g. cross entropy loss). This defines the tradeoff between better | Why do Deep Learning libraries force the cost function to output a scalar?
3 output neurons
The loss function in most applications is chosen such that it calculates a combined loss for these three neurons (e.g. cross entropy loss). This defines the tradeoff between better matching of the target value of neuron 1 at t... | Why do Deep Learning libraries force the cost function to output a scalar?
3 output neurons
The loss function in most applications is chosen such that it calculates a combined loss for these three neurons (e.g. cross entropy loss). This defines the tradeoff between better |
55,913 | Why do Deep Learning libraries force the cost function to output a scalar? | You ask in a comment:
Let's say we backprop the matrix. If we do that we will get 32 gradient updates for each parameter in the neural net. For each parameter, can't we just take the average of the 32 gradients and use that in gradient descent?
Well, suppose you have 1,000,000 parameters. You're suggesting that we ca... | Why do Deep Learning libraries force the cost function to output a scalar? | You ask in a comment:
Let's say we backprop the matrix. If we do that we will get 32 gradient updates for each parameter in the neural net. For each parameter, can't we just take the average of the 3 | Why do Deep Learning libraries force the cost function to output a scalar?
You ask in a comment:
Let's say we backprop the matrix. If we do that we will get 32 gradient updates for each parameter in the neural net. For each parameter, can't we just take the average of the 32 gradients and use that in gradient descent?... | Why do Deep Learning libraries force the cost function to output a scalar?
You ask in a comment:
Let's say we backprop the matrix. If we do that we will get 32 gradient updates for each parameter in the neural net. For each parameter, can't we just take the average of the 3 |
55,914 | Consistency of estimators in simple linear regression | We'll look at $\hat{\beta}_0 = \bar{y} - \hat{\beta}_1 \bar{x}$ first. The law of large numbers says that $\bar{y}$ converges to $\text{E}(y) = \beta_0 + \beta_1 \text{E}(x)$ and if $\hat{\beta}_1 \to \beta_1$ then $\hat{\beta}_1 \bar{x}$ converges to $\beta_1 \text{E}(x)$. This means $\hat{\beta}_0$ will be consiste... | Consistency of estimators in simple linear regression | We'll look at $\hat{\beta}_0 = \bar{y} - \hat{\beta}_1 \bar{x}$ first. The law of large numbers says that $\bar{y}$ converges to $\text{E}(y) = \beta_0 + \beta_1 \text{E}(x)$ and if $\hat{\beta}_1 \t | Consistency of estimators in simple linear regression
We'll look at $\hat{\beta}_0 = \bar{y} - \hat{\beta}_1 \bar{x}$ first. The law of large numbers says that $\bar{y}$ converges to $\text{E}(y) = \beta_0 + \beta_1 \text{E}(x)$ and if $\hat{\beta}_1 \to \beta_1$ then $\hat{\beta}_1 \bar{x}$ converges to $\beta_1 \tex... | Consistency of estimators in simple linear regression
We'll look at $\hat{\beta}_0 = \bar{y} - \hat{\beta}_1 \bar{x}$ first. The law of large numbers says that $\bar{y}$ converges to $\text{E}(y) = \beta_0 + \beta_1 \text{E}(x)$ and if $\hat{\beta}_1 \t |
55,915 | Consistency of estimators in simple linear regression | Consider the classic situation in which you assume that the true model is of the form:
$y = \beta_0 + \beta_1x + u$, with $E[u] = 0$ . In this case, the OLS estimator will asymptotically converge to $\beta_0$ and $\beta_1$ provided that $E[xu] = 0$
If you mean consistency in the sense of convergence to the parameters o... | Consistency of estimators in simple linear regression | Consider the classic situation in which you assume that the true model is of the form:
$y = \beta_0 + \beta_1x + u$, with $E[u] = 0$ . In this case, the OLS estimator will asymptotically converge to $ | Consistency of estimators in simple linear regression
Consider the classic situation in which you assume that the true model is of the form:
$y = \beta_0 + \beta_1x + u$, with $E[u] = 0$ . In this case, the OLS estimator will asymptotically converge to $\beta_0$ and $\beta_1$ provided that $E[xu] = 0$
If you mean consi... | Consistency of estimators in simple linear regression
Consider the classic situation in which you assume that the true model is of the form:
$y = \beta_0 + \beta_1x + u$, with $E[u] = 0$ . In this case, the OLS estimator will asymptotically converge to $ |
55,916 | How is a cohort study defined? | A cohort study is an observational study wherein each study participant is observed/measured on the dependent variable at two or more points in time. Any explanatory variable(s) may or may not also be observed/measured at each time of observation/measurement. The observation of the dependent variable across time allows... | How is a cohort study defined? | A cohort study is an observational study wherein each study participant is observed/measured on the dependent variable at two or more points in time. Any explanatory variable(s) may or may not also be | How is a cohort study defined?
A cohort study is an observational study wherein each study participant is observed/measured on the dependent variable at two or more points in time. Any explanatory variable(s) may or may not also be observed/measured at each time of observation/measurement. The observation of the depend... | How is a cohort study defined?
A cohort study is an observational study wherein each study participant is observed/measured on the dependent variable at two or more points in time. Any explanatory variable(s) may or may not also be |
55,917 | How is a cohort study defined? | Here is an example of a cohort in the context of a website-based business (but it generalizes to many other kinds).
Imagine you sell a product online. You care about how many people convert (i.e. subscribe) to your website every day.
Say in month 1, 100 people visited your website and 50 people subscribed. Then in mon... | How is a cohort study defined? | Here is an example of a cohort in the context of a website-based business (but it generalizes to many other kinds).
Imagine you sell a product online. You care about how many people convert (i.e. subs | How is a cohort study defined?
Here is an example of a cohort in the context of a website-based business (but it generalizes to many other kinds).
Imagine you sell a product online. You care about how many people convert (i.e. subscribe) to your website every day.
Say in month 1, 100 people visited your website and 50... | How is a cohort study defined?
Here is an example of a cohort in the context of a website-based business (but it generalizes to many other kinds).
Imagine you sell a product online. You care about how many people convert (i.e. subs |
55,918 | How is a cohort study defined? | Let's first look at the term cohort. Originally it has meant a group of people that were born during a specific period, in specific place and identified by period of birth. This definition made it useful to determine things like death rates as people in the cohort aged over time. Cohort is understood much more broadly ... | How is a cohort study defined? | Let's first look at the term cohort. Originally it has meant a group of people that were born during a specific period, in specific place and identified by period of birth. This definition made it use | How is a cohort study defined?
Let's first look at the term cohort. Originally it has meant a group of people that were born during a specific period, in specific place and identified by period of birth. This definition made it useful to determine things like death rates as people in the cohort aged over time. Cohort i... | How is a cohort study defined?
Let's first look at the term cohort. Originally it has meant a group of people that were born during a specific period, in specific place and identified by period of birth. This definition made it use |
55,919 | Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event | The probability of mating at any given year is $\small \Pr(\text{mate})=m$, and the probability of offspring given a mate has been found is $\small \Pr( \text{single offspring} \vert \text{mate} ) =o$ and it does not change after the mate is found.
The probabilities of getting $k$ offspring after $x$ years depends on t... | Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event | The probability of mating at any given year is $\small \Pr(\text{mate})=m$, and the probability of offspring given a mate has been found is $\small \Pr( \text{single offspring} \vert \text{mate} ) =o$ | Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event
The probability of mating at any given year is $\small \Pr(\text{mate})=m$, and the probability of offspring given a mate has been found is $\small \Pr( \text{single offspring} \vert \text{mate} ) =o$ and it does not chan... | Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event
The probability of mating at any given year is $\small \Pr(\text{mate})=m$, and the probability of offspring given a mate has been found is $\small \Pr( \text{single offspring} \vert \text{mate} ) =o$ |
55,920 | How to obtain the functional derivative in variational inference? | Let's streamline the notation by fixing a function $f$ and considering a functional
$$\mathcal{L}[q] = \int (q(z) f(z) - q(z) \log(q(z))) dz.$$
A variation $h$ is a function for which $q+h$ is still the same kind of function as $q$ (e.g., continuous or non-negative or whatever you need). The effect of changing $q$ to ... | How to obtain the functional derivative in variational inference? | Let's streamline the notation by fixing a function $f$ and considering a functional
$$\mathcal{L}[q] = \int (q(z) f(z) - q(z) \log(q(z))) dz.$$
A variation $h$ is a function for which $q+h$ is still t | How to obtain the functional derivative in variational inference?
Let's streamline the notation by fixing a function $f$ and considering a functional
$$\mathcal{L}[q] = \int (q(z) f(z) - q(z) \log(q(z))) dz.$$
A variation $h$ is a function for which $q+h$ is still the same kind of function as $q$ (e.g., continuous or n... | How to obtain the functional derivative in variational inference?
Let's streamline the notation by fixing a function $f$ and considering a functional
$$\mathcal{L}[q] = \int (q(z) f(z) - q(z) \log(q(z))) dz.$$
A variation $h$ is a function for which $q+h$ is still t |
55,921 | How to weight a Spearman rank correlation by statistical errors? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
This paper might help you.
Here its abstract:
This ma... | How to weight a Spearman rank correlation by statistical errors? | 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 to weight a Spearman rank correlation by statistical errors?
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 to weight a Spearman rank correlation by statistical errors?
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.
|
55,922 | How to weight a Spearman rank correlation by statistical errors? | I hate to be another brainless advocate of Monte Carlo methods, but one solution would be to build up a distribution of p values by taking a large number of samples of your data error distributions. For each data point, generate random errors in x and y (within the envelope defined by the measurement errors for that da... | How to weight a Spearman rank correlation by statistical errors? | I hate to be another brainless advocate of Monte Carlo methods, but one solution would be to build up a distribution of p values by taking a large number of samples of your data error distributions. F | How to weight a Spearman rank correlation by statistical errors?
I hate to be another brainless advocate of Monte Carlo methods, but one solution would be to build up a distribution of p values by taking a large number of samples of your data error distributions. For each data point, generate random errors in x and y (... | How to weight a Spearman rank correlation by statistical errors?
I hate to be another brainless advocate of Monte Carlo methods, but one solution would be to build up a distribution of p values by taking a large number of samples of your data error distributions. F |
55,923 | How to weight a Spearman rank correlation by statistical errors? | You can construct a Spearman-like correlation that takes into account weights.
Let's say, we have two rankings, $Q$ and $R$ and two set of weights $W_q$ and $W_r$ (you can have one of these be all ones if you have only one set of weights). You would have to compute these from your errors. All of these have $n$ elements... | How to weight a Spearman rank correlation by statistical errors? | You can construct a Spearman-like correlation that takes into account weights.
Let's say, we have two rankings, $Q$ and $R$ and two set of weights $W_q$ and $W_r$ (you can have one of these be all one | How to weight a Spearman rank correlation by statistical errors?
You can construct a Spearman-like correlation that takes into account weights.
Let's say, we have two rankings, $Q$ and $R$ and two set of weights $W_q$ and $W_r$ (you can have one of these be all ones if you have only one set of weights). You would have ... | How to weight a Spearman rank correlation by statistical errors?
You can construct a Spearman-like correlation that takes into account weights.
Let's say, we have two rankings, $Q$ and $R$ and two set of weights $W_q$ and $W_r$ (you can have one of these be all one |
55,924 | Why do we trust the p-value when fitting a regression on a single sample? | I assume that you talk about the p-value on the estimated coefficient $\hat{\beta}_1$. (but the reasoning would be similar for $\hat{\beta}_0$).
The theory on linear regression tells us that, if the necessary conditions are fulfilled, then we know the distribution of that estimator namely, it is normal, it has mean equ... | Why do we trust the p-value when fitting a regression on a single sample? | I assume that you talk about the p-value on the estimated coefficient $\hat{\beta}_1$. (but the reasoning would be similar for $\hat{\beta}_0$).
The theory on linear regression tells us that, if the n | Why do we trust the p-value when fitting a regression on a single sample?
I assume that you talk about the p-value on the estimated coefficient $\hat{\beta}_1$. (but the reasoning would be similar for $\hat{\beta}_0$).
The theory on linear regression tells us that, if the necessary conditions are fulfilled, then we kno... | Why do we trust the p-value when fitting a regression on a single sample?
I assume that you talk about the p-value on the estimated coefficient $\hat{\beta}_1$. (but the reasoning would be similar for $\hat{\beta}_0$).
The theory on linear regression tells us that, if the n |
55,925 | Why do we trust the p-value when fitting a regression on a single sample? | "Trusting" the p-value may very well mean misunderstanding it. You make up a model with considerable error and sometimes the regression will detect the linear relation, some times not. The risk is determined by choosing the p-value-threshold alpha.
In the case you have proposed. Each p-value under 0.05 is "right", and ... | Why do we trust the p-value when fitting a regression on a single sample? | "Trusting" the p-value may very well mean misunderstanding it. You make up a model with considerable error and sometimes the regression will detect the linear relation, some times not. The risk is det | Why do we trust the p-value when fitting a regression on a single sample?
"Trusting" the p-value may very well mean misunderstanding it. You make up a model with considerable error and sometimes the regression will detect the linear relation, some times not. The risk is determined by choosing the p-value-threshold alph... | Why do we trust the p-value when fitting a regression on a single sample?
"Trusting" the p-value may very well mean misunderstanding it. You make up a model with considerable error and sometimes the regression will detect the linear relation, some times not. The risk is det |
55,926 | Logistic regression gets better but classification gets worse? | With 318 cases in each group you can examine about 20 predictors without too much risk of overfitting. Your second and third sets of variables combine for 23; a big problem is counting each of your neighborhoods in variable set 1 as a fixed effect, using up another 29 degrees of freedom.
The simplest short-term solutio... | Logistic regression gets better but classification gets worse? | With 318 cases in each group you can examine about 20 predictors without too much risk of overfitting. Your second and third sets of variables combine for 23; a big problem is counting each of your ne | Logistic regression gets better but classification gets worse?
With 318 cases in each group you can examine about 20 predictors without too much risk of overfitting. Your second and third sets of variables combine for 23; a big problem is counting each of your neighborhoods in variable set 1 as a fixed effect, using up... | Logistic regression gets better but classification gets worse?
With 318 cases in each group you can examine about 20 predictors without too much risk of overfitting. Your second and third sets of variables combine for 23; a big problem is counting each of your ne |
55,927 | interpretation of slope estimate of Poisson regression | No. There are two problems, one is an arithmetic to english translation, and one is philosophical.
The phrase "decrease by 0.033 units" is to be interpreted as "subtract 0.033 units from y", which is incorrect.
Better is either
One unit increase in year corresponds to multiplication of y by 0.966.
or
One unit incre... | interpretation of slope estimate of Poisson regression | No. There are two problems, one is an arithmetic to english translation, and one is philosophical.
The phrase "decrease by 0.033 units" is to be interpreted as "subtract 0.033 units from y", which is | interpretation of slope estimate of Poisson regression
No. There are two problems, one is an arithmetic to english translation, and one is philosophical.
The phrase "decrease by 0.033 units" is to be interpreted as "subtract 0.033 units from y", which is incorrect.
Better is either
One unit increase in year correspon... | interpretation of slope estimate of Poisson regression
No. There are two problems, one is an arithmetic to english translation, and one is philosophical.
The phrase "decrease by 0.033 units" is to be interpreted as "subtract 0.033 units from y", which is |
55,928 | Why does the glm function does not return an R^2 value? | The glm function uses a maximum likelihood estimator (or restricted maximum likelihood). Maximum likelihood does not minimize the squared error (this is called [ordinary] least squares). Sometimes both estimators give the same results (in the linear/ordinary case for normal distributed error terms, see here) but this d... | Why does the glm function does not return an R^2 value? | The glm function uses a maximum likelihood estimator (or restricted maximum likelihood). Maximum likelihood does not minimize the squared error (this is called [ordinary] least squares). Sometimes bot | Why does the glm function does not return an R^2 value?
The glm function uses a maximum likelihood estimator (or restricted maximum likelihood). Maximum likelihood does not minimize the squared error (this is called [ordinary] least squares). Sometimes both estimators give the same results (in the linear/ordinary case ... | Why does the glm function does not return an R^2 value?
The glm function uses a maximum likelihood estimator (or restricted maximum likelihood). Maximum likelihood does not minimize the squared error (this is called [ordinary] least squares). Sometimes bot |
55,929 | Can we calculate the probability that a null hypothesis is true, in general? | The term "null hypothesis" is usually used in a frequentist setting, where characteristics of the population, such as its mean, are regarded as fixed, not random. There, it makes no sense to talk about the probability of the null hypothesis.
In a Bayesian setting, these characteristics are regarded as random and we can... | Can we calculate the probability that a null hypothesis is true, in general? | The term "null hypothesis" is usually used in a frequentist setting, where characteristics of the population, such as its mean, are regarded as fixed, not random. There, it makes no sense to talk abou | Can we calculate the probability that a null hypothesis is true, in general?
The term "null hypothesis" is usually used in a frequentist setting, where characteristics of the population, such as its mean, are regarded as fixed, not random. There, it makes no sense to talk about the probability of the null hypothesis.
I... | Can we calculate the probability that a null hypothesis is true, in general?
The term "null hypothesis" is usually used in a frequentist setting, where characteristics of the population, such as its mean, are regarded as fixed, not random. There, it makes no sense to talk abou |
55,930 | How to calculate bias when we have an estimation using simple linear regression? | Bias is the difference between the value of the (population) parameter and the expected value of the estimate of that parameter. As @matthew-drury points out, unless one knows the population, we cannot calculate the bias. Unless your data is from a complete census of the population or from simulation (when the data is ... | How to calculate bias when we have an estimation using simple linear regression? | Bias is the difference between the value of the (population) parameter and the expected value of the estimate of that parameter. As @matthew-drury points out, unless one knows the population, we canno | How to calculate bias when we have an estimation using simple linear regression?
Bias is the difference between the value of the (population) parameter and the expected value of the estimate of that parameter. As @matthew-drury points out, unless one knows the population, we cannot calculate the bias. Unless your data ... | How to calculate bias when we have an estimation using simple linear regression?
Bias is the difference between the value of the (population) parameter and the expected value of the estimate of that parameter. As @matthew-drury points out, unless one knows the population, we canno |
55,931 | Minimizing the median absolute deviation or median absolute error | The shortest half is the shortest interval containing half the distribution or data (when dealing with populations or samples respectively). [Some authors call this interval of the shortest half the shorth, though the term seems to have been coined by Andrews et al (1972) who used it to refer to the mean of the observa... | Minimizing the median absolute deviation or median absolute error | The shortest half is the shortest interval containing half the distribution or data (when dealing with populations or samples respectively). [Some authors call this interval of the shortest half the s | Minimizing the median absolute deviation or median absolute error
The shortest half is the shortest interval containing half the distribution or data (when dealing with populations or samples respectively). [Some authors call this interval of the shortest half the shorth, though the term seems to have been coined by An... | Minimizing the median absolute deviation or median absolute error
The shortest half is the shortest interval containing half the distribution or data (when dealing with populations or samples respectively). [Some authors call this interval of the shortest half the s |
55,932 | Poisson Distribution: Estimating rate parameter and the interval length | Let $t=T_F$. Conditional on the number of occurences $N=n$, the arrival times $t_1,t_2,\dots,t_N$ are known to have the same distribution as the order statstics of $n$ iid unif$(0,t)$ random variables. Hence, the likelihood becomes
\begin{align}
L(\lambda,t) &= P(N=n) f(t_1,t_2,\dots,t_N|N=n) \\
&= \frac{e^{-\lambda ... | Poisson Distribution: Estimating rate parameter and the interval length | Let $t=T_F$. Conditional on the number of occurences $N=n$, the arrival times $t_1,t_2,\dots,t_N$ are known to have the same distribution as the order statstics of $n$ iid unif$(0,t)$ random variable | Poisson Distribution: Estimating rate parameter and the interval length
Let $t=T_F$. Conditional on the number of occurences $N=n$, the arrival times $t_1,t_2,\dots,t_N$ are known to have the same distribution as the order statstics of $n$ iid unif$(0,t)$ random variables. Hence, the likelihood becomes
\begin{align}
... | Poisson Distribution: Estimating rate parameter and the interval length
Let $t=T_F$. Conditional on the number of occurences $N=n$, the arrival times $t_1,t_2,\dots,t_N$ are known to have the same distribution as the order statstics of $n$ iid unif$(0,t)$ random variable |
55,933 | Neural network not i.i.d | There are several ways to have independency assumptions in neural nets. One is that all your samples are independent, i.e. if you have a data base of 10'000 cat pictures, you assume they have all be taken independently of each other.
Another is if you want to regress on certain values. Say you want to regress from the... | Neural network not i.i.d | There are several ways to have independency assumptions in neural nets. One is that all your samples are independent, i.e. if you have a data base of 10'000 cat pictures, you assume they have all be t | Neural network not i.i.d
There are several ways to have independency assumptions in neural nets. One is that all your samples are independent, i.e. if you have a data base of 10'000 cat pictures, you assume they have all be taken independently of each other.
Another is if you want to regress on certain values. Say you... | Neural network not i.i.d
There are several ways to have independency assumptions in neural nets. One is that all your samples are independent, i.e. if you have a data base of 10'000 cat pictures, you assume they have all be t |
55,934 | Neural network not i.i.d | Without aiming for the Math: using non independent and/or unequally distributed variables is possible with ANN. You might trigger some side effects by doing so, like with unequally distributed variables having an overly long training phase, getting stuck in (other) local optima (though this is less of an issue in the a... | Neural network not i.i.d | Without aiming for the Math: using non independent and/or unequally distributed variables is possible with ANN. You might trigger some side effects by doing so, like with unequally distributed variabl | Neural network not i.i.d
Without aiming for the Math: using non independent and/or unequally distributed variables is possible with ANN. You might trigger some side effects by doing so, like with unequally distributed variables having an overly long training phase, getting stuck in (other) local optima (though this is ... | Neural network not i.i.d
Without aiming for the Math: using non independent and/or unequally distributed variables is possible with ANN. You might trigger some side effects by doing so, like with unequally distributed variabl |
55,935 | Creating clusters for binary data | Latent class modeling would be one approach to finding underlying, "hidden" partitions or groupings of diseases. LC is a very flexible method with two broad approaches: replications based on repeated measures across subjects vs replications based on cross-classifying a set of categorical variables with no repeated meas... | Creating clusters for binary data | Latent class modeling would be one approach to finding underlying, "hidden" partitions or groupings of diseases. LC is a very flexible method with two broad approaches: replications based on repeated | Creating clusters for binary data
Latent class modeling would be one approach to finding underlying, "hidden" partitions or groupings of diseases. LC is a very flexible method with two broad approaches: replications based on repeated measures across subjects vs replications based on cross-classifying a set of categoric... | Creating clusters for binary data
Latent class modeling would be one approach to finding underlying, "hidden" partitions or groupings of diseases. LC is a very flexible method with two broad approaches: replications based on repeated |
55,936 | Creating clusters for binary data | Many forms of clustering could work. Since you asked about constructing a dendrogram, it sounds like you want hierarchical clustering. Hierarchical agglomerative clustering is a popular class of methods. You'll have to choose the linkage function, which determines how clusters are merged. UPGMA (aka average linkage) is... | Creating clusters for binary data | Many forms of clustering could work. Since you asked about constructing a dendrogram, it sounds like you want hierarchical clustering. Hierarchical agglomerative clustering is a popular class of metho | Creating clusters for binary data
Many forms of clustering could work. Since you asked about constructing a dendrogram, it sounds like you want hierarchical clustering. Hierarchical agglomerative clustering is a popular class of methods. You'll have to choose the linkage function, which determines how clusters are merg... | Creating clusters for binary data
Many forms of clustering could work. Since you asked about constructing a dendrogram, it sounds like you want hierarchical clustering. Hierarchical agglomerative clustering is a popular class of metho |
55,937 | GLMM- relationship between AICc weight and random effects? | I would strongly advise you to avoid automated model selection procedures such as dredge() (even the function name makes me shiver). There may be some merit in these when you are primarily concerned about prediction for future data, but even in this case it is strongly recommended to use some form of cross-validation, ... | GLMM- relationship between AICc weight and random effects? | I would strongly advise you to avoid automated model selection procedures such as dredge() (even the function name makes me shiver). There may be some merit in these when you are primarily concerned a | GLMM- relationship between AICc weight and random effects?
I would strongly advise you to avoid automated model selection procedures such as dredge() (even the function name makes me shiver). There may be some merit in these when you are primarily concerned about prediction for future data, but even in this case it is ... | GLMM- relationship between AICc weight and random effects?
I would strongly advise you to avoid automated model selection procedures such as dredge() (even the function name makes me shiver). There may be some merit in these when you are primarily concerned a |
55,938 | GLMM- relationship between AICc weight and random effects? | Akaike weights only provide information about the set of models from which they are calculated, so in your example, you can't really learn anything from comparing weights for the glmm set of models to weights for the glm set of models (i.e. Akaike weights won't tell you whether the random effect is appropriate).
There'... | GLMM- relationship between AICc weight and random effects? | Akaike weights only provide information about the set of models from which they are calculated, so in your example, you can't really learn anything from comparing weights for the glmm set of models to | GLMM- relationship between AICc weight and random effects?
Akaike weights only provide information about the set of models from which they are calculated, so in your example, you can't really learn anything from comparing weights for the glmm set of models to weights for the glm set of models (i.e. Akaike weights won't... | GLMM- relationship between AICc weight and random effects?
Akaike weights only provide information about the set of models from which they are calculated, so in your example, you can't really learn anything from comparing weights for the glmm set of models to |
55,939 | In PCA, do the principal components beyond the first optimize any expression? | The first $k$ principal components minimize the squared reconstruction error. That is, we project the data onto the first $k$ principal components, then back into the original space to obtain a 'reconstruction' of the data. The first $k$ principal components are the vectors that minimize the sum of squared distances be... | In PCA, do the principal components beyond the first optimize any expression? | The first $k$ principal components minimize the squared reconstruction error. That is, we project the data onto the first $k$ principal components, then back into the original space to obtain a 'recon | In PCA, do the principal components beyond the first optimize any expression?
The first $k$ principal components minimize the squared reconstruction error. That is, we project the data onto the first $k$ principal components, then back into the original space to obtain a 'reconstruction' of the data. The first $k$ prin... | In PCA, do the principal components beyond the first optimize any expression?
The first $k$ principal components minimize the squared reconstruction error. That is, we project the data onto the first $k$ principal components, then back into the original space to obtain a 'recon |
55,940 | Linear regression polynomial slope constraint in R | First of all, let's write the unconstrained model so that the coefficients are consistently ordered (in this case, from lowest to highest degree):
unconstrained_model <- lm(y ~ x + I(x^2) +I(x^3))
Secondly, constrained least square regression always has higher RMSE on the data sample than unconstrained least square, u... | Linear regression polynomial slope constraint in R | First of all, let's write the unconstrained model so that the coefficients are consistently ordered (in this case, from lowest to highest degree):
unconstrained_model <- lm(y ~ x + I(x^2) +I(x^3))
Se | Linear regression polynomial slope constraint in R
First of all, let's write the unconstrained model so that the coefficients are consistently ordered (in this case, from lowest to highest degree):
unconstrained_model <- lm(y ~ x + I(x^2) +I(x^3))
Secondly, constrained least square regression always has higher RMSE on... | Linear regression polynomial slope constraint in R
First of all, let's write the unconstrained model so that the coefficients are consistently ordered (in this case, from lowest to highest degree):
unconstrained_model <- lm(y ~ x + I(x^2) +I(x^3))
Se |
55,941 | Working with percentages of positive variables | As mentioned in the OP and comments, the sample mean is an unbiased estimator of the population mean so we should not fear any "positive bias" when using it to obtain a point estimate of the forecasted impact ($\mu$).
That said, if the percentages tend to be highly variable, which may happen if you work with small deno... | Working with percentages of positive variables | As mentioned in the OP and comments, the sample mean is an unbiased estimator of the population mean so we should not fear any "positive bias" when using it to obtain a point estimate of the forecaste | Working with percentages of positive variables
As mentioned in the OP and comments, the sample mean is an unbiased estimator of the population mean so we should not fear any "positive bias" when using it to obtain a point estimate of the forecasted impact ($\mu$).
That said, if the percentages tend to be highly variabl... | Working with percentages of positive variables
As mentioned in the OP and comments, the sample mean is an unbiased estimator of the population mean so we should not fear any "positive bias" when using it to obtain a point estimate of the forecaste |
55,942 | Working with percentages of positive variables | I think it depends on what you want to do. Looking at your example from finance, it seems to me as if you want to estimate your total return (in euro or dollar) for a portfolio, using an estimated percentage return on a sample. Let's say you have a sample of securities with values $v_i$, and returns $r_i$, $i=1, 2, \... | Working with percentages of positive variables | I think it depends on what you want to do. Looking at your example from finance, it seems to me as if you want to estimate your total return (in euro or dollar) for a portfolio, using an estimated pe | Working with percentages of positive variables
I think it depends on what you want to do. Looking at your example from finance, it seems to me as if you want to estimate your total return (in euro or dollar) for a portfolio, using an estimated percentage return on a sample. Let's say you have a sample of securities w... | Working with percentages of positive variables
I think it depends on what you want to do. Looking at your example from finance, it seems to me as if you want to estimate your total return (in euro or dollar) for a portfolio, using an estimated pe |
55,943 | Working with percentages of positive variables | Asymmetry of percentage/proportion changes: The issue you have raised in your question is not actually a statistical problem. Rather, it is a mathematical problem about the appropriate way to measure percentage changes in a non-negative quantity. If you want to aggregate positive and negative percentage changes for a... | Working with percentages of positive variables | Asymmetry of percentage/proportion changes: The issue you have raised in your question is not actually a statistical problem. Rather, it is a mathematical problem about the appropriate way to measure | Working with percentages of positive variables
Asymmetry of percentage/proportion changes: The issue you have raised in your question is not actually a statistical problem. Rather, it is a mathematical problem about the appropriate way to measure percentage changes in a non-negative quantity. If you want to aggregate... | Working with percentages of positive variables
Asymmetry of percentage/proportion changes: The issue you have raised in your question is not actually a statistical problem. Rather, it is a mathematical problem about the appropriate way to measure |
55,944 | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | Also consider sparse principal component analysis, and redundancy analysis. The latter is implemented in the R Hmisc package redun function and involves attempting to predict each predictor from all the other predictors. It handles the "wings" issue discussed above. | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | Also consider sparse principal component analysis, and redundancy analysis. The latter is implemented in the R Hmisc package redun function and involves attempting to predict each predictor from all | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
Also consider sparse principal component analysis, and redundancy analysis. The latter is implemented in the R Hmisc package redun function and involves attempting to predict each predictor from all the other predictors. ... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
Also consider sparse principal component analysis, and redundancy analysis. The latter is implemented in the R Hmisc package redun function and involves attempting to predict each predictor from all |
55,945 | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | I'll first remark that conventional PCA is not so well adapted to categorical features (such as whether or not an organism has wings). The reason is that the principal components are generally nontrivial linear combinations of the input features, and it's not always clear what that should mean. For instance the first... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | I'll first remark that conventional PCA is not so well adapted to categorical features (such as whether or not an organism has wings). The reason is that the principal components are generally nontri | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
I'll first remark that conventional PCA is not so well adapted to categorical features (such as whether or not an organism has wings). The reason is that the principal components are generally nontrivial linear combination... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
I'll first remark that conventional PCA is not so well adapted to categorical features (such as whether or not an organism has wings). The reason is that the principal components are generally nontri |
55,946 | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | Having done the two step exercise of PCA followed by clustering more than a few times, I have developed a strong POV. First, there are lots of good reasons for smoothing your inputs with PCA -- most importantly, redundancy is removed. Next and as @hssay notes, the resulting PCA is a linear combination of all of the inp... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | Having done the two step exercise of PCA followed by clustering more than a few times, I have developed a strong POV. First, there are lots of good reasons for smoothing your inputs with PCA -- most i | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
Having done the two step exercise of PCA followed by clustering more than a few times, I have developed a strong POV. First, there are lots of good reasons for smoothing your inputs with PCA -- most importantly, redundancy ... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
Having done the two step exercise of PCA followed by clustering more than a few times, I have developed a strong POV. First, there are lots of good reasons for smoothing your inputs with PCA -- most i |
55,947 | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | Specifically on the question of interpreting the result: you cannot generally pinpoint to individual variables contributing maximum variance. What the result of 3 components contributing maximum variance is this: there are 3 new variables derived by taking a linear combination of original variables which is found to re... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis? | Specifically on the question of interpreting the result: you cannot generally pinpoint to individual variables contributing maximum variance. What the result of 3 components contributing maximum varia | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
Specifically on the question of interpreting the result: you cannot generally pinpoint to individual variables contributing maximum variance. What the result of 3 components contributing maximum variance is this: there are ... | Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?
Specifically on the question of interpreting the result: you cannot generally pinpoint to individual variables contributing maximum variance. What the result of 3 components contributing maximum varia |
55,948 | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | As far as I know, degrees of freedom in Chi Square distribution are related to the number of classes a population can be classified minus the linear restrictions used to estimate the parameters.
Originally, Karl Pearson provided Chi Square statistic to compare observed versus expected values in a contingency table, whe... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | As far as I know, degrees of freedom in Chi Square distribution are related to the number of classes a population can be classified minus the linear restrictions used to estimate the parameters.
Origi | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
As far as I know, degrees of freedom in Chi Square distribution are related to the number of classes a population can be classified minus the linear restrictions used to estimate the parameters.
Originally, Karl Pearson provided C... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
As far as I know, degrees of freedom in Chi Square distribution are related to the number of classes a population can be classified minus the linear restrictions used to estimate the parameters.
Origi |
55,949 | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | This is a much more complicated question that it might first seem, and there was a bitter disagreement between Fisher and Pearson on this question.
With modern computing it is easy to demonstrate by simulation that the distribution is $\chi^2_1$, not $\chi^2_3$, eg
> tests<-replicate(1000,{
+ y<-rbinom(400, 1, .2)
... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | This is a much more complicated question that it might first seem, and there was a bitter disagreement between Fisher and Pearson on this question.
With modern computing it is easy to demonstrate by | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
This is a much more complicated question that it might first seem, and there was a bitter disagreement between Fisher and Pearson on this question.
With modern computing it is easy to demonstrate by simulation that the distributi... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
This is a much more complicated question that it might first seem, and there was a bitter disagreement between Fisher and Pearson on this question.
With modern computing it is easy to demonstrate by |
55,950 | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | If we have a 2x2 table with two variables and sample size n is set, then in essence, the marginal sums of those two variables taken sepparately is also set as n.
That comes from the fact that with marginals we only look at one variable and disregard the other completely. We can imagine deleting the line that devide ... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | If we have a 2x2 table with two variables and sample size n is set, then in essence, the marginal sums of those two variables taken sepparately is also set as n.
That comes from the fact that with m | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
If we have a 2x2 table with two variables and sample size n is set, then in essence, the marginal sums of those two variables taken sepparately is also set as n.
That comes from the fact that with marginals we only look at one v... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
If we have a 2x2 table with two variables and sample size n is set, then in essence, the marginal sums of those two variables taken sepparately is also set as n.
That comes from the fact that with m |
55,951 | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | We have a $M \times N$ contingency table, under H1: no association, there are $MN-1$ number of free parameters. Under H0: $p_{ij} = p_ip_j$, we have $(N-1) + (M-1)$ free parameters,
$$DegreeOfFreedom = MN-1 - (N-1) - (M-1) = (M-1)(N-1)$$ | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1? | We have a $M \times N$ contingency table, under H1: no association, there are $MN-1$ number of free parameters. Under H0: $p_{ij} = p_ip_j$, we have $(N-1) + (M-1)$ free parameters,
$$DegreeOfFreedom | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
We have a $M \times N$ contingency table, under H1: no association, there are $MN-1$ number of free parameters. Under H0: $p_{ij} = p_ip_j$, we have $(N-1) + (M-1)$ free parameters,
$$DegreeOfFreedom = MN-1 - (N-1) - (M-1) = (M-1)... | Why are the degrees of freedom for a chi-square test on a 2x2 contingency table always 1?
We have a $M \times N$ contingency table, under H1: no association, there are $MN-1$ number of free parameters. Under H0: $p_{ij} = p_ip_j$, we have $(N-1) + (M-1)$ free parameters,
$$DegreeOfFreedom |
55,952 | Good text on nonlinear regression (M.S. graduate-level)? | Two pretty standard references would be
Bates, D.M. & Watts, D.G. (1988),
Nonlinear Regression Analysis and Its Applications,
Wiley, New York.
Seber, G.A.F. & Wild, C.J. (1989),
Nonlinear Regression,
Wiley, New York. | Good text on nonlinear regression (M.S. graduate-level)? | Two pretty standard references would be
Bates, D.M. & Watts, D.G. (1988),
Nonlinear Regression Analysis and Its Applications,
Wiley, New York.
Seber, G.A.F. & Wild, C.J. (1989),
Nonlinear Regression | Good text on nonlinear regression (M.S. graduate-level)?
Two pretty standard references would be
Bates, D.M. & Watts, D.G. (1988),
Nonlinear Regression Analysis and Its Applications,
Wiley, New York.
Seber, G.A.F. & Wild, C.J. (1989),
Nonlinear Regression,
Wiley, New York. | Good text on nonlinear regression (M.S. graduate-level)?
Two pretty standard references would be
Bates, D.M. & Watts, D.G. (1988),
Nonlinear Regression Analysis and Its Applications,
Wiley, New York.
Seber, G.A.F. & Wild, C.J. (1989),
Nonlinear Regression |
55,953 | Real-world example on significance testing with large samples | Page 205 of Meehl (1990) briefly describes a study of 57,000 high-school seniors in which 92% of 990 different cross-tabulations (between 45 variables; 45 choose 2 is 990) were statistically significant. Most people who've heard of this study are probably familiar with it from Cohen (1994).
Standing, Sproule, and Khouz... | Real-world example on significance testing with large samples | Page 205 of Meehl (1990) briefly describes a study of 57,000 high-school seniors in which 92% of 990 different cross-tabulations (between 45 variables; 45 choose 2 is 990) were statistically significa | Real-world example on significance testing with large samples
Page 205 of Meehl (1990) briefly describes a study of 57,000 high-school seniors in which 92% of 990 different cross-tabulations (between 45 variables; 45 choose 2 is 990) were statistically significant. Most people who've heard of this study are probably fa... | Real-world example on significance testing with large samples
Page 205 of Meehl (1990) briefly describes a study of 57,000 high-school seniors in which 92% of 990 different cross-tabulations (between 45 variables; 45 choose 2 is 990) were statistically significa |
55,954 | Real-world example on significance testing with large samples | The thing that I find so teethgrating about this expression:
"null hypothesis is almost always false"
is that it underscores the sloppy way with which modern, frequentist hypothesis testing is done. If you adhere to that framework, then it is true, virtually all causal relations are in some, albeit miniscule and com... | Real-world example on significance testing with large samples | The thing that I find so teethgrating about this expression:
"null hypothesis is almost always false"
is that it underscores the sloppy way with which modern, frequentist hypothesis testing is done | Real-world example on significance testing with large samples
The thing that I find so teethgrating about this expression:
"null hypothesis is almost always false"
is that it underscores the sloppy way with which modern, frequentist hypothesis testing is done. If you adhere to that framework, then it is true, virtua... | Real-world example on significance testing with large samples
The thing that I find so teethgrating about this expression:
"null hypothesis is almost always false"
is that it underscores the sloppy way with which modern, frequentist hypothesis testing is done |
55,955 | Real-world example on significance testing with large samples | I think you should into the American's Statistic association statement on p-values.
They do quote that big data researches should not draw any conclusions from p-values by itself. | Real-world example on significance testing with large samples | I think you should into the American's Statistic association statement on p-values.
They do quote that big data researches should not draw any conclusions from p-values by itself. | Real-world example on significance testing with large samples
I think you should into the American's Statistic association statement on p-values.
They do quote that big data researches should not draw any conclusions from p-values by itself. | Real-world example on significance testing with large samples
I think you should into the American's Statistic association statement on p-values.
They do quote that big data researches should not draw any conclusions from p-values by itself. |
55,956 | Constrained optimization in R | Using answer given by @crayfish and a detailed answer on how to put construct constraints here, I was able to come up with a solution.
#define F and S here
F = c(10,10,5)
S = c(8,8,9,8,4)
#loss_fun: to be minimized
loss_fun <- function(A){
P = matrix(A, nrow = n,ncol = m, byrow=T)
T = S*P #proportion matrix * ... | Constrained optimization in R | Using answer given by @crayfish and a detailed answer on how to put construct constraints here, I was able to come up with a solution.
#define F and S here
F = c(10,10,5)
S = c(8,8,9,8,4)
#loss_fun: | Constrained optimization in R
Using answer given by @crayfish and a detailed answer on how to put construct constraints here, I was able to come up with a solution.
#define F and S here
F = c(10,10,5)
S = c(8,8,9,8,4)
#loss_fun: to be minimized
loss_fun <- function(A){
P = matrix(A, nrow = n,ncol = m, byrow=T)
... | Constrained optimization in R
Using answer given by @crayfish and a detailed answer on how to put construct constraints here, I was able to come up with a solution.
#define F and S here
F = c(10,10,5)
S = c(8,8,9,8,4)
#loss_fun: |
55,957 | Constrained optimization in R | I'm not sure if I'm right but help constrOptim {stats} say theta: numeric (vector) starting value (of length p): must be in the feasible region, and your theta is a matrix.
I think here is near to your idea (Input is a vector and the function makes it a matrix).
[EDITED] NOT NEAR because of difference constraints. Ple... | Constrained optimization in R | I'm not sure if I'm right but help constrOptim {stats} say theta: numeric (vector) starting value (of length p): must be in the feasible region, and your theta is a matrix.
I think here is near to yo | Constrained optimization in R
I'm not sure if I'm right but help constrOptim {stats} say theta: numeric (vector) starting value (of length p): must be in the feasible region, and your theta is a matrix.
I think here is near to your idea (Input is a vector and the function makes it a matrix).
[EDITED] NOT NEAR because ... | Constrained optimization in R
I'm not sure if I'm right but help constrOptim {stats} say theta: numeric (vector) starting value (of length p): must be in the feasible region, and your theta is a matrix.
I think here is near to yo |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.