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 |
|---|---|---|---|---|---|---|
38,301 | T-test paradox: can adding a single point very far from the null value change the outcome from significant to nonsignificant? | Why is this a paradox?
You are describing a typical situation which we encounter daily: your hypothesis is rejected, then you add one more observation and it's not rejected anymore. I think the reason why it looks like a paradox of sorts is purely psychological. It's called "framing bias" in behavioral economics.
Let's... | T-test paradox: can adding a single point very far from the null value change the outcome from signi | Why is this a paradox?
You are describing a typical situation which we encounter daily: your hypothesis is rejected, then you add one more observation and it's not rejected anymore. I think the reason | T-test paradox: can adding a single point very far from the null value change the outcome from significant to nonsignificant?
Why is this a paradox?
You are describing a typical situation which we encounter daily: your hypothesis is rejected, then you add one more observation and it's not rejected anymore. I think the ... | T-test paradox: can adding a single point very far from the null value change the outcome from signi
Why is this a paradox?
You are describing a typical situation which we encounter daily: your hypothesis is rejected, then you add one more observation and it's not rejected anymore. I think the reason |
38,302 | Use of Bayesian hierarchical model | To the best of my knowledge, there is no opposition between Bayesian models (BM) and hierarchical Bayesian models (HBM) (see e.g. Relation between Bayesian analysis and Bayesian hierarchical analysis?) and the fact is that, analytically, HBMs are BMs. Hierarchical models simply allow you to design a convoled prior stru... | Use of Bayesian hierarchical model | To the best of my knowledge, there is no opposition between Bayesian models (BM) and hierarchical Bayesian models (HBM) (see e.g. Relation between Bayesian analysis and Bayesian hierarchical analysis? | Use of Bayesian hierarchical model
To the best of my knowledge, there is no opposition between Bayesian models (BM) and hierarchical Bayesian models (HBM) (see e.g. Relation between Bayesian analysis and Bayesian hierarchical analysis?) and the fact is that, analytically, HBMs are BMs. Hierarchical models simply allow ... | Use of Bayesian hierarchical model
To the best of my knowledge, there is no opposition between Bayesian models (BM) and hierarchical Bayesian models (HBM) (see e.g. Relation between Bayesian analysis and Bayesian hierarchical analysis? |
38,303 | Use of Bayesian hierarchical model | In my opinion, there are two different aspects to your question:
when should I use a hierarchical model?
when should I perform a Bayesian analysis?
When should I use a hierarchical model?
An advantage to using hierarchical models is their flexibility in modeling the continuum from all groups have the same parameters ... | Use of Bayesian hierarchical model | In my opinion, there are two different aspects to your question:
when should I use a hierarchical model?
when should I perform a Bayesian analysis?
When should I use a hierarchical model?
An advanta | Use of Bayesian hierarchical model
In my opinion, there are two different aspects to your question:
when should I use a hierarchical model?
when should I perform a Bayesian analysis?
When should I use a hierarchical model?
An advantage to using hierarchical models is their flexibility in modeling the continuum from a... | Use of Bayesian hierarchical model
In my opinion, there are two different aspects to your question:
when should I use a hierarchical model?
when should I perform a Bayesian analysis?
When should I use a hierarchical model?
An advanta |
38,304 | What are neurons in neural networks / how do they work? | You are correct in your overall view of the subject. The neuron is nothing more than a set of inputs, a set of weights, and an activation function. The neuron translates these inputs into a single output, which can then be picked up as input for another layer of neurons later on.
While details can vary between neural n... | What are neurons in neural networks / how do they work? | You are correct in your overall view of the subject. The neuron is nothing more than a set of inputs, a set of weights, and an activation function. The neuron translates these inputs into a single out | What are neurons in neural networks / how do they work?
You are correct in your overall view of the subject. The neuron is nothing more than a set of inputs, a set of weights, and an activation function. The neuron translates these inputs into a single output, which can then be picked up as input for another layer of n... | What are neurons in neural networks / how do they work?
You are correct in your overall view of the subject. The neuron is nothing more than a set of inputs, a set of weights, and an activation function. The neuron translates these inputs into a single out |
38,305 | What are neurons in neural networks / how do they work? | Within an artificial neural network, a neuron is a mathematical function that model the functioning of a biological neuron. Typically, a neuron compute the weighted average of its input, and this sum is passed through a nonlinear function, often called activation function, such as the sigmoid. I attach an image from an... | What are neurons in neural networks / how do they work? | Within an artificial neural network, a neuron is a mathematical function that model the functioning of a biological neuron. Typically, a neuron compute the weighted average of its input, and this sum | What are neurons in neural networks / how do they work?
Within an artificial neural network, a neuron is a mathematical function that model the functioning of a biological neuron. Typically, a neuron compute the weighted average of its input, and this sum is passed through a nonlinear function, often called activation ... | What are neurons in neural networks / how do they work?
Within an artificial neural network, a neuron is a mathematical function that model the functioning of a biological neuron. Typically, a neuron compute the weighted average of its input, and this sum |
38,306 | What are neurons in neural networks / how do they work? | The simplest versions are fairly simple, especially the regression case. If $y$ is your outcome and $X$is your data, the model is
$$
y= Z'\beta
$$
$$
Z=\sigma(X'\alpha)
$$
$$
\sigma(x) = 1/(1+e^{-x})
$$
$\alpha$ and $\beta$ are parameters, and are chosen by an optimizer. Fixing the number of Z's is the same as fixing ... | What are neurons in neural networks / how do they work? | The simplest versions are fairly simple, especially the regression case. If $y$ is your outcome and $X$is your data, the model is
$$
y= Z'\beta
$$
$$
Z=\sigma(X'\alpha)
$$
$$
\sigma(x) = 1/(1+e^{-x})
| What are neurons in neural networks / how do they work?
The simplest versions are fairly simple, especially the regression case. If $y$ is your outcome and $X$is your data, the model is
$$
y= Z'\beta
$$
$$
Z=\sigma(X'\alpha)
$$
$$
\sigma(x) = 1/(1+e^{-x})
$$
$\alpha$ and $\beta$ are parameters, and are chosen by an opt... | What are neurons in neural networks / how do they work?
The simplest versions are fairly simple, especially the regression case. If $y$ is your outcome and $X$is your data, the model is
$$
y= Z'\beta
$$
$$
Z=\sigma(X'\alpha)
$$
$$
\sigma(x) = 1/(1+e^{-x})
|
38,307 | What are neurons in neural networks / how do they work? | In Software Engineering Artifical Neural Networks, Neurons are "containers" of mathematical functions, typically drawn as circles in Artificial Neural Networks graphical representations (see picture below). One or more neurons form a layer -- a set of layers typically disposed in vertical line in Artificial Neural Netw... | What are neurons in neural networks / how do they work? | In Software Engineering Artifical Neural Networks, Neurons are "containers" of mathematical functions, typically drawn as circles in Artificial Neural Networks graphical representations (see picture b | What are neurons in neural networks / how do they work?
In Software Engineering Artifical Neural Networks, Neurons are "containers" of mathematical functions, typically drawn as circles in Artificial Neural Networks graphical representations (see picture below). One or more neurons form a layer -- a set of layers typic... | What are neurons in neural networks / how do they work?
In Software Engineering Artifical Neural Networks, Neurons are "containers" of mathematical functions, typically drawn as circles in Artificial Neural Networks graphical representations (see picture b |
38,308 | Kernel matrix is not positive definite | Most research in kernel methods focuses on Mercer kernels, which have two properties: (1) the function is symmetric: $K(x,y)=K(y,x)$ and (2) the function is positive semi-definite (p.s.d.). The Gaussian covariance function is certainly p.s.d., but I can't recall if it is also p.d. -- perhaps you've mistakenly omitted t... | Kernel matrix is not positive definite | Most research in kernel methods focuses on Mercer kernels, which have two properties: (1) the function is symmetric: $K(x,y)=K(y,x)$ and (2) the function is positive semi-definite (p.s.d.). The Gaussi | Kernel matrix is not positive definite
Most research in kernel methods focuses on Mercer kernels, which have two properties: (1) the function is symmetric: $K(x,y)=K(y,x)$ and (2) the function is positive semi-definite (p.s.d.). The Gaussian covariance function is certainly p.s.d., but I can't recall if it is also p.d.... | Kernel matrix is not positive definite
Most research in kernel methods focuses on Mercer kernels, which have two properties: (1) the function is symmetric: $K(x,y)=K(y,x)$ and (2) the function is positive semi-definite (p.s.d.). The Gaussi |
38,309 | Kernel matrix is not positive definite | I believe I know that example. I worked it in R and got the same problem with singularity. You might try adding some white noise to the model. The squared exponential kernel is very smooth, so if your data points are close together, the covariance matrix goes singular. Recall that at short distances, differentiable fun... | Kernel matrix is not positive definite | I believe I know that example. I worked it in R and got the same problem with singularity. You might try adding some white noise to the model. The squared exponential kernel is very smooth, so if your | Kernel matrix is not positive definite
I believe I know that example. I worked it in R and got the same problem with singularity. You might try adding some white noise to the model. The squared exponential kernel is very smooth, so if your data points are close together, the covariance matrix goes singular. Recall that... | Kernel matrix is not positive definite
I believe I know that example. I worked it in R and got the same problem with singularity. You might try adding some white noise to the model. The squared exponential kernel is very smooth, so if your |
38,310 | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent? | Here is an example of this, attributed to S. Benstein.
Let $X_1, X_2, X_3$ have the joint pmf
$$p\left(x_1, x_2, x_3 \right) =\begin{cases} \frac{1}{4} & \left(x_1, x_2, x_3 \right) \in \left\{ (1,0,0), (0,1,0), (0,0,1), (1,1,1) \right\} \\ 0 & \text{otherwise} \end{cases}$$
Then by summing out the third variable it i... | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent? | Here is an example of this, attributed to S. Benstein.
Let $X_1, X_2, X_3$ have the joint pmf
$$p\left(x_1, x_2, x_3 \right) =\begin{cases} \frac{1}{4} & \left(x_1, x_2, x_3 \right) \in \left\{ (1,0,0 | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
Here is an example of this, attributed to S. Benstein.
Let $X_1, X_2, X_3$ have the joint pmf
$$p\left(x_1, x_2, x_3 \right) =\begin{cases} \frac{1}{4} & \left(x_1, x_2, x_3 \right) \in \left\{ (1,0,0), (0,1,0), (0,0,1), (1,1,1) \right\} \\ 0 & \text{oth... | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
Here is an example of this, attributed to S. Benstein.
Let $X_1, X_2, X_3$ have the joint pmf
$$p\left(x_1, x_2, x_3 \right) =\begin{cases} \frac{1}{4} & \left(x_1, x_2, x_3 \right) \in \left\{ (1,0,0 |
38,311 | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent? | $X$, $Y$ independent Bernoulli$(\frac 12)$ and $Z= X+Y-2XY$ is an example of three random variables that are pairwise independent but not
mutually independent.
It is easy to show that $Z$ is also Bernoulli$(\frac 12)$ and that $(X,Z)$
and $(Y,Z)$ are pairs of independent random variables, and of
course, $(X,Y)$ is a... | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent? | $X$, $Y$ independent Bernoulli$(\frac 12)$ and $Z= X+Y-2XY$ is an example of three random variables that are pairwise independent but not
mutually independent.
It is easy to show that $Z$ is also Be | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
$X$, $Y$ independent Bernoulli$(\frac 12)$ and $Z= X+Y-2XY$ is an example of three random variables that are pairwise independent but not
mutually independent.
It is easy to show that $Z$ is also Bernoulli$(\frac 12)$ and that $(X,Z)$
and $(Y,Z)$ are ... | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
$X$, $Y$ independent Bernoulli$(\frac 12)$ and $Z= X+Y-2XY$ is an example of three random variables that are pairwise independent but not
mutually independent.
It is easy to show that $Z$ is also Be |
38,312 | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent? | One that's perhaps easier to think about comes from a chessboard. Pick a point uniformly on the chessboard and consider
$X_1$: row number (1-8) modulo 2
$X_2$: column number (1-8) modulo 2
$X_3$: color, 0 for white,1 for black.
It's easy to see than any pair of these is independent: rows are independent of columns; ro... | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent? | One that's perhaps easier to think about comes from a chessboard. Pick a point uniformly on the chessboard and consider
$X_1$: row number (1-8) modulo 2
$X_2$: column number (1-8) modulo 2
$X_3$: col | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
One that's perhaps easier to think about comes from a chessboard. Pick a point uniformly on the chessboard and consider
$X_1$: row number (1-8) modulo 2
$X_2$: column number (1-8) modulo 2
$X_3$: color, 0 for white,1 for black.
It's easy to see than any... | $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
One that's perhaps easier to think about comes from a chessboard. Pick a point uniformly on the chessboard and consider
$X_1$: row number (1-8) modulo 2
$X_2$: column number (1-8) modulo 2
$X_3$: col |
38,313 | What to do if residuals are not normally distributed? | You should not remove outliers just because they make the distribution of the residuals non-normal. You may examine the case that has that high residual and see if there are problems with it (the easiest would be if it is a data entry error) but you must justify your deletion on substantive grounds.
Assuming there is... | What to do if residuals are not normally distributed? | You should not remove outliers just because they make the distribution of the residuals non-normal. You may examine the case that has that high residual and see if there are problems with it (the eas | What to do if residuals are not normally distributed?
You should not remove outliers just because they make the distribution of the residuals non-normal. You may examine the case that has that high residual and see if there are problems with it (the easiest would be if it is a data entry error) but you must justify yo... | What to do if residuals are not normally distributed?
You should not remove outliers just because they make the distribution of the residuals non-normal. You may examine the case that has that high residual and see if there are problems with it (the eas |
38,314 | What to do if residuals are not normally distributed? | @PeterFlom has made some good points here. I agree with his three points and his plan of action. Let me clear up one remaining issue:
You are correct to note that only the residuals need to be normally distributed. However, @dsaxton is also right that in the real world, no data (including residuals) are ever perfe... | What to do if residuals are not normally distributed? | @PeterFlom has made some good points here. I agree with his three points and his plan of action. Let me clear up one remaining issue:
You are correct to note that only the residuals need to be nor | What to do if residuals are not normally distributed?
@PeterFlom has made some good points here. I agree with his three points and his plan of action. Let me clear up one remaining issue:
You are correct to note that only the residuals need to be normally distributed. However, @dsaxton is also right that in the re... | What to do if residuals are not normally distributed?
@PeterFlom has made some good points here. I agree with his three points and his plan of action. Let me clear up one remaining issue:
You are correct to note that only the residuals need to be nor |
38,315 | What to do if residuals are not normally distributed? | As this is an optional assumption, just ignore the normality of residuals and go ahead. In most sensitive cases, you can remove or replace the outliers with mean value or justified value to improve the condition. | What to do if residuals are not normally distributed? | As this is an optional assumption, just ignore the normality of residuals and go ahead. In most sensitive cases, you can remove or replace the outliers with mean value or justified value to improve th | What to do if residuals are not normally distributed?
As this is an optional assumption, just ignore the normality of residuals and go ahead. In most sensitive cases, you can remove or replace the outliers with mean value or justified value to improve the condition. | What to do if residuals are not normally distributed?
As this is an optional assumption, just ignore the normality of residuals and go ahead. In most sensitive cases, you can remove or replace the outliers with mean value or justified value to improve th |
38,316 | Is centering a valid solution for multicollinearity? | When the model is additive and linear, centering has nothing to do with collinearity. Centering can only help when there are multiple terms per variable such as square or interaction terms. Even then, centering only helps in a way that doesn't matter to us, because centering does not impact the pooled multiple degree... | Is centering a valid solution for multicollinearity? | When the model is additive and linear, centering has nothing to do with collinearity. Centering can only help when there are multiple terms per variable such as square or interaction terms. Even the | Is centering a valid solution for multicollinearity?
When the model is additive and linear, centering has nothing to do with collinearity. Centering can only help when there are multiple terms per variable such as square or interaction terms. Even then, centering only helps in a way that doesn't matter to us, because... | Is centering a valid solution for multicollinearity?
When the model is additive and linear, centering has nothing to do with collinearity. Centering can only help when there are multiple terms per variable such as square or interaction terms. Even the |
38,317 | Is centering a valid solution for multicollinearity? | (An easy way to find out is to try it and check for multicollinearity using the same methods you had used to discover the multicollinearity the first time ;-)
No, unfortunately, centering $x_1$ and $x_2$ will not help you. When you have multicollinearity with just two variables, you have a (very strong) pairwise corr... | Is centering a valid solution for multicollinearity? | (An easy way to find out is to try it and check for multicollinearity using the same methods you had used to discover the multicollinearity the first time ;-)
No, unfortunately, centering $x_1$ and $ | Is centering a valid solution for multicollinearity?
(An easy way to find out is to try it and check for multicollinearity using the same methods you had used to discover the multicollinearity the first time ;-)
No, unfortunately, centering $x_1$ and $x_2$ will not help you. When you have multicollinearity with just ... | Is centering a valid solution for multicollinearity?
(An easy way to find out is to try it and check for multicollinearity using the same methods you had used to discover the multicollinearity the first time ;-)
No, unfortunately, centering $x_1$ and $ |
38,318 | Is centering a valid solution for multicollinearity? | When you ask if centering is a valid solution to the problem of multicollinearity, then I think it is helpful to discuss what the problem actually is. I say this because there is great disagreement about whether or not multicollinearity is "a problem" that needs a statistical solution. Many people, also many very well-... | Is centering a valid solution for multicollinearity? | When you ask if centering is a valid solution to the problem of multicollinearity, then I think it is helpful to discuss what the problem actually is. I say this because there is great disagreement ab | Is centering a valid solution for multicollinearity?
When you ask if centering is a valid solution to the problem of multicollinearity, then I think it is helpful to discuss what the problem actually is. I say this because there is great disagreement about whether or not multicollinearity is "a problem" that needs a st... | Is centering a valid solution for multicollinearity?
When you ask if centering is a valid solution to the problem of multicollinearity, then I think it is helpful to discuss what the problem actually is. I say this because there is great disagreement ab |
38,319 | Is a p-value a sample statistic, or a population parameter, or neither? | A p-value is a random variable, so it's not a population parameter.
You could certainly argue that it's a statistic:
A statistic (singular) is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of ... | Is a p-value a sample statistic, or a population parameter, or neither? | A p-value is a random variable, so it's not a population parameter.
You could certainly argue that it's a statistic:
A statistic (singular) is a single measure of some attribute of a sample (e.g., it | Is a p-value a sample statistic, or a population parameter, or neither?
A p-value is a random variable, so it's not a population parameter.
You could certainly argue that it's a statistic:
A statistic (singular) is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by ap... | Is a p-value a sample statistic, or a population parameter, or neither?
A p-value is a random variable, so it's not a population parameter.
You could certainly argue that it's a statistic:
A statistic (singular) is a single measure of some attribute of a sample (e.g., it |
38,320 | Is a p-value a sample statistic, or a population parameter, or neither? | A $p$-value is the probability of observing a test static value as or more extreme than the test statistic created from one's data if the null hypothesis is true. You can therefore interpret the $p$-value as a measure of how extreme your test statistic is under H$_{0}$ and the probability distribution attached to H$_{0... | Is a p-value a sample statistic, or a population parameter, or neither? | A $p$-value is the probability of observing a test static value as or more extreme than the test statistic created from one's data if the null hypothesis is true. You can therefore interpret the $p$-v | Is a p-value a sample statistic, or a population parameter, or neither?
A $p$-value is the probability of observing a test static value as or more extreme than the test statistic created from one's data if the null hypothesis is true. You can therefore interpret the $p$-value as a measure of how extreme your test stati... | Is a p-value a sample statistic, or a population parameter, or neither?
A $p$-value is the probability of observing a test static value as or more extreme than the test statistic created from one's data if the null hypothesis is true. You can therefore interpret the $p$-v |
38,321 | Is a p-value a sample statistic, or a population parameter, or neither? | If the test statistic can be called a statistic, then so must the $p$-value: the test statistic is a function of the data under the assumption that the null hypothesis is true. The $p$-value is simply a probability associated with that test statistic. | Is a p-value a sample statistic, or a population parameter, or neither? | If the test statistic can be called a statistic, then so must the $p$-value: the test statistic is a function of the data under the assumption that the null hypothesis is true. The $p$-value is simp | Is a p-value a sample statistic, or a population parameter, or neither?
If the test statistic can be called a statistic, then so must the $p$-value: the test statistic is a function of the data under the assumption that the null hypothesis is true. The $p$-value is simply a probability associated with that test stati... | Is a p-value a sample statistic, or a population parameter, or neither?
If the test statistic can be called a statistic, then so must the $p$-value: the test statistic is a function of the data under the assumption that the null hypothesis is true. The $p$-value is simp |
38,322 | Visualising the variance | If the main concern is "that our customers gets very conscious of the actual number. Even though we try to tell them that a high/low number isn't necessarily bad", then I think you should formally address them by plotting the confidence intervals. Variance is a bad choice because its unit is the square of whatever you'... | Visualising the variance | If the main concern is "that our customers gets very conscious of the actual number. Even though we try to tell them that a high/low number isn't necessarily bad", then I think you should formally add | Visualising the variance
If the main concern is "that our customers gets very conscious of the actual number. Even though we try to tell them that a high/low number isn't necessarily bad", then I think you should formally address them by plotting the confidence intervals. Variance is a bad choice because its unit is th... | Visualising the variance
If the main concern is "that our customers gets very conscious of the actual number. Even though we try to tell them that a high/low number isn't necessarily bad", then I think you should formally add |
38,323 | Visualising the variance | The question can be reduced to "How do I show one value of interest against a reference distribution?". The former, showing a value of interest is the simple part; any dramatic marking at that point on the graph will do. So it will be useful to show different ways of displaying the reference distribution. We need not k... | Visualising the variance | The question can be reduced to "How do I show one value of interest against a reference distribution?". The former, showing a value of interest is the simple part; any dramatic marking at that point o | Visualising the variance
The question can be reduced to "How do I show one value of interest against a reference distribution?". The former, showing a value of interest is the simple part; any dramatic marking at that point on the graph will do. So it will be useful to show different ways of displaying the reference di... | Visualising the variance
The question can be reduced to "How do I show one value of interest against a reference distribution?". The former, showing a value of interest is the simple part; any dramatic marking at that point o |
38,324 | Visualising the variance | As I understand from his comments, Christian wants to add an iconish representation of the variance to an existing plot. We don't know what kind of plot yet. For a dotplot, the moment of inertia representation of the variance possibly is a solution. Taking the standard deviation of the sample as the horizontal radius i... | Visualising the variance | As I understand from his comments, Christian wants to add an iconish representation of the variance to an existing plot. We don't know what kind of plot yet. For a dotplot, the moment of inertia repre | Visualising the variance
As I understand from his comments, Christian wants to add an iconish representation of the variance to an existing plot. We don't know what kind of plot yet. For a dotplot, the moment of inertia representation of the variance possibly is a solution. Taking the standard deviation of the sample a... | Visualising the variance
As I understand from his comments, Christian wants to add an iconish representation of the variance to an existing plot. We don't know what kind of plot yet. For a dotplot, the moment of inertia repre |
38,325 | Visualising the variance | The square root of variance is on the same scale as your data. For a normal distribution, this is known as the standard deviation.
It is a common practise to normalize values to multiples of the standard deviation, such that $+3\sigma$ is considered an unusually high value, whereas $-3\sigma$ is considered unusually lo... | Visualising the variance | The square root of variance is on the same scale as your data. For a normal distribution, this is known as the standard deviation.
It is a common practise to normalize values to multiples of the stand | Visualising the variance
The square root of variance is on the same scale as your data. For a normal distribution, this is known as the standard deviation.
It is a common practise to normalize values to multiples of the standard deviation, such that $+3\sigma$ is considered an unusually high value, whereas $-3\sigma$ i... | Visualising the variance
The square root of variance is on the same scale as your data. For a normal distribution, this is known as the standard deviation.
It is a common practise to normalize values to multiples of the stand |
38,326 | Visualising the variance | I would suggest using bar plots with pairs of bars for the target group next to the reference group, and on top of each bar plot confidence intervals (I's) centered around the top of the bar with length of $2\sigma$, where $\sigma$ is the standard deviation. See example from Wikipedia's Error Bar article: | Visualising the variance | I would suggest using bar plots with pairs of bars for the target group next to the reference group, and on top of each bar plot confidence intervals (I's) centered around the top of the bar with leng | Visualising the variance
I would suggest using bar plots with pairs of bars for the target group next to the reference group, and on top of each bar plot confidence intervals (I's) centered around the top of the bar with length of $2\sigma$, where $\sigma$ is the standard deviation. See example from Wikipedia's Error B... | Visualising the variance
I would suggest using bar plots with pairs of bars for the target group next to the reference group, and on top of each bar plot confidence intervals (I's) centered around the top of the bar with leng |
38,327 | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate] | use pvals.fnc() function the pMCMC here works like p-value which should be less than 0.05 to reject the null hypothesis. | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate] | use pvals.fnc() function the pMCMC here works like p-value which should be less than 0.05 to reject the null hypothesis. | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate]
use pvals.fnc() function the pMCMC here works like p-value which should be less than 0.05 to reject the null hypothesis. | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate]
use pvals.fnc() function the pMCMC here works like p-value which should be less than 0.05 to reject the null hypothesis. |
38,328 | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate] | The lmer package's author made a conscious choice not to create p-values for the fixed effects. Some packages do, but he feels that they are doing simplistic calculations that are misleading. (Many statisticians feel that there's a p-value obsession that causes confusion in and of itself, but that's a separate matter.)... | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate] | The lmer package's author made a conscious choice not to create p-values for the fixed effects. Some packages do, but he feels that they are doing simplistic calculations that are misleading. (Many st | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate]
The lmer package's author made a conscious choice not to create p-values for the fixed effects. Some packages do, but he feels that they are doing simplistic calculations that are misleading. (Many statisticians feel that there's a p-valu... | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate]
The lmer package's author made a conscious choice not to create p-values for the fixed effects. Some packages do, but he feels that they are doing simplistic calculations that are misleading. (Many st |
38,329 | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate] | Install the coda and languageR package and run the pvals.fnc as follows for p-value:
Model.pval<-pvals.fnc(Model, nsim = n, withMCMC = TRUE)
Note that this will not work for level 3 or above in nested random effects models. | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate] | Install the coda and languageR package and run the pvals.fnc as follows for p-value:
Model.pval<-pvals.fnc(Model, nsim = n, withMCMC = TRUE)
Note that this will not work for level 3 or above in nested | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate]
Install the coda and languageR package and run the pvals.fnc as follows for p-value:
Model.pval<-pvals.fnc(Model, nsim = n, withMCMC = TRUE)
Note that this will not work for level 3 or above in nested random effects models. | Can't find p-values in the output from lmer() in the lm4 package in R [duplicate]
Install the coda and languageR package and run the pvals.fnc as follows for p-value:
Model.pval<-pvals.fnc(Model, nsim = n, withMCMC = TRUE)
Note that this will not work for level 3 or above in nested |
38,330 | How to correlate ordinal and nominal variables in SPSS? | You should have a look at multiple correspondence analysis. This is a technique to uncover patterns and structures in categorical data. It is an example of what some people call "French Data Analysis"
In SPSS, you can use the CORRESPONDENCE command. If you prefer the Menu, it is available via "Analyze -> Data Reduction... | How to correlate ordinal and nominal variables in SPSS? | You should have a look at multiple correspondence analysis. This is a technique to uncover patterns and structures in categorical data. It is an example of what some people call "French Data Analysis" | How to correlate ordinal and nominal variables in SPSS?
You should have a look at multiple correspondence analysis. This is a technique to uncover patterns and structures in categorical data. It is an example of what some people call "French Data Analysis"
In SPSS, you can use the CORRESPONDENCE command. If you prefer ... | How to correlate ordinal and nominal variables in SPSS?
You should have a look at multiple correspondence analysis. This is a technique to uncover patterns and structures in categorical data. It is an example of what some people call "French Data Analysis" |
38,331 | How to correlate ordinal and nominal variables in SPSS? | You might want to look at the AUTORECODE command (Transform > Automatic Recode) if you are reading a lot of string data that needs to be converted to numeric.
Parametric and nonparametric correlations are available from the Analyze > Correlate menu for a first look. There are tools available as extensions for color co... | How to correlate ordinal and nominal variables in SPSS? | You might want to look at the AUTORECODE command (Transform > Automatic Recode) if you are reading a lot of string data that needs to be converted to numeric.
Parametric and nonparametric correlations | How to correlate ordinal and nominal variables in SPSS?
You might want to look at the AUTORECODE command (Transform > Automatic Recode) if you are reading a lot of string data that needs to be converted to numeric.
Parametric and nonparametric correlations are available from the Analyze > Correlate menu for a first loo... | How to correlate ordinal and nominal variables in SPSS?
You might want to look at the AUTORECODE command (Transform > Automatic Recode) if you are reading a lot of string data that needs to be converted to numeric.
Parametric and nonparametric correlations |
38,332 | How to correlate ordinal and nominal variables in SPSS? | Try Categorical Regression (Optimal Scaling).
Nominal variables don't have scale. How far is 'divorced' from 'married'? Does not make sense unless you have another measure to help put the nominal variable levels in order and distance from each other.
Ordinal variables don't have scale either. How far is 'fair' from... | How to correlate ordinal and nominal variables in SPSS? | Try Categorical Regression (Optimal Scaling).
Nominal variables don't have scale. How far is 'divorced' from 'married'? Does not make sense unless you have another measure to help put the nominal v | How to correlate ordinal and nominal variables in SPSS?
Try Categorical Regression (Optimal Scaling).
Nominal variables don't have scale. How far is 'divorced' from 'married'? Does not make sense unless you have another measure to help put the nominal variable levels in order and distance from each other.
Ordinal va... | How to correlate ordinal and nominal variables in SPSS?
Try Categorical Regression (Optimal Scaling).
Nominal variables don't have scale. How far is 'divorced' from 'married'? Does not make sense unless you have another measure to help put the nominal v |
38,333 | How to correlate ordinal and nominal variables in SPSS? | Use Transform > Automatic Recode to make two numeric variables that carry the information of your two string variables.
Run a frequency table of the new variables, and make sure the string attributes are correct. E.g. check for misspelling (commute vs communte), plural/singular confusion (cars vs car), and grammatical ... | How to correlate ordinal and nominal variables in SPSS? | Use Transform > Automatic Recode to make two numeric variables that carry the information of your two string variables.
Run a frequency table of the new variables, and make sure the string attributes | How to correlate ordinal and nominal variables in SPSS?
Use Transform > Automatic Recode to make two numeric variables that carry the information of your two string variables.
Run a frequency table of the new variables, and make sure the string attributes are correct. E.g. check for misspelling (commute vs communte), p... | How to correlate ordinal and nominal variables in SPSS?
Use Transform > Automatic Recode to make two numeric variables that carry the information of your two string variables.
Run a frequency table of the new variables, and make sure the string attributes |
38,334 | How to correlate ordinal and nominal variables in SPSS? | A correlation of nominal (e.g. Client yes or no) and ordinal (e.g. 5-point likert scale on satisfaction) variables can be had using chi-square analysis. The 2 x (5?) table (which a researcher might want to reduce to a 2 x 2 table by bucketing categories) will hypothesis test whether a significant relationship exists (c... | How to correlate ordinal and nominal variables in SPSS? | A correlation of nominal (e.g. Client yes or no) and ordinal (e.g. 5-point likert scale on satisfaction) variables can be had using chi-square analysis. The 2 x (5?) table (which a researcher might wa | How to correlate ordinal and nominal variables in SPSS?
A correlation of nominal (e.g. Client yes or no) and ordinal (e.g. 5-point likert scale on satisfaction) variables can be had using chi-square analysis. The 2 x (5?) table (which a researcher might want to reduce to a 2 x 2 table by bucketing categories) will hypo... | How to correlate ordinal and nominal variables in SPSS?
A correlation of nominal (e.g. Client yes or no) and ordinal (e.g. 5-point likert scale on satisfaction) variables can be had using chi-square analysis. The 2 x (5?) table (which a researcher might wa |
38,335 | Patient distance metrics | You asked a difficult question, but I'm a little bit surprised that the various clues that were suggested to you received so little attention. I upvoted all of them because I think they basically are useful responses, though in their actual form they call for further bibliographic work.
Disclaimer: I never had to deal ... | Patient distance metrics | You asked a difficult question, but I'm a little bit surprised that the various clues that were suggested to you received so little attention. I upvoted all of them because I think they basically are | Patient distance metrics
You asked a difficult question, but I'm a little bit surprised that the various clues that were suggested to you received so little attention. I upvoted all of them because I think they basically are useful responses, though in their actual form they call for further bibliographic work.
Disclai... | Patient distance metrics
You asked a difficult question, but I'm a little bit surprised that the various clues that were suggested to you received so little attention. I upvoted all of them because I think they basically are |
38,336 | Patient distance metrics | I might be misunderstanding your goals here, but to me it sounds like a multi-dimensional scaling (MDS) problem. I've never used MDS myself, but my sense is that it should allow you to derive a global measure of similarity as well as dimensional measures of similarity. My memory is that it is able to handle both conti... | Patient distance metrics | I might be misunderstanding your goals here, but to me it sounds like a multi-dimensional scaling (MDS) problem. I've never used MDS myself, but my sense is that it should allow you to derive a globa | Patient distance metrics
I might be misunderstanding your goals here, but to me it sounds like a multi-dimensional scaling (MDS) problem. I've never used MDS myself, but my sense is that it should allow you to derive a global measure of similarity as well as dimensional measures of similarity. My memory is that it is ... | Patient distance metrics
I might be misunderstanding your goals here, but to me it sounds like a multi-dimensional scaling (MDS) problem. I've never used MDS myself, but my sense is that it should allow you to derive a globa |
38,337 | Patient distance metrics | The whole field of Cluster Analysis is relevant to your concept of multi-variable statistical distance. The linked book on the subject is very short and pretty good. | Patient distance metrics | The whole field of Cluster Analysis is relevant to your concept of multi-variable statistical distance. The linked book on the subject is very short and pretty good. | Patient distance metrics
The whole field of Cluster Analysis is relevant to your concept of multi-variable statistical distance. The linked book on the subject is very short and pretty good. | Patient distance metrics
The whole field of Cluster Analysis is relevant to your concept of multi-variable statistical distance. The linked book on the subject is very short and pretty good. |
38,338 | Patient distance metrics | The simple idea is to make PCA and base distance of few first components (yet I don't like this technique because of assumptions it makes).
The complex idea is to use machine learning; the resulting distances will expose the classifier structure, so will be about as good as the classification accuracy. The simplest app... | Patient distance metrics | The simple idea is to make PCA and base distance of few first components (yet I don't like this technique because of assumptions it makes).
The complex idea is to use machine learning; the resulting d | Patient distance metrics
The simple idea is to make PCA and base distance of few first components (yet I don't like this technique because of assumptions it makes).
The complex idea is to use machine learning; the resulting distances will expose the classifier structure, so will be about as good as the classification a... | Patient distance metrics
The simple idea is to make PCA and base distance of few first components (yet I don't like this technique because of assumptions it makes).
The complex idea is to use machine learning; the resulting d |
38,339 | Patient distance metrics | There is a subfield called Distance Metric Learning. One such method is Information Theoretic Metric Learning (ITML). | Patient distance metrics | There is a subfield called Distance Metric Learning. One such method is Information Theoretic Metric Learning (ITML). | Patient distance metrics
There is a subfield called Distance Metric Learning. One such method is Information Theoretic Metric Learning (ITML). | Patient distance metrics
There is a subfield called Distance Metric Learning. One such method is Information Theoretic Metric Learning (ITML). |
38,340 | How would YOU compute IMDB movie rating? | First, define the theoretical construct of interest. There are many ways that a rating can be defined:
What is the theoretical target population? The entire world, English speakers, people who visit IMDB, people who have seen the movie in question?
What is the target time frame? It is the rating of the movie now or av... | How would YOU compute IMDB movie rating? | First, define the theoretical construct of interest. There are many ways that a rating can be defined:
What is the theoretical target population? The entire world, English speakers, people who visit | How would YOU compute IMDB movie rating?
First, define the theoretical construct of interest. There are many ways that a rating can be defined:
What is the theoretical target population? The entire world, English speakers, people who visit IMDB, people who have seen the movie in question?
What is the target time frame... | How would YOU compute IMDB movie rating?
First, define the theoretical construct of interest. There are many ways that a rating can be defined:
What is the theoretical target population? The entire world, English speakers, people who visit |
38,341 | How would YOU compute IMDB movie rating? | Partial answer. See the help page entitled: The vote average for film "X" should be Y! Why are you displaying another rating?
In short, IMDb uses:
a complex voter weighting system to make sure
that the final rating is
representative of the general voting
population and not subject to over
influence from indiv... | How would YOU compute IMDB movie rating? | Partial answer. See the help page entitled: The vote average for film "X" should be Y! Why are you displaying another rating?
In short, IMDb uses:
a complex voter weighting system to make sure
tha | How would YOU compute IMDB movie rating?
Partial answer. See the help page entitled: The vote average for film "X" should be Y! Why are you displaying another rating?
In short, IMDb uses:
a complex voter weighting system to make sure
that the final rating is
representative of the general voting
population and n... | How would YOU compute IMDB movie rating?
Partial answer. See the help page entitled: The vote average for film "X" should be Y! Why are you displaying another rating?
In short, IMDb uses:
a complex voter weighting system to make sure
tha |
38,342 | How would YOU compute IMDB movie rating? | Whats wrong with my score? Why is it not ideal (because IMDB didn't
use it)?
If the score was only for your use, then nothing is wrong with your calculation.
However, IMDB try to make it difficult for people to obviously influence the final score.
If you had to compute. How would you have done it? What factors you... | How would YOU compute IMDB movie rating? | Whats wrong with my score? Why is it not ideal (because IMDB didn't
use it)?
If the score was only for your use, then nothing is wrong with your calculation.
However, IMDB try to make it difficult | How would YOU compute IMDB movie rating?
Whats wrong with my score? Why is it not ideal (because IMDB didn't
use it)?
If the score was only for your use, then nothing is wrong with your calculation.
However, IMDB try to make it difficult for people to obviously influence the final score.
If you had to compute. How... | How would YOU compute IMDB movie rating?
Whats wrong with my score? Why is it not ideal (because IMDB didn't
use it)?
If the score was only for your use, then nothing is wrong with your calculation.
However, IMDB try to make it difficult |
38,343 | How can I determine accuracy of past probability calculations? | What you're looking for are called Scoring Rules, which are ways of evaluating probabilistic forecasts. They were invented in the 1950s by weather forecasters, and there has been a been a bit of work on them in the statistics community, but I don't know of any books on the topic.
One thing you could do would be to bin ... | How can I determine accuracy of past probability calculations? | What you're looking for are called Scoring Rules, which are ways of evaluating probabilistic forecasts. They were invented in the 1950s by weather forecasters, and there has been a been a bit of work | How can I determine accuracy of past probability calculations?
What you're looking for are called Scoring Rules, which are ways of evaluating probabilistic forecasts. They were invented in the 1950s by weather forecasters, and there has been a been a bit of work on them in the statistics community, but I don't know of ... | How can I determine accuracy of past probability calculations?
What you're looking for are called Scoring Rules, which are ways of evaluating probabilistic forecasts. They were invented in the 1950s by weather forecasters, and there has been a been a bit of work |
38,344 | How can I determine accuracy of past probability calculations? | In their classic book on the Federalist papers, Mosteller and Wallace argue for a log penalty function: you penalize yourself $-\log(p)$ when you predict an event with probability $p$ and it occurs; the penalty for it not occurring equals $-\log(1-p)$. Thus, the penalty is high when whatever happens is unexpected acco... | How can I determine accuracy of past probability calculations? | In their classic book on the Federalist papers, Mosteller and Wallace argue for a log penalty function: you penalize yourself $-\log(p)$ when you predict an event with probability $p$ and it occurs; t | How can I determine accuracy of past probability calculations?
In their classic book on the Federalist papers, Mosteller and Wallace argue for a log penalty function: you penalize yourself $-\log(p)$ when you predict an event with probability $p$ and it occurs; the penalty for it not occurring equals $-\log(1-p)$. Thu... | How can I determine accuracy of past probability calculations?
In their classic book on the Federalist papers, Mosteller and Wallace argue for a log penalty function: you penalize yourself $-\log(p)$ when you predict an event with probability $p$ and it occurs; t |
38,345 | Standard Error of Noise Variance in Least Squares | The other answer here shows you the variance of the estimator of the error variance under the assumption that the errors are normally distributed, which is the specified form in the Gaussian regression model. I would counsel against using this method, since it is often the case that the actual data we use in a regress... | Standard Error of Noise Variance in Least Squares | The other answer here shows you the variance of the estimator of the error variance under the assumption that the errors are normally distributed, which is the specified form in the Gaussian regressio | Standard Error of Noise Variance in Least Squares
The other answer here shows you the variance of the estimator of the error variance under the assumption that the errors are normally distributed, which is the specified form in the Gaussian regression model. I would counsel against using this method, since it is often... | Standard Error of Noise Variance in Least Squares
The other answer here shows you the variance of the estimator of the error variance under the assumption that the errors are normally distributed, which is the specified form in the Gaussian regressio |
38,346 | Standard Error of Noise Variance in Least Squares | $\DeclareMathOperator{\Var}{Var}$
Suppose the design matrix is $N \times (p + 1)$, I am assuming you want to calculate the variance of $\hat{\sigma}^2 = \frac{1}{N - p - 1}\epsilon'(I - H)\epsilon$, which is an unbiased estimator of $\sigma^2$, where $I$ is the order $N + 1$ identity matrix and $H = X(X'X)^{-1}X'$. In... | Standard Error of Noise Variance in Least Squares | $\DeclareMathOperator{\Var}{Var}$
Suppose the design matrix is $N \times (p + 1)$, I am assuming you want to calculate the variance of $\hat{\sigma}^2 = \frac{1}{N - p - 1}\epsilon'(I - H)\epsilon$, w | Standard Error of Noise Variance in Least Squares
$\DeclareMathOperator{\Var}{Var}$
Suppose the design matrix is $N \times (p + 1)$, I am assuming you want to calculate the variance of $\hat{\sigma}^2 = \frac{1}{N - p - 1}\epsilon'(I - H)\epsilon$, which is an unbiased estimator of $\sigma^2$, where $I$ is the order $N... | Standard Error of Noise Variance in Least Squares
$\DeclareMathOperator{\Var}{Var}$
Suppose the design matrix is $N \times (p + 1)$, I am assuming you want to calculate the variance of $\hat{\sigma}^2 = \frac{1}{N - p - 1}\epsilon'(I - H)\epsilon$, w |
38,347 | How do you determine if there is a significant relationship between two variables with several factors affecting it, using R? | I presume that you want to know whether the linear relation between $x$ and $y$ is different depending on those additional variables, which I also presume to not be confounders. Thus, you don't want to control for them but you rather want to learn their interaction with the treatment $x$.
If that is all true, use as fo... | How do you determine if there is a significant relationship between two variables with several facto | I presume that you want to know whether the linear relation between $x$ and $y$ is different depending on those additional variables, which I also presume to not be confounders. Thus, you don't want t | How do you determine if there is a significant relationship between two variables with several factors affecting it, using R?
I presume that you want to know whether the linear relation between $x$ and $y$ is different depending on those additional variables, which I also presume to not be confounders. Thus, you don't ... | How do you determine if there is a significant relationship between two variables with several facto
I presume that you want to know whether the linear relation between $x$ and $y$ is different depending on those additional variables, which I also presume to not be confounders. Thus, you don't want t |
38,348 | How do you determine if there is a significant relationship between two variables with several factors affecting it, using R? | I disagree with @frank's advice to include interactions (with $x$) but no main effects for the stimulus, lighting and colony variables. But see How do you deal with "nested" variables in a regression model? for an important exception to this rule.
Moreover, a scatterplot of the data reveals that the two colonies are o... | How do you determine if there is a significant relationship between two variables with several facto | I disagree with @frank's advice to include interactions (with $x$) but no main effects for the stimulus, lighting and colony variables. But see How do you deal with "nested" variables in a regression | How do you determine if there is a significant relationship between two variables with several factors affecting it, using R?
I disagree with @frank's advice to include interactions (with $x$) but no main effects for the stimulus, lighting and colony variables. But see How do you deal with "nested" variables in a regre... | How do you determine if there is a significant relationship between two variables with several facto
I disagree with @frank's advice to include interactions (with $x$) but no main effects for the stimulus, lighting and colony variables. But see How do you deal with "nested" variables in a regression |
38,349 | How do you determine if there is a significant relationship between two variables with several factors affecting it, using R? | We assume that the question is how to determine whether stimulus is statistically significant in the presence of the other variables. First let us try a mixed model with colony as a random effect. Unfortunately, using the data in the question, this results in a singular model which can also be seen from the zero rando... | How do you determine if there is a significant relationship between two variables with several facto | We assume that the question is how to determine whether stimulus is statistically significant in the presence of the other variables. First let us try a mixed model with colony as a random effect. Un | How do you determine if there is a significant relationship between two variables with several factors affecting it, using R?
We assume that the question is how to determine whether stimulus is statistically significant in the presence of the other variables. First let us try a mixed model with colony as a random effec... | How do you determine if there is a significant relationship between two variables with several facto
We assume that the question is how to determine whether stimulus is statistically significant in the presence of the other variables. First let us try a mixed model with colony as a random effect. Un |
38,350 | How can I fit distribution for data which "almost fits"? | The overwhelming majority of datasets do not perfectly fit any parameterised class of distributions used in probability theory.$^\dagger$ Those classes of distributions represent an infinitesimally small sliver of the set of all distributions and so it is rare that a dataset comes from one of these classes. As a resu... | How can I fit distribution for data which "almost fits"? | The overwhelming majority of datasets do not perfectly fit any parameterised class of distributions used in probability theory.$^\dagger$ Those classes of distributions represent an infinitesimally s | How can I fit distribution for data which "almost fits"?
The overwhelming majority of datasets do not perfectly fit any parameterised class of distributions used in probability theory.$^\dagger$ Those classes of distributions represent an infinitesimally small sliver of the set of all distributions and so it is rare t... | How can I fit distribution for data which "almost fits"?
The overwhelming majority of datasets do not perfectly fit any parameterised class of distributions used in probability theory.$^\dagger$ Those classes of distributions represent an infinitesimally s |
38,351 | How can I fit distribution for data which "almost fits"? | The answer by @Ben, which you've already accepted, is great.
I'll just add that a Beta distribution has bounded support (assumes an upper maximum), whereas you're dealing with distances, which don't naturally lend themselves to such an assumption. Moreover, the QQ plot indicates a potential uncertainty in the tail of t... | How can I fit distribution for data which "almost fits"? | The answer by @Ben, which you've already accepted, is great.
I'll just add that a Beta distribution has bounded support (assumes an upper maximum), whereas you're dealing with distances, which don't n | How can I fit distribution for data which "almost fits"?
The answer by @Ben, which you've already accepted, is great.
I'll just add that a Beta distribution has bounded support (assumes an upper maximum), whereas you're dealing with distances, which don't naturally lend themselves to such an assumption. Moreover, the Q... | How can I fit distribution for data which "almost fits"?
The answer by @Ben, which you've already accepted, is great.
I'll just add that a Beta distribution has bounded support (assumes an upper maximum), whereas you're dealing with distances, which don't n |
38,352 | Is a boxplot useful, when it doesn't even look like a box? | Visualisations need to be chosen based on the properties of the data and the message you are trying to convey. Clearly, boxplots do not communicate the distribution of this data well. Given that you have just 40 entries in each group and most values are identical, you might consider using a table, a dotplot, or transl... | Is a boxplot useful, when it doesn't even look like a box? | Visualisations need to be chosen based on the properties of the data and the message you are trying to convey. Clearly, boxplots do not communicate the distribution of this data well. Given that you h | Is a boxplot useful, when it doesn't even look like a box?
Visualisations need to be chosen based on the properties of the data and the message you are trying to convey. Clearly, boxplots do not communicate the distribution of this data well. Given that you have just 40 entries in each group and most values are identic... | Is a boxplot useful, when it doesn't even look like a box?
Visualisations need to be chosen based on the properties of the data and the message you are trying to convey. Clearly, boxplots do not communicate the distribution of this data well. Given that you h |
38,353 | Is a boxplot useful, when it doesn't even look like a box? | The boxplot doesn't visualize your data effectively. (For a discussion of the advantages and disadvantages of boxplots see How should we do boxplots with small samples?
.)
Other types of graphs (except a barplot as suggested by @ Bernhard) would have trouble with you data because there is almost no variability within l... | Is a boxplot useful, when it doesn't even look like a box? | The boxplot doesn't visualize your data effectively. (For a discussion of the advantages and disadvantages of boxplots see How should we do boxplots with small samples?
.)
Other types of graphs (excep | Is a boxplot useful, when it doesn't even look like a box?
The boxplot doesn't visualize your data effectively. (For a discussion of the advantages and disadvantages of boxplots see How should we do boxplots with small samples?
.)
Other types of graphs (except a barplot as suggested by @ Bernhard) would have trouble wi... | Is a boxplot useful, when it doesn't even look like a box?
The boxplot doesn't visualize your data effectively. (For a discussion of the advantages and disadvantages of boxplots see How should we do boxplots with small samples?
.)
Other types of graphs (excep |
38,354 | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | All else being equal, more data is always better. So #3 is clearly the best option.
Imbalanced data is not really a problem, and sacrificing more data for balance is throwing away free information (as Stephan Kolassa notes, the cost of data collection could be a concern - I am ignoring that for now).
See the following ... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | All else being equal, more data is always better. So #3 is clearly the best option.
Imbalanced data is not really a problem, and sacrificing more data for balance is throwing away free information (as | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
All else being equal, more data is always better. So #3 is clearly the best option.
Imbalanced data is not really a problem, and sacrificing more data for balance is throwing away free information (as Stephan Kolassa notes, the cost of da... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
All else being equal, more data is always better. So #3 is clearly the best option.
Imbalanced data is not really a problem, and sacrificing more data for balance is throwing away free information (as |
38,355 | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | More data per group is always better than less data. It doesn't matter what sample sizes are off other groups.
The imbalance "problem" means that if you can collect only 1000 data points, it's usually better to have 500:500 than 100:900, but 100:900 will be better than 100:100 simply because there is more information o... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | More data per group is always better than less data. It doesn't matter what sample sizes are off other groups.
The imbalance "problem" means that if you can collect only 1000 data points, it's usually | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
More data per group is always better than less data. It doesn't matter what sample sizes are off other groups.
The imbalance "problem" means that if you can collect only 1000 data points, it's usually better to have 500:500 than 100:900, ... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
More data per group is always better than less data. It doesn't matter what sample sizes are off other groups.
The imbalance "problem" means that if you can collect only 1000 data points, it's usually |
38,356 | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | You have a trade-off between wanting the data to be balanced and preferring more data. As you said, it always depends on the data. Moreover, some metrics are more robust towards imbalance than others. Without any further information, I would choose option 1 or 2.
You could also try to augment your dataset by oversampli... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | You have a trade-off between wanting the data to be balanced and preferring more data. As you said, it always depends on the data. Moreover, some metrics are more robust towards imbalance than others. | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
You have a trade-off between wanting the data to be balanced and preferring more data. As you said, it always depends on the data. Moreover, some metrics are more robust towards imbalance than others. Without any further information, I wo... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
You have a trade-off between wanting the data to be balanced and preferring more data. As you said, it always depends on the data. Moreover, some metrics are more robust towards imbalance than others. |
38,357 | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | Presumably there is some analysis or model training you intend to do with this data.
Depending on what that is, there may be an a priori way to know how many samples you need (power analysis).
Even if there isn't a closed form solution, you could use simulation to get some idea of how much data is needed. You could gen... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data? | Presumably there is some analysis or model training you intend to do with this data.
Depending on what that is, there may be an a priori way to know how many samples you need (power analysis).
Even if | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
Presumably there is some analysis or model training you intend to do with this data.
Depending on what that is, there may be an a priori way to know how many samples you need (power analysis).
Even if there isn't a closed form solution, y... | Data Imbalance: what would be an ideal number(ratio) of newly added class's data?
Presumably there is some analysis or model training you intend to do with this data.
Depending on what that is, there may be an a priori way to know how many samples you need (power analysis).
Even if |
38,358 | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3? | There are two forms of the geometric distribution. The one we use here counts the number $X$ of Bernoulli trials until the
first Success occurs, where the Success probability is $p,$ so that the PDF is $$f_X(x) = p(1-p)^x,$$ for $x = 1, 2, 3, \dots$ and $$E(X) = \mu_X = 1/p.$$ [The alternative
version counts the number... | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3? | There are two forms of the geometric distribution. The one we use here counts the number $X$ of Bernoulli trials until the
first Success occurs, where the Success probability is $p,$ so that the PDF i | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3?
There are two forms of the geometric distribution. The one we use here counts the number $X$ of Bernoulli trials until the
first Success occurs, where the Success probability is $p,$ so that the PDF is $$f_X(x) = p(1-p)^x,$$ ... | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3?
There are two forms of the geometric distribution. The one we use here counts the number $X$ of Bernoulli trials until the
first Success occurs, where the Success probability is $p,$ so that the PDF i |
38,359 | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3? | This answer consists of two parts. The first part develops a basic insight about long sequences of repetitions of an experiment. This insight is conveyed by a simple diagram of the experimental results. The second part quickly answers the question by applying this insight.
The insight
Consider any probabilistic even... | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3? | This answer consists of two parts. The first part develops a basic insight about long sequences of repetitions of an experiment. This insight is conveyed by a simple diagram of the experimental resu | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3?
This answer consists of two parts. The first part develops a basic insight about long sequences of repetitions of an experiment. This insight is conveyed by a simple diagram of the experimental results. The second part qui... | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3?
This answer consists of two parts. The first part develops a basic insight about long sequences of repetitions of an experiment. This insight is conveyed by a simple diagram of the experimental resu |
38,360 | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3? | For a nonnegative integer-valued discrete random variable $X$, it is a standard result (see e.g. here on stats.SE) that
$$E[X] = \sum_{n=0}^\infty P(X > n).$$
When $X$ is a geometric random variable with parameter $p$ that takes on values $1, 2, 3, \ldots$ (which is the case here since $X$ is the number of the trial on... | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3? | For a nonnegative integer-valued discrete random variable $X$, it is a standard result (see e.g. here on stats.SE) that
$$E[X] = \sum_{n=0}^\infty P(X > n).$$
When $X$ is a geometric random variable w | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3?
For a nonnegative integer-valued discrete random variable $X$, it is a standard result (see e.g. here on stats.SE) that
$$E[X] = \sum_{n=0}^\infty P(X > n).$$
When $X$ is a geometric random variable with parameter $p$ that ta... | When we roll a fair die, why is 6 the expected number of rolls after which we get our first 3?
For a nonnegative integer-valued discrete random variable $X$, it is a standard result (see e.g. here on stats.SE) that
$$E[X] = \sum_{n=0}^\infty P(X > n).$$
When $X$ is a geometric random variable w |
38,361 | What is the history of $p < 0.05$ or 95% confidence? | See this historical article by Stigler (2008) in Chance, about Fisher's influence (as you suggest).
Much of early significance testing used the standard normal distribution.
As cut-off values get smaller than $-2.0$ there is rapidly diminishing tail
probability. So if one wants a relatively small tail probability witho... | What is the history of $p < 0.05$ or 95% confidence? | See this historical article by Stigler (2008) in Chance, about Fisher's influence (as you suggest).
Much of early significance testing used the standard normal distribution.
As cut-off values get smal | What is the history of $p < 0.05$ or 95% confidence?
See this historical article by Stigler (2008) in Chance, about Fisher's influence (as you suggest).
Much of early significance testing used the standard normal distribution.
As cut-off values get smaller than $-2.0$ there is rapidly diminishing tail
probability. So i... | What is the history of $p < 0.05$ or 95% confidence?
See this historical article by Stigler (2008) in Chance, about Fisher's influence (as you suggest).
Much of early significance testing used the standard normal distribution.
As cut-off values get smal |
38,362 | What is the history of $p < 0.05$ or 95% confidence? | Fisher suggested the 0.05 level indirectly. He mentioned that two standard deviations is an easy rule for significance, and the 0.05 level is what approximately corresponds to it.
From Fisher's 1925 'Statistical methods for research workers'
If, therefore, we know the standard deviation of a population, we can calcula... | What is the history of $p < 0.05$ or 95% confidence? | Fisher suggested the 0.05 level indirectly. He mentioned that two standard deviations is an easy rule for significance, and the 0.05 level is what approximately corresponds to it.
From Fisher's 1925 ' | What is the history of $p < 0.05$ or 95% confidence?
Fisher suggested the 0.05 level indirectly. He mentioned that two standard deviations is an easy rule for significance, and the 0.05 level is what approximately corresponds to it.
From Fisher's 1925 'Statistical methods for research workers'
If, therefore, we know t... | What is the history of $p < 0.05$ or 95% confidence?
Fisher suggested the 0.05 level indirectly. He mentioned that two standard deviations is an easy rule for significance, and the 0.05 level is what approximately corresponds to it.
From Fisher's 1925 ' |
38,363 | What is the history of $p < 0.05$ or 95% confidence? | As I remember it, it was indeed Fisher who threw 0,05 out there, as a suggestion, and this has been taken as law in many circles since then. I don't have the book at hand, but I read the passage once, and it can probably be found through a quick Google search.
I am not that familiar with decision theory, so I can't def... | What is the history of $p < 0.05$ or 95% confidence? | As I remember it, it was indeed Fisher who threw 0,05 out there, as a suggestion, and this has been taken as law in many circles since then. I don't have the book at hand, but I read the passage once, | What is the history of $p < 0.05$ or 95% confidence?
As I remember it, it was indeed Fisher who threw 0,05 out there, as a suggestion, and this has been taken as law in many circles since then. I don't have the book at hand, but I read the passage once, and it can probably be found through a quick Google search.
I am n... | What is the history of $p < 0.05$ or 95% confidence?
As I remember it, it was indeed Fisher who threw 0,05 out there, as a suggestion, and this has been taken as law in many circles since then. I don't have the book at hand, but I read the passage once, |
38,364 | Flipping Coins : Probability of Sequences vs Probability of Individuals | By default, str_count does not count overlapping occurrances of the specified pattern. The substring 1111 can overlap with itself substantially, whereas the substring 1110 cannot overlap with itself. Consequently, your calculation for the first substring is substantially biased --- you are substantially undercounting... | Flipping Coins : Probability of Sequences vs Probability of Individuals | By default, str_count does not count overlapping occurrances of the specified pattern. The substring 1111 can overlap with itself substantially, whereas the substring 1110 cannot overlap with itself. | Flipping Coins : Probability of Sequences vs Probability of Individuals
By default, str_count does not count overlapping occurrances of the specified pattern. The substring 1111 can overlap with itself substantially, whereas the substring 1110 cannot overlap with itself. Consequently, your calculation for the first s... | Flipping Coins : Probability of Sequences vs Probability of Individuals
By default, str_count does not count overlapping occurrances of the specified pattern. The substring 1111 can overlap with itself substantially, whereas the substring 1110 cannot overlap with itself. |
38,365 | Flipping Coins : Probability of Sequences vs Probability of Individuals | EDIT
The reason you are getting a different percentage for HHHH and HHHT is that you are calculating the instances of 1111 and 1110 in a very long string. you are not breaking these into blocks of 4. In a very long string it is more likely for you to have 3 ones in a row than it is to have 4 ones in a row. Since you ar... | Flipping Coins : Probability of Sequences vs Probability of Individuals | EDIT
The reason you are getting a different percentage for HHHH and HHHT is that you are calculating the instances of 1111 and 1110 in a very long string. you are not breaking these into blocks of 4. | Flipping Coins : Probability of Sequences vs Probability of Individuals
EDIT
The reason you are getting a different percentage for HHHH and HHHT is that you are calculating the instances of 1111 and 1110 in a very long string. you are not breaking these into blocks of 4. In a very long string it is more likely for you ... | Flipping Coins : Probability of Sequences vs Probability of Individuals
EDIT
The reason you are getting a different percentage for HHHH and HHHT is that you are calculating the instances of 1111 and 1110 in a very long string. you are not breaking these into blocks of 4. |
38,366 | Flipping Coins : Probability of Sequences vs Probability of Individuals | Ah my friend, you are making a very simple mistake. In your simulation, you are computing the proportion of times a person could flip 4 heads in a row. But that is not what you have wagered.
You enter the bet having seen the three heads and have wagered only on the result of the next flip. Because each flip is indep... | Flipping Coins : Probability of Sequences vs Probability of Individuals | Ah my friend, you are making a very simple mistake. In your simulation, you are computing the proportion of times a person could flip 4 heads in a row. But that is not what you have wagered.
You ent | Flipping Coins : Probability of Sequences vs Probability of Individuals
Ah my friend, you are making a very simple mistake. In your simulation, you are computing the proportion of times a person could flip 4 heads in a row. But that is not what you have wagered.
You enter the bet having seen the three heads and have ... | Flipping Coins : Probability of Sequences vs Probability of Individuals
Ah my friend, you are making a very simple mistake. In your simulation, you are computing the proportion of times a person could flip 4 heads in a row. But that is not what you have wagered.
You ent |
38,367 | Underestimation of standard error | This is what's going on
> summary(row_std)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.05212 0.69485 0.91762 0.94109 1.15915 2.56883
> summary(row_std^2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.002717 0.482820 0.842034 1.001564 1.343628 6.598870
Because $s^2$ is unbiased for $\sigma^2$, it is... | Underestimation of standard error | This is what's going on
> summary(row_std)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.05212 0.69485 0.91762 0.94109 1.15915 2.56883
> summary(row_std^2)
Min. 1st Qu. Median Mean 3 | Underestimation of standard error
This is what's going on
> summary(row_std)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.05212 0.69485 0.91762 0.94109 1.15915 2.56883
> summary(row_std^2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.002717 0.482820 0.842034 1.001564 1.343628 6.598870
Because $s^2$... | Underestimation of standard error
This is what's going on
> summary(row_std)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.05212 0.69485 0.91762 0.94109 1.15915 2.56883
> summary(row_std^2)
Min. 1st Qu. Median Mean 3 |
38,368 | Underestimation of standard error | By Jensen’s inequality, the sample standard deviation is an underestimate (in expectation) of the true standard deviation, since the square root is concave and $S^2$ is unbiased for the second central moment. | Underestimation of standard error | By Jensen’s inequality, the sample standard deviation is an underestimate (in expectation) of the true standard deviation, since the square root is concave and $S^2$ is unbiased for the second central | Underestimation of standard error
By Jensen’s inequality, the sample standard deviation is an underestimate (in expectation) of the true standard deviation, since the square root is concave and $S^2$ is unbiased for the second central moment. | Underestimation of standard error
By Jensen’s inequality, the sample standard deviation is an underestimate (in expectation) of the true standard deviation, since the square root is concave and $S^2$ is unbiased for the second central |
38,369 | Absolute Value of Uniform | No, because given $X,X'$, you have the values for $Y,Y'$. So, the probability is either $1$ or $0$, depending on $x,x'$:
$$P(Y\leq Y'|X=x,X'=x')=\mathbb I(|x|\leq |x'|)$$ | Absolute Value of Uniform | No, because given $X,X'$, you have the values for $Y,Y'$. So, the probability is either $1$ or $0$, depending on $x,x'$:
$$P(Y\leq Y'|X=x,X'=x')=\mathbb I(|x|\leq |x'|)$$ | Absolute Value of Uniform
No, because given $X,X'$, you have the values for $Y,Y'$. So, the probability is either $1$ or $0$, depending on $x,x'$:
$$P(Y\leq Y'|X=x,X'=x')=\mathbb I(|x|\leq |x'|)$$ | Absolute Value of Uniform
No, because given $X,X'$, you have the values for $Y,Y'$. So, the probability is either $1$ or $0$, depending on $x,x'$:
$$P(Y\leq Y'|X=x,X'=x')=\mathbb I(|x|\leq |x'|)$$ |
38,370 | Absolute Value of Uniform | No, that is false. Once you condition on $X$ and $X'$ the event $Y \leqslant Y'$ is deterministic. Specifically, you have:
$$\mathbb{P}(Y \leqslant Y'|X=x, X'=x') = \mathbb{I}(|x| \leqslant |x'|).$$ | Absolute Value of Uniform | No, that is false. Once you condition on $X$ and $X'$ the event $Y \leqslant Y'$ is deterministic. Specifically, you have:
$$\mathbb{P}(Y \leqslant Y'|X=x, X'=x') = \mathbb{I}(|x| \leqslant |x'|).$$ | Absolute Value of Uniform
No, that is false. Once you condition on $X$ and $X'$ the event $Y \leqslant Y'$ is deterministic. Specifically, you have:
$$\mathbb{P}(Y \leqslant Y'|X=x, X'=x') = \mathbb{I}(|x| \leqslant |x'|).$$ | Absolute Value of Uniform
No, that is false. Once you condition on $X$ and $X'$ the event $Y \leqslant Y'$ is deterministic. Specifically, you have:
$$\mathbb{P}(Y \leqslant Y'|X=x, X'=x') = \mathbb{I}(|x| \leqslant |x'|).$$ |
38,371 | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline) | cyclicSpline already contains the constant vector in its span so if you additionally add an intercept it'll be rank deficient.
Matrix::rankMatrix(cyclicSpline) shows that cyclicSpline is full rank by itself and doing lm(y ~ cyclicSpline - 1) will fix the issue.
To confirm that this really is the case, we can compute th... | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline) | cyclicSpline already contains the constant vector in its span so if you additionally add an intercept it'll be rank deficient.
Matrix::rankMatrix(cyclicSpline) shows that cyclicSpline is full rank by | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)
cyclicSpline already contains the constant vector in its span so if you additionally add an intercept it'll be rank deficient.
Matrix::rankMatrix(cyclicSpline) shows that cyclicSpline is full rank by itself and doing lm(y ~ cyclicSpl... | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)
cyclicSpline already contains the constant vector in its span so if you additionally add an intercept it'll be rank deficient.
Matrix::rankMatrix(cyclicSpline) shows that cyclicSpline is full rank by |
38,372 | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline) | As jld writes, your splines contain the constant 1 in their span, so you should fit a model without an intercept.
As a matter of fact, the splines sum rowwise to 1: rowSums(cyclicSpline) gives you a constant vector of 1s.
Here is a plot of x against its spline transform, which shows very nicely how the splines add to 1... | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline) | As jld writes, your splines contain the constant 1 in their span, so you should fit a model without an intercept.
As a matter of fact, the splines sum rowwise to 1: rowSums(cyclicSpline) gives you a c | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)
As jld writes, your splines contain the constant 1 in their span, so you should fit a model without an intercept.
As a matter of fact, the splines sum rowwise to 1: rowSums(cyclicSpline) gives you a constant vector of 1s.
Here is a p... | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)
As jld writes, your splines contain the constant 1 in their span, so you should fit a model without an intercept.
As a matter of fact, the splines sum rowwise to 1: rowSums(cyclicSpline) gives you a c |
38,373 | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline) | I'm sure this lack of identification is due to your model also including a constant (intercept). mgcv is certainly applying identifiability constraints on cyclic splines it creates using cSplineDes() but that happens in other functions as you want to apply those constraints through the smooth.construct.xxxx functions w... | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline) | I'm sure this lack of identification is due to your model also including a constant (intercept). mgcv is certainly applying identifiability constraints on cyclic splines it creates using cSplineDes() | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)
I'm sure this lack of identification is due to your model also including a constant (intercept). mgcv is certainly applying identifiability constraints on cyclic splines it creates using cSplineDes() but that happens in other functio... | Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)
I'm sure this lack of identification is due to your model also including a constant (intercept). mgcv is certainly applying identifiability constraints on cyclic splines it creates using cSplineDes() |
38,374 | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the analysis [duplicate] | Bootstrapping involves resampling your data randomly. Thus, each time you bootstrap, a different (re)sample will be drawn. Therefore, the results of different bootstrap runs will be different.
If these differences are large, then you should be suspicious that your bootstrap may not be working well. If the differences a... | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the a | Bootstrapping involves resampling your data randomly. Thus, each time you bootstrap, a different (re)sample will be drawn. Therefore, the results of different bootstrap runs will be different.
If thes | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the analysis [duplicate]
Bootstrapping involves resampling your data randomly. Thus, each time you bootstrap, a different (re)sample will be drawn. Therefore, the results of different bootstrap runs will be different.
If thes... | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the a
Bootstrapping involves resampling your data randomly. Thus, each time you bootstrap, a different (re)sample will be drawn. Therefore, the results of different bootstrap runs will be different.
If thes |
38,375 | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the analysis [duplicate] | This is totally normal and why we set a random seed (to get the same randomization each time) via set seed in R or np.random.seed in Python.
The way bootstrap works is to take many random samples, with replacement, of your data, so there should be small fluctuations in your calculated values as those random samples var... | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the a | This is totally normal and why we set a random seed (to get the same randomization each time) via set seed in R or np.random.seed in Python.
The way bootstrap works is to take many random samples, wit | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the analysis [duplicate]
This is totally normal and why we set a random seed (to get the same randomization each time) via set seed in R or np.random.seed in Python.
The way bootstrap works is to take many random samples, wit... | Why Bootstrapping standard errors and 95% confidence intervals change each time I re-conducted the a
This is totally normal and why we set a random seed (to get the same randomization each time) via set seed in R or np.random.seed in Python.
The way bootstrap works is to take many random samples, wit |
38,376 | What is a metric can I use to calculate the distance between labels? | It really depends on what kind of words you are referring to. There are two distance that I wish to talk about :
Edit Distance
If you wish to capture difference in terms of how different two sequence are, you can use levenshtein
distance or Damerau-Levenshtein distance. Mathematically for a word $A$ or $B$, the levens... | What is a metric can I use to calculate the distance between labels? | It really depends on what kind of words you are referring to. There are two distance that I wish to talk about :
Edit Distance
If you wish to capture difference in terms of how different two sequence | What is a metric can I use to calculate the distance between labels?
It really depends on what kind of words you are referring to. There are two distance that I wish to talk about :
Edit Distance
If you wish to capture difference in terms of how different two sequence are, you can use levenshtein
distance or Damerau-L... | What is a metric can I use to calculate the distance between labels?
It really depends on what kind of words you are referring to. There are two distance that I wish to talk about :
Edit Distance
If you wish to capture difference in terms of how different two sequence |
38,377 | What is a metric can I use to calculate the distance between labels? | You can still use the Hamming distance for 5 letters.
Another metric than you can use is the Levenshtein distance - the minimum number of single-character edits required to change one word into the other.
If there is some meaning to the order of your letters, such that for example the distance between a and c is large... | What is a metric can I use to calculate the distance between labels? | You can still use the Hamming distance for 5 letters.
Another metric than you can use is the Levenshtein distance - the minimum number of single-character edits required to change one word into the o | What is a metric can I use to calculate the distance between labels?
You can still use the Hamming distance for 5 letters.
Another metric than you can use is the Levenshtein distance - the minimum number of single-character edits required to change one word into the other.
If there is some meaning to the order of your... | What is a metric can I use to calculate the distance between labels?
You can still use the Hamming distance for 5 letters.
Another metric than you can use is the Levenshtein distance - the minimum number of single-character edits required to change one word into the o |
38,378 | What is a metric can I use to calculate the distance between labels? | It sounds to me like you may be looking for a simple sum of absolute differences (also called L1 distance).
Assuming that we can extend your ordinal relation $a < b < c < d < e$ into a metric (e.g. $b - a = c - b = 1$, $e - a = 4$, etc.), then you can let the difference between two words of the same length be the sum ... | What is a metric can I use to calculate the distance between labels? | It sounds to me like you may be looking for a simple sum of absolute differences (also called L1 distance).
Assuming that we can extend your ordinal relation $a < b < c < d < e$ into a metric (e.g. $ | What is a metric can I use to calculate the distance between labels?
It sounds to me like you may be looking for a simple sum of absolute differences (also called L1 distance).
Assuming that we can extend your ordinal relation $a < b < c < d < e$ into a metric (e.g. $b - a = c - b = 1$, $e - a = 4$, etc.), then you ca... | What is a metric can I use to calculate the distance between labels?
It sounds to me like you may be looking for a simple sum of absolute differences (also called L1 distance).
Assuming that we can extend your ordinal relation $a < b < c < d < e$ into a metric (e.g. $ |
38,379 | What is a metric can I use to calculate the distance between labels? | Usually when people talk about word similarity, they refer to something like Yohanes Alfredo's answer.
In your case, you want to take into account the sort order of the characters. In that case, it might be that hobbs has the answer you need.
Do you want to find distance according to the overall sort order of the word?... | What is a metric can I use to calculate the distance between labels? | Usually when people talk about word similarity, they refer to something like Yohanes Alfredo's answer.
In your case, you want to take into account the sort order of the characters. In that case, it mi | What is a metric can I use to calculate the distance between labels?
Usually when people talk about word similarity, they refer to something like Yohanes Alfredo's answer.
In your case, you want to take into account the sort order of the characters. In that case, it might be that hobbs has the answer you need.
Do you w... | What is a metric can I use to calculate the distance between labels?
Usually when people talk about word similarity, they refer to something like Yohanes Alfredo's answer.
In your case, you want to take into account the sort order of the characters. In that case, it mi |
38,380 | Calculate accelerated bootstrap interval in R | First a warning... the Bootstrap (as with most statistical methods) is unlikely to be reliable with such a small sample size. I would exercise caution if $n=6$ is a standard sample size in your case.
Lets simulate some data
set.seed(42)
n <- 30 #Sample size
x <- round(runif(n, 0, 100))
Lets refer to your index as $\th... | Calculate accelerated bootstrap interval in R | First a warning... the Bootstrap (as with most statistical methods) is unlikely to be reliable with such a small sample size. I would exercise caution if $n=6$ is a standard sample size in your case.
| Calculate accelerated bootstrap interval in R
First a warning... the Bootstrap (as with most statistical methods) is unlikely to be reliable with such a small sample size. I would exercise caution if $n=6$ is a standard sample size in your case.
Lets simulate some data
set.seed(42)
n <- 30 #Sample size
x <- round(runif... | Calculate accelerated bootstrap interval in R
First a warning... the Bootstrap (as with most statistical methods) is unlikely to be reliable with such a small sample size. I would exercise caution if $n=6$ is a standard sample size in your case.
|
38,381 | Calculate accelerated bootstrap interval in R | Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.
A couple of notes. I copied my general code for using boot.ci with a function from here (with the caveat that I am the author of the code).
The results are similar to those of @knrumsey.
I can't conf... | Calculate accelerated bootstrap interval in R | Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.
A couple of notes. I copied my general code for using boot.ci with a function f | Calculate accelerated bootstrap interval in R
Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.
A couple of notes. I copied my general code for using boot.ci with a function from here (with the caveat that I am the author of the code).
The results a... | Calculate accelerated bootstrap interval in R
Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.
A couple of notes. I copied my general code for using boot.ci with a function f |
38,382 | Calculate accelerated bootstrap interval in R | Saw this approach and tried replication it with code in Python, following the steps outlined by @knrumsey. The results are similar.
# the libraries
import pandas as pd
import numpy as np
from scipy import stats
# for bootstrapping
rng = np.random.default_rng()
# random seed
import random
random.seed(42)
Data simulat... | Calculate accelerated bootstrap interval in R | Saw this approach and tried replication it with code in Python, following the steps outlined by @knrumsey. The results are similar.
# the libraries
import pandas as pd
import numpy as np
from scipy im | Calculate accelerated bootstrap interval in R
Saw this approach and tried replication it with code in Python, following the steps outlined by @knrumsey. The results are similar.
# the libraries
import pandas as pd
import numpy as np
from scipy import stats
# for bootstrapping
rng = np.random.default_rng()
# random se... | Calculate accelerated bootstrap interval in R
Saw this approach and tried replication it with code in Python, following the steps outlined by @knrumsey. The results are similar.
# the libraries
import pandas as pd
import numpy as np
from scipy im |
38,383 | Calculate accelerated bootstrap interval in R | There is a problem with your index. It is not dimensionless. The first term of the index is dimensionless, but the second term has the dimension (1/X). Thus it is not only not dimensionless, but it is also non-homogeneous. Please check if it is correct. | Calculate accelerated bootstrap interval in R | There is a problem with your index. It is not dimensionless. The first term of the index is dimensionless, but the second term has the dimension (1/X). Thus it is not only not dimensionless, but it | Calculate accelerated bootstrap interval in R
There is a problem with your index. It is not dimensionless. The first term of the index is dimensionless, but the second term has the dimension (1/X). Thus it is not only not dimensionless, but it is also non-homogeneous. Please check if it is correct. | Calculate accelerated bootstrap interval in R
There is a problem with your index. It is not dimensionless. The first term of the index is dimensionless, but the second term has the dimension (1/X). Thus it is not only not dimensionless, but it |
38,384 | Why are Poisson regression coefficients biased? | The default link function is the log function for Poisson, this means:
$$\mathbb{E}[y]=\exp\left(\log(5)+\log(x)\right)$$
If you specify your glm model as y ~ log(x) then you should recover "1" as the coefficient and "log(5)" as the intercept | Why are Poisson regression coefficients biased? | The default link function is the log function for Poisson, this means:
$$\mathbb{E}[y]=\exp\left(\log(5)+\log(x)\right)$$
If you specify your glm model as y ~ log(x) then you should recover "1" as the | Why are Poisson regression coefficients biased?
The default link function is the log function for Poisson, this means:
$$\mathbb{E}[y]=\exp\left(\log(5)+\log(x)\right)$$
If you specify your glm model as y ~ log(x) then you should recover "1" as the coefficient and "log(5)" as the intercept | Why are Poisson regression coefficients biased?
The default link function is the log function for Poisson, this means:
$$\mathbb{E}[y]=\exp\left(\log(5)+\log(x)\right)$$
If you specify your glm model as y ~ log(x) then you should recover "1" as the |
38,385 | Why are Poisson regression coefficients biased? | That isn't how poisson regression works. The link function for poisson regression is the log, so if you did something like
x<-runif(100)
eta<- 5*x
lam<- exp(eta)
y<-rpois(length(lam), lam)
model<- glm(y~x, family = 'poisson')
Then you would recover the proper estimates for the coefficient of x and the intercept.
Yo... | Why are Poisson regression coefficients biased? | That isn't how poisson regression works. The link function for poisson regression is the log, so if you did something like
x<-runif(100)
eta<- 5*x
lam<- exp(eta)
y<-rpois(length(lam), lam)
model<- gl | Why are Poisson regression coefficients biased?
That isn't how poisson regression works. The link function for poisson regression is the log, so if you did something like
x<-runif(100)
eta<- 5*x
lam<- exp(eta)
y<-rpois(length(lam), lam)
model<- glm(y~x, family = 'poisson')
Then you would recover the proper estimates ... | Why are Poisson regression coefficients biased?
That isn't how poisson regression works. The link function for poisson regression is the log, so if you did something like
x<-runif(100)
eta<- 5*x
lam<- exp(eta)
y<-rpois(length(lam), lam)
model<- gl |
38,386 | How can I visualize an ordinal variable predicting a continuous outcome? | The plot you shown is pretty good. But I think you can improve the data-ink ratio (invented by Edward Tufte) even more by showing all the datapoints. You can do this by adding jitter to the x-axis.
Another improvement is to emphasise that the ordinal variable is categorical and not continuous. You can do this by using... | How can I visualize an ordinal variable predicting a continuous outcome? | The plot you shown is pretty good. But I think you can improve the data-ink ratio (invented by Edward Tufte) even more by showing all the datapoints. You can do this by adding jitter to the x-axis.
A | How can I visualize an ordinal variable predicting a continuous outcome?
The plot you shown is pretty good. But I think you can improve the data-ink ratio (invented by Edward Tufte) even more by showing all the datapoints. You can do this by adding jitter to the x-axis.
Another improvement is to emphasise that the ord... | How can I visualize an ordinal variable predicting a continuous outcome?
The plot you shown is pretty good. But I think you can improve the data-ink ratio (invented by Edward Tufte) even more by showing all the datapoints. You can do this by adding jitter to the x-axis.
A |
38,387 | How can I visualize an ordinal variable predicting a continuous outcome? | The problem with this is that there's no way of knowing how many dots are bunched up together. Two solutions I've seen:
Box plot
This would give you tighter box if data points are bunched up together.
Bubble chart
Not sure if this is the official name, but basically you put the vertical axis into bins. The size of the... | How can I visualize an ordinal variable predicting a continuous outcome? | The problem with this is that there's no way of knowing how many dots are bunched up together. Two solutions I've seen:
Box plot
This would give you tighter box if data points are bunched up together. | How can I visualize an ordinal variable predicting a continuous outcome?
The problem with this is that there's no way of knowing how many dots are bunched up together. Two solutions I've seen:
Box plot
This would give you tighter box if data points are bunched up together.
Bubble chart
Not sure if this is the official... | How can I visualize an ordinal variable predicting a continuous outcome?
The problem with this is that there's no way of knowing how many dots are bunched up together. Two solutions I've seen:
Box plot
This would give you tighter box if data points are bunched up together. |
38,388 | How can I visualize an ordinal variable predicting a continuous outcome? | In addition to the box plot suggested by Art, I suggest a violin plot:
Explicitly showing the median and interquartile range, as done in the above image, is optional.
Quoting from Wikipedia:
Violin plots are similar to box plots, except that they also show the probability density of the data at different values, usua... | How can I visualize an ordinal variable predicting a continuous outcome? | In addition to the box plot suggested by Art, I suggest a violin plot:
Explicitly showing the median and interquartile range, as done in the above image, is optional.
Quoting from Wikipedia:
Violin | How can I visualize an ordinal variable predicting a continuous outcome?
In addition to the box plot suggested by Art, I suggest a violin plot:
Explicitly showing the median and interquartile range, as done in the above image, is optional.
Quoting from Wikipedia:
Violin plots are similar to box plots, except that the... | How can I visualize an ordinal variable predicting a continuous outcome?
In addition to the box plot suggested by Art, I suggest a violin plot:
Explicitly showing the median and interquartile range, as done in the above image, is optional.
Quoting from Wikipedia:
Violin |
38,389 | How can I visualize an ordinal variable predicting a continuous outcome? | To your scatterplot, I would add a large point indicating the mean Y-value at every unique X-value, and also do one or more of the following:
Square-root (or cube-root) transform your Y-axis. Both these
transformations can deal with zeroes, unlike log transformations.
Cube roots can also deal with negative numbers.
M... | How can I visualize an ordinal variable predicting a continuous outcome? | To your scatterplot, I would add a large point indicating the mean Y-value at every unique X-value, and also do one or more of the following:
Square-root (or cube-root) transform your Y-axis. Both t | How can I visualize an ordinal variable predicting a continuous outcome?
To your scatterplot, I would add a large point indicating the mean Y-value at every unique X-value, and also do one or more of the following:
Square-root (or cube-root) transform your Y-axis. Both these
transformations can deal with zeroes, unli... | How can I visualize an ordinal variable predicting a continuous outcome?
To your scatterplot, I would add a large point indicating the mean Y-value at every unique X-value, and also do one or more of the following:
Square-root (or cube-root) transform your Y-axis. Both t |
38,390 | How can I visualize an ordinal variable predicting a continuous outcome? | You state that one variable is ordinal, then you decide to treat it as interval. Is that reasonable? There is no way for us to know, as you have not said what the ordinal variable actually is. If you do decide to keep it as ordinal, then what to do depends on your sample size. If N is very large then I like the box plo... | How can I visualize an ordinal variable predicting a continuous outcome? | You state that one variable is ordinal, then you decide to treat it as interval. Is that reasonable? There is no way for us to know, as you have not said what the ordinal variable actually is. If you | How can I visualize an ordinal variable predicting a continuous outcome?
You state that one variable is ordinal, then you decide to treat it as interval. Is that reasonable? There is no way for us to know, as you have not said what the ordinal variable actually is. If you do decide to keep it as ordinal, then what to d... | How can I visualize an ordinal variable predicting a continuous outcome?
You state that one variable is ordinal, then you decide to treat it as interval. Is that reasonable? There is no way for us to know, as you have not said what the ordinal variable actually is. If you |
38,391 | How can I visualize an ordinal variable predicting a continuous outcome? | The basic idea of regression is that the probability distribution of $y$ depends on $x$: there is some family of distributions $P_x(y)$. It's generally assumed that these distributions are all normal with a constant standard deviation (homoscedasticity), leaving only the mean as depending on $x$: $p(Y=y) = N(\mu_x,\sig... | How can I visualize an ordinal variable predicting a continuous outcome? | The basic idea of regression is that the probability distribution of $y$ depends on $x$: there is some family of distributions $P_x(y)$. It's generally assumed that these distributions are all normal | How can I visualize an ordinal variable predicting a continuous outcome?
The basic idea of regression is that the probability distribution of $y$ depends on $x$: there is some family of distributions $P_x(y)$. It's generally assumed that these distributions are all normal with a constant standard deviation (homoscedast... | How can I visualize an ordinal variable predicting a continuous outcome?
The basic idea of regression is that the probability distribution of $y$ depends on $x$: there is some family of distributions $P_x(y)$. It's generally assumed that these distributions are all normal |
38,392 | What does 1 with an inequality in the subscript mean? [duplicate] | $\mathbb{1}_{x\ge a}$ is an indicator function, that is equal to $1$ when $x\ge a$ and zero otherwise. Multiplying by it is a fancy, math way of saying that everything else is equal to zero. In this case, it says that only cases greater or equal to $a$ can be observed. | What does 1 with an inequality in the subscript mean? [duplicate] | $\mathbb{1}_{x\ge a}$ is an indicator function, that is equal to $1$ when $x\ge a$ and zero otherwise. Multiplying by it is a fancy, math way of saying that everything else is equal to zero. In this c | What does 1 with an inequality in the subscript mean? [duplicate]
$\mathbb{1}_{x\ge a}$ is an indicator function, that is equal to $1$ when $x\ge a$ and zero otherwise. Multiplying by it is a fancy, math way of saying that everything else is equal to zero. In this case, it says that only cases greater or equal to $a$ c... | What does 1 with an inequality in the subscript mean? [duplicate]
$\mathbb{1}_{x\ge a}$ is an indicator function, that is equal to $1$ when $x\ge a$ and zero otherwise. Multiplying by it is a fancy, math way of saying that everything else is equal to zero. In this c |
38,393 | What does 1 with an inequality in the subscript mean? [duplicate] | The I in the formula is the indicator function. In this case it equals 1 when x>=a and zero otherwise. | What does 1 with an inequality in the subscript mean? [duplicate] | The I in the formula is the indicator function. In this case it equals 1 when x>=a and zero otherwise. | What does 1 with an inequality in the subscript mean? [duplicate]
The I in the formula is the indicator function. In this case it equals 1 when x>=a and zero otherwise. | What does 1 with an inequality in the subscript mean? [duplicate]
The I in the formula is the indicator function. In this case it equals 1 when x>=a and zero otherwise. |
38,394 | Is there a continuous version of the Uniform distribution? | This is a familiar problem in theoretical mathematics, where it helps the analysis when you don't have to worry about lack of differentiability. The standard solution, sometimes called "mollification," is to convolve the density with a scaled, zero-centered, infinitely differentiable density (often of compact support)... | Is there a continuous version of the Uniform distribution? | This is a familiar problem in theoretical mathematics, where it helps the analysis when you don't have to worry about lack of differentiability. The standard solution, sometimes called "mollification | Is there a continuous version of the Uniform distribution?
This is a familiar problem in theoretical mathematics, where it helps the analysis when you don't have to worry about lack of differentiability. The standard solution, sometimes called "mollification," is to convolve the density with a scaled, zero-centered, i... | Is there a continuous version of the Uniform distribution?
This is a familiar problem in theoretical mathematics, where it helps the analysis when you don't have to worry about lack of differentiability. The standard solution, sometimes called "mollification |
38,395 | Is there a continuous version of the Uniform distribution? | The standard continuous uniform distribution $\text{U}(a,b)$ distribution has a continuous CDF that is differentiable (in the regular sense) at all points except the edges of its support, $x = a, b$. Since probability theory defines density functions using Radon-Nikodym derivatives, we can still ascribe values to the ... | Is there a continuous version of the Uniform distribution? | The standard continuous uniform distribution $\text{U}(a,b)$ distribution has a continuous CDF that is differentiable (in the regular sense) at all points except the edges of its support, $x = a, b$. | Is there a continuous version of the Uniform distribution?
The standard continuous uniform distribution $\text{U}(a,b)$ distribution has a continuous CDF that is differentiable (in the regular sense) at all points except the edges of its support, $x = a, b$. Since probability theory defines density functions using Rad... | Is there a continuous version of the Uniform distribution?
The standard continuous uniform distribution $\text{U}(a,b)$ distribution has a continuous CDF that is differentiable (in the regular sense) at all points except the edges of its support, $x = a, b$. |
38,396 | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory? | Karl Popper has argued for a general mindset that should be employed by a scientist. The frequentist null hypothesis testing was designed in a way that is consistent with this kind of thinking about scientific method. However this does not mean that is is the only way how you could conduct hypothesis tests! In Bayesi... | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory? | Karl Popper has argued for a general mindset that should be employed by a scientist. The frequentist null hypothesis testing was designed in a way that is consistent with this kind of thinking about | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory?
Karl Popper has argued for a general mindset that should be employed by a scientist. The frequentist null hypothesis testing was designed in a way that is consistent with this kind of thinking about scientific method. Ho... | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory?
Karl Popper has argued for a general mindset that should be employed by a scientist. The frequentist null hypothesis testing was designed in a way that is consistent with this kind of thinking about |
38,397 | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory? | It depends on what you mean that Popper had nothing to with debate.
IN some sense it is half correct
In other sense, its WRONGER THAN WRONG; ultimately,he rejected priors or inductive logic; and he was intimately connected with these issues. The foundations of probability is generally considered to be his best work.
D... | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory? | It depends on what you mean that Popper had nothing to with debate.
IN some sense it is half correct
In other sense, its WRONGER THAN WRONG; ultimately,he rejected priors or inductive logic; and he wa | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory?
It depends on what you mean that Popper had nothing to with debate.
IN some sense it is half correct
In other sense, its WRONGER THAN WRONG; ultimately,he rejected priors or inductive logic; and he was intimately connecte... | Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory?
It depends on what you mean that Popper had nothing to with debate.
IN some sense it is half correct
In other sense, its WRONGER THAN WRONG; ultimately,he rejected priors or inductive logic; and he wa |
38,398 | probability of gamma greater than exponential | If $X$ has density function $\lambda \frac{(\lambda x)^2}{\Gamma(3)}\exp(-\lambda x)\mathbf 1_{\{x\colon x > 0\}}$ and independent $Y$ has density function $\exp(-y)\mathbf 1_{\{y\colon x > 0\}}$, then
\begin{align}
P\{X < Y\} &= \int_{0}^\infty \lambda \frac{(\lambda x)^2}{\Gamma(3)}\exp(-\lambda x) \int_{x}^\infty \e... | probability of gamma greater than exponential | If $X$ has density function $\lambda \frac{(\lambda x)^2}{\Gamma(3)}\exp(-\lambda x)\mathbf 1_{\{x\colon x > 0\}}$ and independent $Y$ has density function $\exp(-y)\mathbf 1_{\{y\colon x > 0\}}$, the | probability of gamma greater than exponential
If $X$ has density function $\lambda \frac{(\lambda x)^2}{\Gamma(3)}\exp(-\lambda x)\mathbf 1_{\{x\colon x > 0\}}$ and independent $Y$ has density function $\exp(-y)\mathbf 1_{\{y\colon x > 0\}}$, then
\begin{align}
P\{X < Y\} &= \int_{0}^\infty \lambda \frac{(\lambda x)^2}... | probability of gamma greater than exponential
If $X$ has density function $\lambda \frac{(\lambda x)^2}{\Gamma(3)}\exp(-\lambda x)\mathbf 1_{\{x\colon x > 0\}}$ and independent $Y$ has density function $\exp(-y)\mathbf 1_{\{y\colon x > 0\}}$, the |
38,399 | probability of gamma greater than exponential | There is a relationship between gamma and beta random variables that leads to a general expression for $P[X>Y]$ for any two independent gamma random variables.
If $X \sim \rm{Gamma}(\alpha_1,\beta_1)$ and $Y \sim \rm{Gamma}(\alpha_2,\beta_2),$ where $\alpha$ is the shape parameter, $\beta$ is the scale parameter, and t... | probability of gamma greater than exponential | There is a relationship between gamma and beta random variables that leads to a general expression for $P[X>Y]$ for any two independent gamma random variables.
If $X \sim \rm{Gamma}(\alpha_1,\beta_1)$ | probability of gamma greater than exponential
There is a relationship between gamma and beta random variables that leads to a general expression for $P[X>Y]$ for any two independent gamma random variables.
If $X \sim \rm{Gamma}(\alpha_1,\beta_1)$ and $Y \sim \rm{Gamma}(\alpha_2,\beta_2),$ where $\alpha$ is the shape pa... | probability of gamma greater than exponential
There is a relationship between gamma and beta random variables that leads to a general expression for $P[X>Y]$ for any two independent gamma random variables.
If $X \sim \rm{Gamma}(\alpha_1,\beta_1)$ |
38,400 | probability of gamma greater than exponential | The rote way to compute $P[Y>X]$ is by double integral
$$\int_0^\infty f_X(x) dx \int_x^\infty f_Y(y) dy $$
Where the inner integral may be recognized as the survival function of $Y$, an exponential with parameter $\lambda=1$, at $x$, equal to $e^{-x}$. Then the remaining integral
$$\int_0^\infty e^{-x} f_X(x) dx $$
ma... | probability of gamma greater than exponential | The rote way to compute $P[Y>X]$ is by double integral
$$\int_0^\infty f_X(x) dx \int_x^\infty f_Y(y) dy $$
Where the inner integral may be recognized as the survival function of $Y$, an exponential w | probability of gamma greater than exponential
The rote way to compute $P[Y>X]$ is by double integral
$$\int_0^\infty f_X(x) dx \int_x^\infty f_Y(y) dy $$
Where the inner integral may be recognized as the survival function of $Y$, an exponential with parameter $\lambda=1$, at $x$, equal to $e^{-x}$. Then the remaining i... | probability of gamma greater than exponential
The rote way to compute $P[Y>X]$ is by double integral
$$\int_0^\infty f_X(x) dx \int_x^\infty f_Y(y) dy $$
Where the inner integral may be recognized as the survival function of $Y$, an exponential w |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.