idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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8,701 | How to design and implement an asymmetric loss function for regression? | As mentioned in the comments above, quantile regression uses an asymmetric loss function ( linear but with different slopes for positive and negative errors). The quadratic (squared loss) analog of quantile regression is expectile regression.
You can google quantile regression for the references. For expectile regress... | How to design and implement an asymmetric loss function for regression? | As mentioned in the comments above, quantile regression uses an asymmetric loss function ( linear but with different slopes for positive and negative errors). The quadratic (squared loss) analog of qu | How to design and implement an asymmetric loss function for regression?
As mentioned in the comments above, quantile regression uses an asymmetric loss function ( linear but with different slopes for positive and negative errors). The quadratic (squared loss) analog of quantile regression is expectile regression.
You ... | How to design and implement an asymmetric loss function for regression?
As mentioned in the comments above, quantile regression uses an asymmetric loss function ( linear but with different slopes for positive and negative errors). The quadratic (squared loss) analog of qu |
8,702 | How to design and implement an asymmetric loss function for regression? | This sort of unequal weighting is often done in classification problems with two classes. The Bayes rule can be modifed using a loss function that that weights the loss higher for one error than the other. This will lead to a rule that produces unequal error rates.
In regression it would certainly be possible to cons... | How to design and implement an asymmetric loss function for regression? | This sort of unequal weighting is often done in classification problems with two classes. The Bayes rule can be modifed using a loss function that that weights the loss higher for one error than the | How to design and implement an asymmetric loss function for regression?
This sort of unequal weighting is often done in classification problems with two classes. The Bayes rule can be modifed using a loss function that that weights the loss higher for one error than the other. This will lead to a rule that produces u... | How to design and implement an asymmetric loss function for regression?
This sort of unequal weighting is often done in classification problems with two classes. The Bayes rule can be modifed using a loss function that that weights the loss higher for one error than the |
8,703 | AIC versus cross validation in time series: the small sample case | Taking theoretical considerations aside, Akaike Information Criterion is just likelihood penalized by the degrees of freedom. What follows, AIC accounts for uncertainty in the data (-2LL) and makes the assumption that more parameters leads to higher risk of overfitting (2k). Cross-validation just looks at the test set ... | AIC versus cross validation in time series: the small sample case | Taking theoretical considerations aside, Akaike Information Criterion is just likelihood penalized by the degrees of freedom. What follows, AIC accounts for uncertainty in the data (-2LL) and makes th | AIC versus cross validation in time series: the small sample case
Taking theoretical considerations aside, Akaike Information Criterion is just likelihood penalized by the degrees of freedom. What follows, AIC accounts for uncertainty in the data (-2LL) and makes the assumption that more parameters leads to higher risk... | AIC versus cross validation in time series: the small sample case
Taking theoretical considerations aside, Akaike Information Criterion is just likelihood penalized by the degrees of freedom. What follows, AIC accounts for uncertainty in the data (-2LL) and makes th |
8,704 | AIC versus cross validation in time series: the small sample case | Hm - if your ultimate goal is to predict, why do you intend to do model selection at all? As far as I know, it is well established both in the "traditional" statistical literature and the machine learning literature that model averaging is superior when it comes to prediction. Put simply, model averaging means that you... | AIC versus cross validation in time series: the small sample case | Hm - if your ultimate goal is to predict, why do you intend to do model selection at all? As far as I know, it is well established both in the "traditional" statistical literature and the machine lear | AIC versus cross validation in time series: the small sample case
Hm - if your ultimate goal is to predict, why do you intend to do model selection at all? As far as I know, it is well established both in the "traditional" statistical literature and the machine learning literature that model averaging is superior when ... | AIC versus cross validation in time series: the small sample case
Hm - if your ultimate goal is to predict, why do you intend to do model selection at all? As far as I know, it is well established both in the "traditional" statistical literature and the machine lear |
8,705 | AIC versus cross validation in time series: the small sample case | My idea is, do both and see. It's direct to use AIC. Smaller the AIC, better the model. But one cannot depend on AIC and say such model is the best. So, if you have a pool of ARIMA models, take each and check on forecasting for the existing values and see which model predicts the closest to the existing time series dat... | AIC versus cross validation in time series: the small sample case | My idea is, do both and see. It's direct to use AIC. Smaller the AIC, better the model. But one cannot depend on AIC and say such model is the best. So, if you have a pool of ARIMA models, take each a | AIC versus cross validation in time series: the small sample case
My idea is, do both and see. It's direct to use AIC. Smaller the AIC, better the model. But one cannot depend on AIC and say such model is the best. So, if you have a pool of ARIMA models, take each and check on forecasting for the existing values and se... | AIC versus cross validation in time series: the small sample case
My idea is, do both and see. It's direct to use AIC. Smaller the AIC, better the model. But one cannot depend on AIC and say such model is the best. So, if you have a pool of ARIMA models, take each a |
8,706 | Two dice rolls - same number in sequence | The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6).
The probability of rolling any number twice in a row is 1/6, because there are six ways to roll a specific number twice in a row (6 x 1/36). Another way to t... | Two dice rolls - same number in sequence | The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6).
The probability of rolling any number | Two dice rolls - same number in sequence
The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6).
The probability of rolling any number twice in a row is 1/6, because there are six ways to roll a specific number tw... | Two dice rolls - same number in sequence
The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6).
The probability of rolling any number |
8,707 | Two dice rolls - same number in sequence | To make it perfectly clear, consider the sample space for rolling a die twice.
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6,... | Two dice rolls - same number in sequence | To make it perfectly clear, consider the sample space for rolling a die twice.
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3 | Two dice rolls - same number in sequence
To make it perfectly clear, consider the sample space for rolling a die twice.
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, ... | Two dice rolls - same number in sequence
To make it perfectly clear, consider the sample space for rolling a die twice.
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3 |
8,708 | Two dice rolls - same number in sequence | Conceptually, this is just asking "what are the chances a second die matches the result of the first". Suppose I rolled a die, secretly, and asked you to match the outcome with your own roll.
No matter which number I rolled, there is a 1/6 chance that your die matches my roll, as there is a 1/6 chance any die roll com... | Two dice rolls - same number in sequence | Conceptually, this is just asking "what are the chances a second die matches the result of the first". Suppose I rolled a die, secretly, and asked you to match the outcome with your own roll.
No matt | Two dice rolls - same number in sequence
Conceptually, this is just asking "what are the chances a second die matches the result of the first". Suppose I rolled a die, secretly, and asked you to match the outcome with your own roll.
No matter which number I rolled, there is a 1/6 chance that your die matches my roll, ... | Two dice rolls - same number in sequence
Conceptually, this is just asking "what are the chances a second die matches the result of the first". Suppose I rolled a die, secretly, and asked you to match the outcome with your own roll.
No matt |
8,709 | Two dice rolls - same number in sequence | If you roll a 1 then on the second roll (for a fair 6 sided die) the probability that the second roll is a 1 is 1/6 (assuming independence. This would be true for any other possible first roll. | Two dice rolls - same number in sequence | If you roll a 1 then on the second roll (for a fair 6 sided die) the probability that the second roll is a 1 is 1/6 (assuming independence. This would be true for any other possible first roll. | Two dice rolls - same number in sequence
If you roll a 1 then on the second roll (for a fair 6 sided die) the probability that the second roll is a 1 is 1/6 (assuming independence. This would be true for any other possible first roll. | Two dice rolls - same number in sequence
If you roll a 1 then on the second roll (for a fair 6 sided die) the probability that the second roll is a 1 is 1/6 (assuming independence. This would be true for any other possible first roll. |
8,710 | Two dice rolls - same number in sequence | i would look at it as a combination problem . where you are asked what possible combinations are thre that have same numbers on first and second roll. combinations are 6 (11,22,33,44,55,66)
from a total possibilities 6*6=36
so probability is 6/36 | Two dice rolls - same number in sequence | i would look at it as a combination problem . where you are asked what possible combinations are thre that have same numbers on first and second roll. combinations are 6 (11,22,33,44,55,66)
from a to | Two dice rolls - same number in sequence
i would look at it as a combination problem . where you are asked what possible combinations are thre that have same numbers on first and second roll. combinations are 6 (11,22,33,44,55,66)
from a total possibilities 6*6=36
so probability is 6/36 | Two dice rolls - same number in sequence
i would look at it as a combination problem . where you are asked what possible combinations are thre that have same numbers on first and second roll. combinations are 6 (11,22,33,44,55,66)
from a to |
8,711 | Two dice rolls - same number in sequence | Hope this helps :
Probability for the first roll to turn up as 1 : 1/6
Probability for the second roll also to turn up as 1 : 1/6
Therefore , probability that the first two rolls turn up as 1 is (1/6*1/6) = 1/36
Now the probability that the first two rolls turn up as 2 is (1/6*1/6) = 1/36
.
.
.
.
Same applies for 3,4,... | Two dice rolls - same number in sequence | Hope this helps :
Probability for the first roll to turn up as 1 : 1/6
Probability for the second roll also to turn up as 1 : 1/6
Therefore , probability that the first two rolls turn up as 1 is (1/6* | Two dice rolls - same number in sequence
Hope this helps :
Probability for the first roll to turn up as 1 : 1/6
Probability for the second roll also to turn up as 1 : 1/6
Therefore , probability that the first two rolls turn up as 1 is (1/6*1/6) = 1/36
Now the probability that the first two rolls turn up as 2 is (1/6*1... | Two dice rolls - same number in sequence
Hope this helps :
Probability for the first roll to turn up as 1 : 1/6
Probability for the second roll also to turn up as 1 : 1/6
Therefore , probability that the first two rolls turn up as 1 is (1/6* |
8,712 | Two dice rolls - same number in sequence | Since I didn't see this exact way of framing it above:
For your first roll there are 6 possible answers, and 6 acceptable answers (as any number 1-6 is acceptable).
6/6
For the second roll there are 6 possible answers, but now only 1 will match the first roll.
1/6
6/6 * 1/6 = 1/6 | Two dice rolls - same number in sequence | Since I didn't see this exact way of framing it above:
For your first roll there are 6 possible answers, and 6 acceptable answers (as any number 1-6 is acceptable).
6/6
For the second roll there are 6 | Two dice rolls - same number in sequence
Since I didn't see this exact way of framing it above:
For your first roll there are 6 possible answers, and 6 acceptable answers (as any number 1-6 is acceptable).
6/6
For the second roll there are 6 possible answers, but now only 1 will match the first roll.
1/6
6/6 * 1/6 = 1/... | Two dice rolls - same number in sequence
Since I didn't see this exact way of framing it above:
For your first roll there are 6 possible answers, and 6 acceptable answers (as any number 1-6 is acceptable).
6/6
For the second roll there are 6 |
8,713 | Two dice rolls - same number in sequence | I guess you are confused because it did not mention an exact number. If the question said something like rolling a die twice and getting a 1 twice then you are correct but since it did not say so, the same is true for getting a 1,2 3 or any other number. Thus since there are 6 numbers that can turn up that way, it will... | Two dice rolls - same number in sequence | I guess you are confused because it did not mention an exact number. If the question said something like rolling a die twice and getting a 1 twice then you are correct but since it did not say so, the | Two dice rolls - same number in sequence
I guess you are confused because it did not mention an exact number. If the question said something like rolling a die twice and getting a 1 twice then you are correct but since it did not say so, the same is true for getting a 1,2 3 or any other number. Thus since there are 6 n... | Two dice rolls - same number in sequence
I guess you are confused because it did not mention an exact number. If the question said something like rolling a die twice and getting a 1 twice then you are correct but since it did not say so, the |
8,714 | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? | Budding statisticians in Statistics 101 with no mathematical skills beyond high-school algebra should consider
\begin{align}
E\left[(X-a)^2\right] &= E\bigr[\big(X-\mu + \mu -a\big)^2\bigr] & {\scriptstyle{\text{Here,}~\mu ~ \text{denotes the mean of} ~ X}}\\
&= E\bigr[\big((X-\mu) + (\mu -a)\big)^2\bigr]\\
&= E\bigr[(... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var | Budding statisticians in Statistics 101 with no mathematical skills beyond high-school algebra should consider
\begin{align}
E\left[(X-a)^2\right] &= E\bigr[\big(X-\mu + \mu -a\big)^2\bigr] & {\script | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
Budding statisticians in Statistics 101 with no mathematical skills beyond high-school algebra should consider
\begin{align}
E\left[(X-a)^2\right] &= E\bigr[\big(X-\mu + \mu -a\big)^2\bigr] & {\scriptstyle{\text{H... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var
Budding statisticians in Statistics 101 with no mathematical skills beyond high-school algebra should consider
\begin{align}
E\left[(X-a)^2\right] &= E\bigr[\big(X-\mu + \mu -a\big)^2\bigr] & {\script |
8,715 | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? | The expression is $\mathbb E[(X-a)^2]$. We'll differentiate and equate the expression to $0$:
$$\begin{align}\frac{d}{da}\mathbb E[(X-a)^2]&=\mathbb E\left[\frac{d}{da}(X-a)^2\right]\\&=\mathbb E[-2(X-a)]\\&=0\end{align}$$
Then, $\mathbb E[-2X +2a]=0\rightarrow \mathbb E[2X]=\mathbb E[2a]=2a\rightarrow a=\mathbb E[X]$.... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var | The expression is $\mathbb E[(X-a)^2]$. We'll differentiate and equate the expression to $0$:
$$\begin{align}\frac{d}{da}\mathbb E[(X-a)^2]&=\mathbb E\left[\frac{d}{da}(X-a)^2\right]\\&=\mathbb E[-2(X | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
The expression is $\mathbb E[(X-a)^2]$. We'll differentiate and equate the expression to $0$:
$$\begin{align}\frac{d}{da}\mathbb E[(X-a)^2]&=\mathbb E\left[\frac{d}{da}(X-a)^2\right]\\&=\mathbb E[-2(X-a)]\\&=0\end... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var
The expression is $\mathbb E[(X-a)^2]$. We'll differentiate and equate the expression to $0$:
$$\begin{align}\frac{d}{da}\mathbb E[(X-a)^2]&=\mathbb E\left[\frac{d}{da}(X-a)^2\right]\\&=\mathbb E[-2(X |
8,716 | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? | Assuming that you have $n$ values $\{x_1, x_2, \ldots, x_n\}$, the mean squared difference from each value $x_i$ to some number $a$ is:
$$
m(a)=\frac{1}{n}\sum_{i=1}^{n}(x_i-a)^2
$$
We could ignore the term $\frac{1}{n}$ but I'm leaving it in. Expand the square and manipulate:
$$
m(a)=\frac{1}{n}\left(\sum_{i=1}^{n}x_{... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var | Assuming that you have $n$ values $\{x_1, x_2, \ldots, x_n\}$, the mean squared difference from each value $x_i$ to some number $a$ is:
$$
m(a)=\frac{1}{n}\sum_{i=1}^{n}(x_i-a)^2
$$
We could ignore th | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
Assuming that you have $n$ values $\{x_1, x_2, \ldots, x_n\}$, the mean squared difference from each value $x_i$ to some number $a$ is:
$$
m(a)=\frac{1}{n}\sum_{i=1}^{n}(x_i-a)^2
$$
We could ignore the term $\frac... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var
Assuming that you have $n$ values $\{x_1, x_2, \ldots, x_n\}$, the mean squared difference from each value $x_i$ to some number $a$ is:
$$
m(a)=\frac{1}{n}\sum_{i=1}^{n}(x_i-a)^2
$$
We could ignore th |
8,717 | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? | A quick one:
This follows from a property of moments (a rule to transform the center)
$$E\left[(x-\hat{x})^n\right] = \sum_{i=0}^n {n \choose i} E\left[(x-a)^i\right] (a-\hat{x})^{n-i}$$
which becomes for $n=2$ and $a=\mu=E[X]$
$$E \left[(x-\hat{x})^2\right] = \underbrace{E \left[(x-\mu)^2\right] }_{=\text{Var}(x)} +... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var | A quick one:
This follows from a property of moments (a rule to transform the center)
$$E\left[(x-\hat{x})^n\right] = \sum_{i=0}^n {n \choose i} E\left[(x-a)^i\right] (a-\hat{x})^{n-i}$$
which become | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
A quick one:
This follows from a property of moments (a rule to transform the center)
$$E\left[(x-\hat{x})^n\right] = \sum_{i=0}^n {n \choose i} E\left[(x-a)^i\right] (a-\hat{x})^{n-i}$$
which becomes for $n=2$ a... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var
A quick one:
This follows from a property of moments (a rule to transform the center)
$$E\left[(x-\hat{x})^n\right] = \sum_{i=0}^n {n \choose i} E\left[(x-a)^i\right] (a-\hat{x})^{n-i}$$
which become |
8,718 | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? | Just work it out.
$$\frac{\partial}{\partial c}E[(X-c)^2]=E\left[ \frac{\partial}{\partial c}(X-c)^2 \right]=2E\left[ X-c \right]$$
Setting this to zero, $E[X]=c$ is the only stationary point and it's obviously not a maximum.
.
(there's an invocation of the dominated convergence theorem or near offer in there to justif... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var | Just work it out.
$$\frac{\partial}{\partial c}E[(X-c)^2]=E\left[ \frac{\partial}{\partial c}(X-c)^2 \right]=2E\left[ X-c \right]$$
Setting this to zero, $E[X]=c$ is the only stationary point and it's | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
Just work it out.
$$\frac{\partial}{\partial c}E[(X-c)^2]=E\left[ \frac{\partial}{\partial c}(X-c)^2 \right]=2E\left[ X-c \right]$$
Setting this to zero, $E[X]=c$ is the only stationary point and it's obviously no... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var
Just work it out.
$$\frac{\partial}{\partial c}E[(X-c)^2]=E\left[ \frac{\partial}{\partial c}(X-c)^2 \right]=2E\left[ X-c \right]$$
Setting this to zero, $E[X]=c$ is the only stationary point and it's |
8,719 | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? | I have another geometric perspective which my college suggested me. In essence "the value $M$" that you are looking for is a factor such that $M\cdot\mathbb{1}$ is a projection of $X$ onto subspace generated by $\mathbb{1}$ in $L^2(\Omega, A, P)$ space where $\mathbb{1}$ is a constant random variable equal 1 almost eve... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var | I have another geometric perspective which my college suggested me. In essence "the value $M$" that you are looking for is a factor such that $M\cdot\mathbb{1}$ is a projection of $X$ onto subspace ge | How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?
I have another geometric perspective which my college suggested me. In essence "the value $M$" that you are looking for is a factor such that $M\cdot\mathbb{1}$ is a projection of $X$ onto subspace generated by $\... | How can I prove mathematically that the mean of a distribution is the measure that minimizes the var
I have another geometric perspective which my college suggested me. In essence "the value $M$" that you are looking for is a factor such that $M\cdot\mathbb{1}$ is a projection of $X$ onto subspace ge |
8,720 | Does mean=mode imply a symmetric distribution? | Mean = mode doesn't imply symmetry.
Even if mean = median = mode you still don't necessarily have symmetry.
And in anticipation of the potential followup -- even if mean=median=mode and the third central moment is zero (so moment-skewness is 0), you still don't necessarily have symmetry.
... but there was a followup t... | Does mean=mode imply a symmetric distribution? | Mean = mode doesn't imply symmetry.
Even if mean = median = mode you still don't necessarily have symmetry.
And in anticipation of the potential followup -- even if mean=median=mode and the third cen | Does mean=mode imply a symmetric distribution?
Mean = mode doesn't imply symmetry.
Even if mean = median = mode you still don't necessarily have symmetry.
And in anticipation of the potential followup -- even if mean=median=mode and the third central moment is zero (so moment-skewness is 0), you still don't necessaril... | Does mean=mode imply a symmetric distribution?
Mean = mode doesn't imply symmetry.
Even if mean = median = mode you still don't necessarily have symmetry.
And in anticipation of the potential followup -- even if mean=median=mode and the third cen |
8,721 | Does mean=mode imply a symmetric distribution? | Try this set of numbers:
\begin{align}
X &= \{2,3,5,5,10\} \\[10pt]
{\rm mean}(X) &= 5 \\
{\rm median}(X) &= 5 \\
{\rm mode}(X) &= 5
\end{align}
I wouldn't call that distribution symmetrical. | Does mean=mode imply a symmetric distribution? | Try this set of numbers:
\begin{align}
X &= \{2,3,5,5,10\} \\[10pt]
{\rm mean}(X) &= 5 \\
{\rm median}(X) &= 5 \\
{\rm mode}(X) &= 5
\end{align}
I wouldn't call that distribution symmetrical. | Does mean=mode imply a symmetric distribution?
Try this set of numbers:
\begin{align}
X &= \{2,3,5,5,10\} \\[10pt]
{\rm mean}(X) &= 5 \\
{\rm median}(X) &= 5 \\
{\rm mode}(X) &= 5
\end{align}
I wouldn't call that distribution symmetrical. | Does mean=mode imply a symmetric distribution?
Try this set of numbers:
\begin{align}
X &= \{2,3,5,5,10\} \\[10pt]
{\rm mean}(X) &= 5 \\
{\rm median}(X) &= 5 \\
{\rm mode}(X) &= 5
\end{align}
I wouldn't call that distribution symmetrical. |
8,722 | Does mean=mode imply a symmetric distribution? | No.
Let $X$ be a discrete random variable with $p(X = -2) = \tfrac{1}{6}$, $p(X = 0) = \tfrac{1}{2}$, and $p(X = 1) = \tfrac{1}{3}$. Obviously, $X$ is not symmetric, but its mean and mode are both 0. | Does mean=mode imply a symmetric distribution? | No.
Let $X$ be a discrete random variable with $p(X = -2) = \tfrac{1}{6}$, $p(X = 0) = \tfrac{1}{2}$, and $p(X = 1) = \tfrac{1}{3}$. Obviously, $X$ is not symmetric, but its mean and mode are both 0. | Does mean=mode imply a symmetric distribution?
No.
Let $X$ be a discrete random variable with $p(X = -2) = \tfrac{1}{6}$, $p(X = 0) = \tfrac{1}{2}$, and $p(X = 1) = \tfrac{1}{3}$. Obviously, $X$ is not symmetric, but its mean and mode are both 0. | Does mean=mode imply a symmetric distribution?
No.
Let $X$ be a discrete random variable with $p(X = -2) = \tfrac{1}{6}$, $p(X = 0) = \tfrac{1}{2}$, and $p(X = 1) = \tfrac{1}{3}$. Obviously, $X$ is not symmetric, but its mean and mode are both 0. |
8,723 | Does mean=mode imply a symmetric distribution? | To repeat an answer I gave elsewhere, but fits here too:
$$\mathbb{P}(X=n) = \left\{
\begin{array}{ll}
0.03 & n=-3 \\
0.04 & n=-2 \\
0.25 & n=-1 \\
0.40 & n=0 \\
0.15 & n=1 \\
0.12 & n=2 \\
0.01 & n=3
\end{array}
\right.$$
which not only has mean, ... | Does mean=mode imply a symmetric distribution? | To repeat an answer I gave elsewhere, but fits here too:
$$\mathbb{P}(X=n) = \left\{
\begin{array}{ll}
0.03 & n=-3 \\
0.04 & n=-2 \\
0.25 & n=-1 \\
0.40 & n=0 \\
| Does mean=mode imply a symmetric distribution?
To repeat an answer I gave elsewhere, but fits here too:
$$\mathbb{P}(X=n) = \left\{
\begin{array}{ll}
0.03 & n=-3 \\
0.04 & n=-2 \\
0.25 & n=-1 \\
0.40 & n=0 \\
0.15 & n=1 \\
0.12 & n=2 \\
0.01 & n=3
\end... | Does mean=mode imply a symmetric distribution?
To repeat an answer I gave elsewhere, but fits here too:
$$\mathbb{P}(X=n) = \left\{
\begin{array}{ll}
0.03 & n=-3 \\
0.04 & n=-2 \\
0.25 & n=-1 \\
0.40 & n=0 \\
|
8,724 | Visualising many variables in one plot | Fortuitously or otherwise, your example is of optimal size (up to 7 values for each of 15
groups) first, to show that there is a problem graphically; and second, to allow other and
fairly simple solutions. The graph is of a kind often called spaghetti by people in
different fields, although it's not always clear whethe... | Visualising many variables in one plot | Fortuitously or otherwise, your example is of optimal size (up to 7 values for each of 15
groups) first, to show that there is a problem graphically; and second, to allow other and
fairly simple solut | Visualising many variables in one plot
Fortuitously or otherwise, your example is of optimal size (up to 7 values for each of 15
groups) first, to show that there is a problem graphically; and second, to allow other and
fairly simple solutions. The graph is of a kind often called spaghetti by people in
different fields... | Visualising many variables in one plot
Fortuitously or otherwise, your example is of optimal size (up to 7 values for each of 15
groups) first, to show that there is a problem graphically; and second, to allow other and
fairly simple solut |
8,725 | Visualising many variables in one plot | As a complement to Nick's answer, here's some R code for making a similar plot using simulated data:
library(ggplot2)
get_df <- function(label="group A", n_obs=10, drift=runif(1)) {
df <- data.frame(time=seq(1, n_obs), label=label)
df$y <- df$time * drift + cumsum(rnorm(n_obs))
return(df)
}
df_list <- lapp... | Visualising many variables in one plot | As a complement to Nick's answer, here's some R code for making a similar plot using simulated data:
library(ggplot2)
get_df <- function(label="group A", n_obs=10, drift=runif(1)) {
df <- data.fr | Visualising many variables in one plot
As a complement to Nick's answer, here's some R code for making a similar plot using simulated data:
library(ggplot2)
get_df <- function(label="group A", n_obs=10, drift=runif(1)) {
df <- data.frame(time=seq(1, n_obs), label=label)
df$y <- df$time * drift + cumsum(rnorm(n... | Visualising many variables in one plot
As a complement to Nick's answer, here's some R code for making a similar plot using simulated data:
library(ggplot2)
get_df <- function(label="group A", n_obs=10, drift=runif(1)) {
df <- data.fr |
8,726 | Visualising many variables in one plot | For those wanting to use a ggplot2 approach in R consider the facetshade function in the package extracat. This offers a general approach, not just for line plots. Here is an example with scatterplots (from the foot of this page):
data(olives, package="extracat")
library(scales)
fs1 <- facetshade(data = olives,
... | Visualising many variables in one plot | For those wanting to use a ggplot2 approach in R consider the facetshade function in the package extracat. This offers a general approach, not just for line plots. Here is an example with scatterplo | Visualising many variables in one plot
For those wanting to use a ggplot2 approach in R consider the facetshade function in the package extracat. This offers a general approach, not just for line plots. Here is an example with scatterplots (from the foot of this page):
data(olives, package="extracat")
library(scales)... | Visualising many variables in one plot
For those wanting to use a ggplot2 approach in R consider the facetshade function in the package extracat. This offers a general approach, not just for line plots. Here is an example with scatterplo |
8,727 | Visualising many variables in one plot | Here is a solution inspired by Ch. 11.3, the section on "Texas Housing Data", in Hadley Wickham's Book on ggplot2. Here I fit a linear model to each time series , take the residuals (which are centered around mean 0), and draw a summary line in a different color.
library(ggplot2)
library(dplyr)
#works with dplyr versio... | Visualising many variables in one plot | Here is a solution inspired by Ch. 11.3, the section on "Texas Housing Data", in Hadley Wickham's Book on ggplot2. Here I fit a linear model to each time series , take the residuals (which are centere | Visualising many variables in one plot
Here is a solution inspired by Ch. 11.3, the section on "Texas Housing Data", in Hadley Wickham's Book on ggplot2. Here I fit a linear model to each time series , take the residuals (which are centered around mean 0), and draw a summary line in a different color.
library(ggplot2)
... | Visualising many variables in one plot
Here is a solution inspired by Ch. 11.3, the section on "Texas Housing Data", in Hadley Wickham's Book on ggplot2. Here I fit a linear model to each time series , take the residuals (which are centere |
8,728 | What is the difference between something being "true" and 'true with probability 1"? | If something is true, then it is true with probability of one. Or at least let us assume that without raising further complications. But something with probability of one is not necessarily true. This is the notion of something being almost surely true.
Example
Suppose we sample uniformly on the interval $x \in [0,1] \... | What is the difference between something being "true" and 'true with probability 1"? | If something is true, then it is true with probability of one. Or at least let us assume that without raising further complications. But something with probability of one is not necessarily true. This | What is the difference between something being "true" and 'true with probability 1"?
If something is true, then it is true with probability of one. Or at least let us assume that without raising further complications. But something with probability of one is not necessarily true. This is the notion of something being a... | What is the difference between something being "true" and 'true with probability 1"?
If something is true, then it is true with probability of one. Or at least let us assume that without raising further complications. But something with probability of one is not necessarily true. This |
8,729 | What is the difference between something being "true" and 'true with probability 1"? | This difference occurs because of the difference between probability and possibility
This answer is based on a longer paper O'Neill (2014) that looks at the interaction of a binary possibility operator and a probability measure. Have a look at this paper if you'd like a more detailed exposition of the subject covered ... | What is the difference between something being "true" and 'true with probability 1"? | This difference occurs because of the difference between probability and possibility
This answer is based on a longer paper O'Neill (2014) that looks at the interaction of a binary possibility operato | What is the difference between something being "true" and 'true with probability 1"?
This difference occurs because of the difference between probability and possibility
This answer is based on a longer paper O'Neill (2014) that looks at the interaction of a binary possibility operator and a probability measure. Have ... | What is the difference between something being "true" and 'true with probability 1"?
This difference occurs because of the difference between probability and possibility
This answer is based on a longer paper O'Neill (2014) that looks at the interaction of a binary possibility operato |
8,730 | What is the difference between something being "true" and 'true with probability 1"? | As Galen indicated, this is the concept of almost surely or almost everywhere.
To provide a more general framework, consider a measure space $(X, \mathfrak A, \mu). $ For a measurable set $A\in \mathfrak A, $ a property $\mathsf Q$ holds almost everywhere on $A$, provided there exists a null set $A_0\subset A$ that is... | What is the difference between something being "true" and 'true with probability 1"? | As Galen indicated, this is the concept of almost surely or almost everywhere.
To provide a more general framework, consider a measure space $(X, \mathfrak A, \mu). $ For a measurable set $A\in \mathf | What is the difference between something being "true" and 'true with probability 1"?
As Galen indicated, this is the concept of almost surely or almost everywhere.
To provide a more general framework, consider a measure space $(X, \mathfrak A, \mu). $ For a measurable set $A\in \mathfrak A, $ a property $\mathsf Q$ hol... | What is the difference between something being "true" and 'true with probability 1"?
As Galen indicated, this is the concept of almost surely or almost everywhere.
To provide a more general framework, consider a measure space $(X, \mathfrak A, \mu). $ For a measurable set $A\in \mathf |
8,731 | What is the difference between something being "true" and 'true with probability 1"? | A probability is just a function that satisfies a set of axioms, and maps subsets of the sample space to real numbers between $0$ and $1$. A widely used one is Kolmogorov axioms. Therefore, if you construct your own function that satisfies that set of axioms, no matter what it is, and you have a set which is mapped to ... | What is the difference between something being "true" and 'true with probability 1"? | A probability is just a function that satisfies a set of axioms, and maps subsets of the sample space to real numbers between $0$ and $1$. A widely used one is Kolmogorov axioms. Therefore, if you con | What is the difference between something being "true" and 'true with probability 1"?
A probability is just a function that satisfies a set of axioms, and maps subsets of the sample space to real numbers between $0$ and $1$. A widely used one is Kolmogorov axioms. Therefore, if you construct your own function that satis... | What is the difference between something being "true" and 'true with probability 1"?
A probability is just a function that satisfies a set of axioms, and maps subsets of the sample space to real numbers between $0$ and $1$. A widely used one is Kolmogorov axioms. Therefore, if you con |
8,732 | What is the difference between something being "true" and 'true with probability 1"? | Consider the (-1,-1)-(+1,+1) sheet with a point sized hole in the origin.
It is true with probability 1 that a random point within (-1,-1)-(+1,+1) in the sheet. But there is a point that meets that definition that isn't on the sheet. So it is not true that a point within (-1,-1)-(+1,+1) is on the sheet.
There is no dif... | What is the difference between something being "true" and 'true with probability 1"? | Consider the (-1,-1)-(+1,+1) sheet with a point sized hole in the origin.
It is true with probability 1 that a random point within (-1,-1)-(+1,+1) in the sheet. But there is a point that meets that de | What is the difference between something being "true" and 'true with probability 1"?
Consider the (-1,-1)-(+1,+1) sheet with a point sized hole in the origin.
It is true with probability 1 that a random point within (-1,-1)-(+1,+1) in the sheet. But there is a point that meets that definition that isn't on the sheet. S... | What is the difference between something being "true" and 'true with probability 1"?
Consider the (-1,-1)-(+1,+1) sheet with a point sized hole in the origin.
It is true with probability 1 that a random point within (-1,-1)-(+1,+1) in the sheet. But there is a point that meets that de |
8,733 | Why is a mixture of two normally distributed variables only bimodal if their means differ by at least two times the common standard deviation? | This figure from the the paper linked in that wiki article provides a nice illustration:
The proof they provide is based on the fact that normal distributions are concave within one SD of their mean (the SD being the inflection point of the normal pdf, where it goes from concave to convex). Thus, if you add two normal... | Why is a mixture of two normally distributed variables only bimodal if their means differ by at leas | This figure from the the paper linked in that wiki article provides a nice illustration:
The proof they provide is based on the fact that normal distributions are concave within one SD of their mean | Why is a mixture of two normally distributed variables only bimodal if their means differ by at least two times the common standard deviation?
This figure from the the paper linked in that wiki article provides a nice illustration:
The proof they provide is based on the fact that normal distributions are concave withi... | Why is a mixture of two normally distributed variables only bimodal if their means differ by at leas
This figure from the the paper linked in that wiki article provides a nice illustration:
The proof they provide is based on the fact that normal distributions are concave within one SD of their mean |
8,734 | Why is a mixture of two normally distributed variables only bimodal if their means differ by at least two times the common standard deviation? | This is a case where pictures can be deceiving, because this result is a special characteristic of normal mixtures: an analog does not necessarily hold for other mixtures, even when the components are symmetric unimodal distributions! For instance, an equal mixture of two Student t distributions separated by a little ... | Why is a mixture of two normally distributed variables only bimodal if their means differ by at leas | This is a case where pictures can be deceiving, because this result is a special characteristic of normal mixtures: an analog does not necessarily hold for other mixtures, even when the components are | Why is a mixture of two normally distributed variables only bimodal if their means differ by at least two times the common standard deviation?
This is a case where pictures can be deceiving, because this result is a special characteristic of normal mixtures: an analog does not necessarily hold for other mixtures, even ... | Why is a mixture of two normally distributed variables only bimodal if their means differ by at leas
This is a case where pictures can be deceiving, because this result is a special characteristic of normal mixtures: an analog does not necessarily hold for other mixtures, even when the components are |
8,735 | Why is a mixture of two normally distributed variables only bimodal if their means differ by at least two times the common standard deviation? | Comment from above pasted here for continuity:
"[F]ormally, for a 50:50 mixture of two normal distributions with the same SD σ, if you write the density $$f(x)=0.5g_1(x)+0.5g_2(x)$$ in full form showing the parameters, you will see that its second derivative changes sign at the midpoint between the two means when the d... | Why is a mixture of two normally distributed variables only bimodal if their means differ by at leas | Comment from above pasted here for continuity:
"[F]ormally, for a 50:50 mixture of two normal distributions with the same SD σ, if you write the density $$f(x)=0.5g_1(x)+0.5g_2(x)$$ in full form showi | Why is a mixture of two normally distributed variables only bimodal if their means differ by at least two times the common standard deviation?
Comment from above pasted here for continuity:
"[F]ormally, for a 50:50 mixture of two normal distributions with the same SD σ, if you write the density $$f(x)=0.5g_1(x)+0.5g_2(... | Why is a mixture of two normally distributed variables only bimodal if their means differ by at leas
Comment from above pasted here for continuity:
"[F]ormally, for a 50:50 mixture of two normal distributions with the same SD σ, if you write the density $$f(x)=0.5g_1(x)+0.5g_2(x)$$ in full form showi |
8,736 | Why Not Prune Your Neural Network? | Pruning is indeed remarkably effective and I think it is pretty commonly used on networks which are "deployed" for use after training.
The catch about pruning is that you can only increase efficiency, speed, etc. after training is done. You still have to train with the full size network. Most computation time throughou... | Why Not Prune Your Neural Network? | Pruning is indeed remarkably effective and I think it is pretty commonly used on networks which are "deployed" for use after training.
The catch about pruning is that you can only increase efficiency, | Why Not Prune Your Neural Network?
Pruning is indeed remarkably effective and I think it is pretty commonly used on networks which are "deployed" for use after training.
The catch about pruning is that you can only increase efficiency, speed, etc. after training is done. You still have to train with the full size netwo... | Why Not Prune Your Neural Network?
Pruning is indeed remarkably effective and I think it is pretty commonly used on networks which are "deployed" for use after training.
The catch about pruning is that you can only increase efficiency, |
8,737 | Why Not Prune Your Neural Network? | In addition to the points raised in the other answers, a pruned network may not be faster. Common machine learning frameworks have very efficient optimizations for computing dense matrix multiplications (i.e. normal, unpruned layers), but those algorithms can't take any additional advantage of the fact that some weight... | Why Not Prune Your Neural Network? | In addition to the points raised in the other answers, a pruned network may not be faster. Common machine learning frameworks have very efficient optimizations for computing dense matrix multiplicatio | Why Not Prune Your Neural Network?
In addition to the points raised in the other answers, a pruned network may not be faster. Common machine learning frameworks have very efficient optimizations for computing dense matrix multiplications (i.e. normal, unpruned layers), but those algorithms can't take any additional adv... | Why Not Prune Your Neural Network?
In addition to the points raised in the other answers, a pruned network may not be faster. Common machine learning frameworks have very efficient optimizations for computing dense matrix multiplicatio |
8,738 | Why Not Prune Your Neural Network? | As mentioned previously, you need to train on large networks in order to prune them. There are some theories as to why, but the one I'm most familiar with is the "golden ticket" theory. Presented in "The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks" by Jonathan Frankle, Michael Carbin the golde... | Why Not Prune Your Neural Network? | As mentioned previously, you need to train on large networks in order to prune them. There are some theories as to why, but the one I'm most familiar with is the "golden ticket" theory. Presented in " | Why Not Prune Your Neural Network?
As mentioned previously, you need to train on large networks in order to prune them. There are some theories as to why, but the one I'm most familiar with is the "golden ticket" theory. Presented in "The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks" by Jonathan... | Why Not Prune Your Neural Network?
As mentioned previously, you need to train on large networks in order to prune them. There are some theories as to why, but the one I'm most familiar with is the "golden ticket" theory. Presented in " |
8,739 | How to understand "nonlinear" as in "nonlinear dimensionality reduction"? | Dimensionality reduction means that you map each many-dimensional vector into a low-dimensional vector. In other words, you represent (replace) each many-dimensional vector by a low-dimensional vector.
Linear dimensionality reduction means that components of the low-dimensional vector are given by linear functions of t... | How to understand "nonlinear" as in "nonlinear dimensionality reduction"? | Dimensionality reduction means that you map each many-dimensional vector into a low-dimensional vector. In other words, you represent (replace) each many-dimensional vector by a low-dimensional vector | How to understand "nonlinear" as in "nonlinear dimensionality reduction"?
Dimensionality reduction means that you map each many-dimensional vector into a low-dimensional vector. In other words, you represent (replace) each many-dimensional vector by a low-dimensional vector.
Linear dimensionality reduction means that c... | How to understand "nonlinear" as in "nonlinear dimensionality reduction"?
Dimensionality reduction means that you map each many-dimensional vector into a low-dimensional vector. In other words, you represent (replace) each many-dimensional vector by a low-dimensional vector |
8,740 | How to understand "nonlinear" as in "nonlinear dimensionality reduction"? | A picture is worth a thousand words:
Here we are looking for 1-dimensional structure in 2D. The points lie along an S-shaped curve. PCA tries to describe the data with a linear 1-dimensional manifold, which is simply a line; of course a line fits these data quite bad. Isomap is looking for a nonlinear (i.e. curved!) 1... | How to understand "nonlinear" as in "nonlinear dimensionality reduction"? | A picture is worth a thousand words:
Here we are looking for 1-dimensional structure in 2D. The points lie along an S-shaped curve. PCA tries to describe the data with a linear 1-dimensional manifold | How to understand "nonlinear" as in "nonlinear dimensionality reduction"?
A picture is worth a thousand words:
Here we are looking for 1-dimensional structure in 2D. The points lie along an S-shaped curve. PCA tries to describe the data with a linear 1-dimensional manifold, which is simply a line; of course a line fit... | How to understand "nonlinear" as in "nonlinear dimensionality reduction"?
A picture is worth a thousand words:
Here we are looking for 1-dimensional structure in 2D. The points lie along an S-shaped curve. PCA tries to describe the data with a linear 1-dimensional manifold |
8,741 | Binomial confidence interval estimation - why is it not symmetric? | They're believed to be symmetric because quite often a normal approximation is used. This one works well enough in case p lies around 0.5. binom.test on the other hand reports "exact" Clopper-Pearson intervals, which are based on the F distribution (see here for the exact formulas of both approaches). If we would impl... | Binomial confidence interval estimation - why is it not symmetric? | They're believed to be symmetric because quite often a normal approximation is used. This one works well enough in case p lies around 0.5. binom.test on the other hand reports "exact" Clopper-Pearson | Binomial confidence interval estimation - why is it not symmetric?
They're believed to be symmetric because quite often a normal approximation is used. This one works well enough in case p lies around 0.5. binom.test on the other hand reports "exact" Clopper-Pearson intervals, which are based on the F distribution (see... | Binomial confidence interval estimation - why is it not symmetric?
They're believed to be symmetric because quite often a normal approximation is used. This one works well enough in case p lies around 0.5. binom.test on the other hand reports "exact" Clopper-Pearson |
8,742 | Binomial confidence interval estimation - why is it not symmetric? | To see why it should not be symmetric, think of the situation where $p=0.9$ and you get 9 successes in 10 trials. Then $\hat{p}=0.9$ and the 95% CI for $p$ is [0.554, 0.997]. The upper limit cannot be greater than 1 obviously, so most of the uncertainty must fall to the left of $\hat{p}$. | Binomial confidence interval estimation - why is it not symmetric? | To see why it should not be symmetric, think of the situation where $p=0.9$ and you get 9 successes in 10 trials. Then $\hat{p}=0.9$ and the 95% CI for $p$ is [0.554, 0.997]. The upper limit cannot be | Binomial confidence interval estimation - why is it not symmetric?
To see why it should not be symmetric, think of the situation where $p=0.9$ and you get 9 successes in 10 trials. Then $\hat{p}=0.9$ and the 95% CI for $p$ is [0.554, 0.997]. The upper limit cannot be greater than 1 obviously, so most of the uncertainty... | Binomial confidence interval estimation - why is it not symmetric?
To see why it should not be symmetric, think of the situation where $p=0.9$ and you get 9 successes in 10 trials. Then $\hat{p}=0.9$ and the 95% CI for $p$ is [0.554, 0.997]. The upper limit cannot be |
8,743 | Binomial confidence interval estimation - why is it not symmetric? | There are symmetric confidence intervals for the Binomial distribution: asymmetry is not forced on us, despite all the reasons already mentioned. The symmetric intervals are usually considered inferior in that
Although they are numerically symmetric, they are not symmetric in probability: that is, their one-tailed co... | Binomial confidence interval estimation - why is it not symmetric? | There are symmetric confidence intervals for the Binomial distribution: asymmetry is not forced on us, despite all the reasons already mentioned. The symmetric intervals are usually considered inferi | Binomial confidence interval estimation - why is it not symmetric?
There are symmetric confidence intervals for the Binomial distribution: asymmetry is not forced on us, despite all the reasons already mentioned. The symmetric intervals are usually considered inferior in that
Although they are numerically symmetric, ... | Binomial confidence interval estimation - why is it not symmetric?
There are symmetric confidence intervals for the Binomial distribution: asymmetry is not forced on us, despite all the reasons already mentioned. The symmetric intervals are usually considered inferi |
8,744 | Binomial confidence interval estimation - why is it not symmetric? | @Joris mentioned the symmetric or "asymptotic" interval, that is most likely the one you are expecting. @Joris also mentioned the "exact" Clopper-Pearson intervals and gave you a reference which looks very nice. There is another confidence interval for proportions which you will likely encounter (note it is also not ... | Binomial confidence interval estimation - why is it not symmetric? | @Joris mentioned the symmetric or "asymptotic" interval, that is most likely the one you are expecting. @Joris also mentioned the "exact" Clopper-Pearson intervals and gave you a reference which look | Binomial confidence interval estimation - why is it not symmetric?
@Joris mentioned the symmetric or "asymptotic" interval, that is most likely the one you are expecting. @Joris also mentioned the "exact" Clopper-Pearson intervals and gave you a reference which looks very nice. There is another confidence interval fo... | Binomial confidence interval estimation - why is it not symmetric?
@Joris mentioned the symmetric or "asymptotic" interval, that is most likely the one you are expecting. @Joris also mentioned the "exact" Clopper-Pearson intervals and gave you a reference which look |
8,745 | Binomial confidence interval estimation - why is it not symmetric? | Binomial distribution is just not symmetric, yet this fact emerges especially for $p$ near $0$ or $1$ and for small $n$; most people use it for $p\approx 0.5$ and so the confusion. | Binomial confidence interval estimation - why is it not symmetric? | Binomial distribution is just not symmetric, yet this fact emerges especially for $p$ near $0$ or $1$ and for small $n$; most people use it for $p\approx 0.5$ and so the confusion. | Binomial confidence interval estimation - why is it not symmetric?
Binomial distribution is just not symmetric, yet this fact emerges especially for $p$ near $0$ or $1$ and for small $n$; most people use it for $p\approx 0.5$ and so the confusion. | Binomial confidence interval estimation - why is it not symmetric?
Binomial distribution is just not symmetric, yet this fact emerges especially for $p$ near $0$ or $1$ and for small $n$; most people use it for $p\approx 0.5$ and so the confusion. |
8,746 | Binomial confidence interval estimation - why is it not symmetric? | I know that it has been a while, but I thought that I would chime in here. Given n and p, it is simple to compute the probability of a particular number of successes directly using the binomial distribution. One can then examine the distribution to see that it is not symmetric. It will approach symmetry for large np... | Binomial confidence interval estimation - why is it not symmetric? | I know that it has been a while, but I thought that I would chime in here. Given n and p, it is simple to compute the probability of a particular number of successes directly using the binomial distr | Binomial confidence interval estimation - why is it not symmetric?
I know that it has been a while, but I thought that I would chime in here. Given n and p, it is simple to compute the probability of a particular number of successes directly using the binomial distribution. One can then examine the distribution to se... | Binomial confidence interval estimation - why is it not symmetric?
I know that it has been a while, but I thought that I would chime in here. Given n and p, it is simple to compute the probability of a particular number of successes directly using the binomial distr |
8,747 | What is the expected correlation between residual and the dependent variable? | In the regression model:
$$y_i=\mathbf{x}_i'\beta+u_i$$
the usual assumption is that $(y_i,\mathbf{x}_i,u_i)$, $i=1,...,n$ is an iid sample. Under assumptions that $E\mathbf{x}_iu_i=0$ and $E(\mathbf{x}_i\mathbf{x}_i')$ has full rank, the ordinary least squares estimator:
$$\widehat{\beta}=\left(\sum_{i=1}^n\mathbf{x}_... | What is the expected correlation between residual and the dependent variable? | In the regression model:
$$y_i=\mathbf{x}_i'\beta+u_i$$
the usual assumption is that $(y_i,\mathbf{x}_i,u_i)$, $i=1,...,n$ is an iid sample. Under assumptions that $E\mathbf{x}_iu_i=0$ and $E(\mathbf{ | What is the expected correlation between residual and the dependent variable?
In the regression model:
$$y_i=\mathbf{x}_i'\beta+u_i$$
the usual assumption is that $(y_i,\mathbf{x}_i,u_i)$, $i=1,...,n$ is an iid sample. Under assumptions that $E\mathbf{x}_iu_i=0$ and $E(\mathbf{x}_i\mathbf{x}_i')$ has full rank, the ord... | What is the expected correlation between residual and the dependent variable?
In the regression model:
$$y_i=\mathbf{x}_i'\beta+u_i$$
the usual assumption is that $(y_i,\mathbf{x}_i,u_i)$, $i=1,...,n$ is an iid sample. Under assumptions that $E\mathbf{x}_iu_i=0$ and $E(\mathbf{ |
8,748 | What is the expected correlation between residual and the dependent variable? | The correlation depends on the $R^2$. If $R^2$ is high, it means that much of variation in your dependent variable can be attributed to variation in your independent variables, and NOT your error term.
However, if $R^2$ is low, then it means that much of the variation in your dependent variable is unrelated to variati... | What is the expected correlation between residual and the dependent variable? | The correlation depends on the $R^2$. If $R^2$ is high, it means that much of variation in your dependent variable can be attributed to variation in your independent variables, and NOT your error ter | What is the expected correlation between residual and the dependent variable?
The correlation depends on the $R^2$. If $R^2$ is high, it means that much of variation in your dependent variable can be attributed to variation in your independent variables, and NOT your error term.
However, if $R^2$ is low, then it means... | What is the expected correlation between residual and the dependent variable?
The correlation depends on the $R^2$. If $R^2$ is high, it means that much of variation in your dependent variable can be attributed to variation in your independent variables, and NOT your error ter |
8,749 | What is the expected correlation between residual and the dependent variable? | I find this topic quite interesting and current answers are unfortunately incomplete or partly misleading - despite the relevance and high popularity of this question.
By definition of classical OLS framework there should be no relationship between $y ̂$ and $\hat u$, since the residuals obtained are per construction u... | What is the expected correlation between residual and the dependent variable? | I find this topic quite interesting and current answers are unfortunately incomplete or partly misleading - despite the relevance and high popularity of this question.
By definition of classical OLS f | What is the expected correlation between residual and the dependent variable?
I find this topic quite interesting and current answers are unfortunately incomplete or partly misleading - despite the relevance and high popularity of this question.
By definition of classical OLS framework there should be no relationship b... | What is the expected correlation between residual and the dependent variable?
I find this topic quite interesting and current answers are unfortunately incomplete or partly misleading - despite the relevance and high popularity of this question.
By definition of classical OLS f |
8,750 | What is the expected correlation between residual and the dependent variable? | The Adam's answer is wrong. Even with a model that fits data perfectly, you can still get high correlation between residuals and dependent variable. That's the reason no regression book asks you to check this correlation. You can find the answer on Dr. Draper's "Applied Regression Analysis" book. | What is the expected correlation between residual and the dependent variable? | The Adam's answer is wrong. Even with a model that fits data perfectly, you can still get high correlation between residuals and dependent variable. That's the reason no regression book asks you to ch | What is the expected correlation between residual and the dependent variable?
The Adam's answer is wrong. Even with a model that fits data perfectly, you can still get high correlation between residuals and dependent variable. That's the reason no regression book asks you to check this correlation. You can find the ans... | What is the expected correlation between residual and the dependent variable?
The Adam's answer is wrong. Even with a model that fits data perfectly, you can still get high correlation between residuals and dependent variable. That's the reason no regression book asks you to ch |
8,751 | What is the expected correlation between residual and the dependent variable? | So, the residuals are your unexplained variance, the difference between your model's predictions and the actual outcome you're modeling. In practice, few models produced through linear regression will have all residuals close to zero unless linear regression is being used to analyze a mechanical or fixed process.
Ideal... | What is the expected correlation between residual and the dependent variable? | So, the residuals are your unexplained variance, the difference between your model's predictions and the actual outcome you're modeling. In practice, few models produced through linear regression will | What is the expected correlation between residual and the dependent variable?
So, the residuals are your unexplained variance, the difference between your model's predictions and the actual outcome you're modeling. In practice, few models produced through linear regression will have all residuals close to zero unless l... | What is the expected correlation between residual and the dependent variable?
So, the residuals are your unexplained variance, the difference between your model's predictions and the actual outcome you're modeling. In practice, few models produced through linear regression will |
8,752 | Testing for linear dependence among the columns of a matrix | You seem to ask a really provoking question: how to detect, given a singular correlation (or covariance, or sum-of-squares-and-cross-product) matrix, which column is linearly dependent on which. I tentatively suppose that sweep operation could help. Here is my probe in SPSS (not R) to illustrate.
Let's generate some da... | Testing for linear dependence among the columns of a matrix | You seem to ask a really provoking question: how to detect, given a singular correlation (or covariance, or sum-of-squares-and-cross-product) matrix, which column is linearly dependent on which. I ten | Testing for linear dependence among the columns of a matrix
You seem to ask a really provoking question: how to detect, given a singular correlation (or covariance, or sum-of-squares-and-cross-product) matrix, which column is linearly dependent on which. I tentatively suppose that sweep operation could help. Here is my... | Testing for linear dependence among the columns of a matrix
You seem to ask a really provoking question: how to detect, given a singular correlation (or covariance, or sum-of-squares-and-cross-product) matrix, which column is linearly dependent on which. I ten |
8,753 | Testing for linear dependence among the columns of a matrix | Here's a straightforward approach: compute the rank of the matrix that results from removing each of the columns. The columns which, when removed, result in the highest rank are the linearly dependent ones (since removing those does not decrease rank, while removing a linearly independent column does).
In R:
rankifrem... | Testing for linear dependence among the columns of a matrix | Here's a straightforward approach: compute the rank of the matrix that results from removing each of the columns. The columns which, when removed, result in the highest rank are the linearly dependen | Testing for linear dependence among the columns of a matrix
Here's a straightforward approach: compute the rank of the matrix that results from removing each of the columns. The columns which, when removed, result in the highest rank are the linearly dependent ones (since removing those does not decrease rank, while r... | Testing for linear dependence among the columns of a matrix
Here's a straightforward approach: compute the rank of the matrix that results from removing each of the columns. The columns which, when removed, result in the highest rank are the linearly dependen |
8,754 | Testing for linear dependence among the columns of a matrix | The question asks about "identifying underlying [linear] relationships" among variables.
The quick and easy way to detect relationships is to regress any other variable (use a constant, even) against those variables using your favorite software: any good regression procedure will detect and diagnose collinearity. (You... | Testing for linear dependence among the columns of a matrix | The question asks about "identifying underlying [linear] relationships" among variables.
The quick and easy way to detect relationships is to regress any other variable (use a constant, even) against | Testing for linear dependence among the columns of a matrix
The question asks about "identifying underlying [linear] relationships" among variables.
The quick and easy way to detect relationships is to regress any other variable (use a constant, even) against those variables using your favorite software: any good regre... | Testing for linear dependence among the columns of a matrix
The question asks about "identifying underlying [linear] relationships" among variables.
The quick and easy way to detect relationships is to regress any other variable (use a constant, even) against |
8,755 | Testing for linear dependence among the columns of a matrix | What I'd try to do here for diagnostic purposes is to take the $502\times 480$ matrix (that is, the transpose) and determine the singular values of the matrix (for diagnostic purposes, you don't need the full singular value decomposition... yet). Once you have the 480 singular values, check how many of those are "small... | Testing for linear dependence among the columns of a matrix | What I'd try to do here for diagnostic purposes is to take the $502\times 480$ matrix (that is, the transpose) and determine the singular values of the matrix (for diagnostic purposes, you don't need | Testing for linear dependence among the columns of a matrix
What I'd try to do here for diagnostic purposes is to take the $502\times 480$ matrix (that is, the transpose) and determine the singular values of the matrix (for diagnostic purposes, you don't need the full singular value decomposition... yet). Once you have... | Testing for linear dependence among the columns of a matrix
What I'd try to do here for diagnostic purposes is to take the $502\times 480$ matrix (that is, the transpose) and determine the singular values of the matrix (for diagnostic purposes, you don't need |
8,756 | Testing for linear dependence among the columns of a matrix | Not that the answer @Whuber gave really needs to be expanded on but I thought I'd provide a brief description of the math.
If the linear combination $\mathbf{X'Xv}=\mathbf{0}$ for $\mathbf{v}\neq\mathbf{0}$ then $\mathbf{v}$ is an eigenvector of $\mathbf{X'X}$ associated with eigenvalue $\lambda=0$. The eigenvectors an... | Testing for linear dependence among the columns of a matrix | Not that the answer @Whuber gave really needs to be expanded on but I thought I'd provide a brief description of the math.
If the linear combination $\mathbf{X'Xv}=\mathbf{0}$ for $\mathbf{v}\neq\math | Testing for linear dependence among the columns of a matrix
Not that the answer @Whuber gave really needs to be expanded on but I thought I'd provide a brief description of the math.
If the linear combination $\mathbf{X'Xv}=\mathbf{0}$ for $\mathbf{v}\neq\mathbf{0}$ then $\mathbf{v}$ is an eigenvector of $\mathbf{X'X}$... | Testing for linear dependence among the columns of a matrix
Not that the answer @Whuber gave really needs to be expanded on but I thought I'd provide a brief description of the math.
If the linear combination $\mathbf{X'Xv}=\mathbf{0}$ for $\mathbf{v}\neq\math |
8,757 | Testing for linear dependence among the columns of a matrix | I ran into this issue roughly two weeks ago and decided that I needed to revisit it because when dealing with massive data sets, it is impossible to do these things manually.
I created a for() loop that calculates the rank of the matrix one column at a time. So for the first iteration, the rank will be 1. The second, ... | Testing for linear dependence among the columns of a matrix | I ran into this issue roughly two weeks ago and decided that I needed to revisit it because when dealing with massive data sets, it is impossible to do these things manually.
I created a for() loop t | Testing for linear dependence among the columns of a matrix
I ran into this issue roughly two weeks ago and decided that I needed to revisit it because when dealing with massive data sets, it is impossible to do these things manually.
I created a for() loop that calculates the rank of the matrix one column at a time. ... | Testing for linear dependence among the columns of a matrix
I ran into this issue roughly two weeks ago and decided that I needed to revisit it because when dealing with massive data sets, it is impossible to do these things manually.
I created a for() loop t |
8,758 | Testing for linear dependence among the columns of a matrix | Rank, r of a matrix = number of linearly independent columns (or rows) of a matrix. For a n by n matrix A, rank(A) = n => all columns (or rows) are linearly independent. | Testing for linear dependence among the columns of a matrix | Rank, r of a matrix = number of linearly independent columns (or rows) of a matrix. For a n by n matrix A, rank(A) = n => all columns (or rows) are linearly independent. | Testing for linear dependence among the columns of a matrix
Rank, r of a matrix = number of linearly independent columns (or rows) of a matrix. For a n by n matrix A, rank(A) = n => all columns (or rows) are linearly independent. | Testing for linear dependence among the columns of a matrix
Rank, r of a matrix = number of linearly independent columns (or rows) of a matrix. For a n by n matrix A, rank(A) = n => all columns (or rows) are linearly independent. |
8,759 | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" conclusion? | In theory, yes...
The results of individual studies may be insignificant but viewed together, the results may be significant.
In theory you can proceed by treating the results $y_i$ of study $i$ like any other random variable.
Let $y_i$ be some random variable (eg. the estimate from study $i$). Then if $y_i$ are indepe... | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" | In theory, yes...
The results of individual studies may be insignificant but viewed together, the results may be significant.
In theory you can proceed by treating the results $y_i$ of study $i$ like | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" conclusion?
In theory, yes...
The results of individual studies may be insignificant but viewed together, the results may be significant.
In theory you can proceed by treating the results $y_i$ of study $i$ like any othe... | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant"
In theory, yes...
The results of individual studies may be insignificant but viewed together, the results may be significant.
In theory you can proceed by treating the results $y_i$ of study $i$ like |
8,760 | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" conclusion? | Yes. Suppose you have $N$ p-values from $N$ independent studies.
Fisher's test
(EDIT - in response to @mdewey's useful comment below, it is relevant to distinguish between different meta tests. I spell out the case of another meta test mentioned by mdewey below)
The classical Fisher meta test (see Fisher (1932), "Stat... | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" | Yes. Suppose you have $N$ p-values from $N$ independent studies.
Fisher's test
(EDIT - in response to @mdewey's useful comment below, it is relevant to distinguish between different meta tests. I spe | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" conclusion?
Yes. Suppose you have $N$ p-values from $N$ independent studies.
Fisher's test
(EDIT - in response to @mdewey's useful comment below, it is relevant to distinguish between different meta tests. I spell out t... | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant"
Yes. Suppose you have $N$ p-values from $N$ independent studies.
Fisher's test
(EDIT - in response to @mdewey's useful comment below, it is relevant to distinguish between different meta tests. I spe |
8,761 | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" conclusion? | The answer to this depends on what method you use for combining $p$-values. Other answers have considered some of these but here I focus on one method for which the answer to the original question is no.
The minimum $p$ method, also known as Tippett's method,
is usually described in terms
of a rejection at the $\alpha_... | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" | The answer to this depends on what method you use for combining $p$-values. Other answers have considered some of these but here I focus on one method for which the answer to the original question is | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant" conclusion?
The answer to this depends on what method you use for combining $p$-values. Other answers have considered some of these but here I focus on one method for which the answer to the original question is no.
The ... | Can a meta-analysis of studies which are all "not statistically signficant" lead to a "significant"
The answer to this depends on what method you use for combining $p$-values. Other answers have considered some of these but here I focus on one method for which the answer to the original question is |
8,762 | What are good data visualization techniques to compare distributions? | I am going to elaborate my comment, as suggested by @gung. I will also include the violin plot suggested by @Alexander, for completeness. Some of these tools can be used for comparing more than two samples.
# Required packages
library(sn)
library(aplpack)
library(vioplot)
library(moments)
library(beanplot)
# Simulate... | What are good data visualization techniques to compare distributions? | I am going to elaborate my comment, as suggested by @gung. I will also include the violin plot suggested by @Alexander, for completeness. Some of these tools can be used for comparing more than two sa | What are good data visualization techniques to compare distributions?
I am going to elaborate my comment, as suggested by @gung. I will also include the violin plot suggested by @Alexander, for completeness. Some of these tools can be used for comparing more than two samples.
# Required packages
library(sn)
library(ap... | What are good data visualization techniques to compare distributions?
I am going to elaborate my comment, as suggested by @gung. I will also include the violin plot suggested by @Alexander, for completeness. Some of these tools can be used for comparing more than two sa |
8,763 | What are good data visualization techniques to compare distributions? | After exploring a bit more on your suggestions I found this kind of plot to complement @Procastinator 's answer. It is called 'bee swarm' and is a mixture of box plot with violin plot with the same detail level as scatter plot.
beeswarm R package | What are good data visualization techniques to compare distributions? | After exploring a bit more on your suggestions I found this kind of plot to complement @Procastinator 's answer. It is called 'bee swarm' and is a mixture of box plot with violin plot with the same de | What are good data visualization techniques to compare distributions?
After exploring a bit more on your suggestions I found this kind of plot to complement @Procastinator 's answer. It is called 'bee swarm' and is a mixture of box plot with violin plot with the same detail level as scatter plot.
beeswarm R package | What are good data visualization techniques to compare distributions?
After exploring a bit more on your suggestions I found this kind of plot to complement @Procastinator 's answer. It is called 'bee swarm' and is a mixture of box plot with violin plot with the same de |
8,764 | What are good data visualization techniques to compare distributions? | Here's a nice tutorial from Nathan Yau's Flowing Data blog using R and US state-level crime data. It shows:
Box-and-Whisker Plots (which you already use)
Histograms
Kernel Density Plots
Rug Plots
Violin Plots
Bean Plots (a weird combo of a box plot, density plot, with a rug in the middle).
Lately, I find myself plott... | What are good data visualization techniques to compare distributions? | Here's a nice tutorial from Nathan Yau's Flowing Data blog using R and US state-level crime data. It shows:
Box-and-Whisker Plots (which you already use)
Histograms
Kernel Density Plots
Rug Plots
Vio | What are good data visualization techniques to compare distributions?
Here's a nice tutorial from Nathan Yau's Flowing Data blog using R and US state-level crime data. It shows:
Box-and-Whisker Plots (which you already use)
Histograms
Kernel Density Plots
Rug Plots
Violin Plots
Bean Plots (a weird combo of a box plot,... | What are good data visualization techniques to compare distributions?
Here's a nice tutorial from Nathan Yau's Flowing Data blog using R and US state-level crime data. It shows:
Box-and-Whisker Plots (which you already use)
Histograms
Kernel Density Plots
Rug Plots
Vio |
8,765 | What are good data visualization techniques to compare distributions? | A note:
You want to answer questions about your data, and not create questions about the visualization method itself. Often, boring is better. It does make comparisons of comparisons easier to comprehend too.
An Answer:
The need for simple formatting beyond R's base package probably explains the popularity of Hadley'... | What are good data visualization techniques to compare distributions? | A note:
You want to answer questions about your data, and not create questions about the visualization method itself. Often, boring is better. It does make comparisons of comparisons easier to compr | What are good data visualization techniques to compare distributions?
A note:
You want to answer questions about your data, and not create questions about the visualization method itself. Often, boring is better. It does make comparisons of comparisons easier to comprehend too.
An Answer:
The need for simple formatti... | What are good data visualization techniques to compare distributions?
A note:
You want to answer questions about your data, and not create questions about the visualization method itself. Often, boring is better. It does make comparisons of comparisons easier to compr |
8,766 | What are good data visualization techniques to compare distributions? | There is a concept specifically for comparing distributions, which ought to be better known: the relative distribution.
Let's say we have random variables $Y_0, Y$ with cumulative distribution functions $F_0, F$ and we want to compare them, using $F_0$ as a reference.
Define
$$
R = F_0(Y)
$$
The distribution of the... | What are good data visualization techniques to compare distributions? | There is a concept specifically for comparing distributions, which ought to be better known: the relative distribution.
Let's say we have random variables $Y_0, Y$ with cumulative distribution functio | What are good data visualization techniques to compare distributions?
There is a concept specifically for comparing distributions, which ought to be better known: the relative distribution.
Let's say we have random variables $Y_0, Y$ with cumulative distribution functions $F_0, F$ and we want to compare them, using $F... | What are good data visualization techniques to compare distributions?
There is a concept specifically for comparing distributions, which ought to be better known: the relative distribution.
Let's say we have random variables $Y_0, Y$ with cumulative distribution functio |
8,767 | What are good data visualization techniques to compare distributions? | I strongly recommend quantile plots, here in the first instance plots of the data in rank order (observed quantiles) against cumulative probability. Many quantile plots are explicitly plots against some other quantiles, and may be called quantile-quantile plots or QQ-plots. A plot against cumulative probability is not ... | What are good data visualization techniques to compare distributions? | I strongly recommend quantile plots, here in the first instance plots of the data in rank order (observed quantiles) against cumulative probability. Many quantile plots are explicitly plots against so | What are good data visualization techniques to compare distributions?
I strongly recommend quantile plots, here in the first instance plots of the data in rank order (observed quantiles) against cumulative probability. Many quantile plots are explicitly plots against some other quantiles, and may be called quantile-qua... | What are good data visualization techniques to compare distributions?
I strongly recommend quantile plots, here in the first instance plots of the data in rank order (observed quantiles) against cumulative probability. Many quantile plots are explicitly plots against so |
8,768 | What are good data visualization techniques to compare distributions? | I like to just estimate the densities and plot them,
head(iris)
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 ... | What are good data visualization techniques to compare distributions? | I like to just estimate the densities and plot them,
head(iris)
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 | What are good data visualization techniques to compare distributions?
I like to just estimate the densities and plot them,
head(iris)
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 ... | What are good data visualization techniques to compare distributions?
I like to just estimate the densities and plot them,
head(iris)
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 |
8,769 | Multiple Imputation by Chained Equations (MICE) Explained | MICE is a multiple imputation method used to replace missing data values in a data set under certain assumptions about the data missingness mechanism (e.g., the data are missing at random, the data are missing completely at random).
If you start out with a data set which includes missing values in one or more of its va... | Multiple Imputation by Chained Equations (MICE) Explained | MICE is a multiple imputation method used to replace missing data values in a data set under certain assumptions about the data missingness mechanism (e.g., the data are missing at random, the data ar | Multiple Imputation by Chained Equations (MICE) Explained
MICE is a multiple imputation method used to replace missing data values in a data set under certain assumptions about the data missingness mechanism (e.g., the data are missing at random, the data are missing completely at random).
If you start out with a data ... | Multiple Imputation by Chained Equations (MICE) Explained
MICE is a multiple imputation method used to replace missing data values in a data set under certain assumptions about the data missingness mechanism (e.g., the data are missing at random, the data ar |
8,770 | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? | Indeed, there is no guarantee that top principal components (PCs) have more predictive power than the low-variance ones.
Real-world examples can be found where this is not the case, and it is easy to construct an artificial example where e.g. only the smallest PC has any relation to $y$ at all.
This topic was discussed... | How can top principal components retain the predictive power on a dependent variable (or even lead t | Indeed, there is no guarantee that top principal components (PCs) have more predictive power than the low-variance ones.
Real-world examples can be found where this is not the case, and it is easy to | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)?
Indeed, there is no guarantee that top principal components (PCs) have more predictive power than the low-variance ones.
Real-world examples can be found where this is not the case, and it is easy ... | How can top principal components retain the predictive power on a dependent variable (or even lead t
Indeed, there is no guarantee that top principal components (PCs) have more predictive power than the low-variance ones.
Real-world examples can be found where this is not the case, and it is easy to |
8,771 | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? | In addition to the answers that already focus on the mathematical properties, I'd like to comment from an experimental point of view.
Summary: data generation processes are often optimized in a way that makes the data suitable for principal component (PCR) or partial least squares (PLS) regression.
I'm analytical ch... | How can top principal components retain the predictive power on a dependent variable (or even lead t | In addition to the answers that already focus on the mathematical properties, I'd like to comment from an experimental point of view.
Summary: data generation processes are often optimized in a way t | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)?
In addition to the answers that already focus on the mathematical properties, I'd like to comment from an experimental point of view.
Summary: data generation processes are often optimized in a wa... | How can top principal components retain the predictive power on a dependent variable (or even lead t
In addition to the answers that already focus on the mathematical properties, I'd like to comment from an experimental point of view.
Summary: data generation processes are often optimized in a way t |
8,772 | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? | PCA is sometimes used to correct problems caused by collinear variables so that most of the variation in the X space is captured by the K principal components.
But this mathematical problem is of course not the same as capturing most of variation both in X, Y space in such way that unexplained variation is as small a... | How can top principal components retain the predictive power on a dependent variable (or even lead t | PCA is sometimes used to correct problems caused by collinear variables so that most of the variation in the X space is captured by the K principal components.
But this mathematical problem is of co | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)?
PCA is sometimes used to correct problems caused by collinear variables so that most of the variation in the X space is captured by the K principal components.
But this mathematical problem is of... | How can top principal components retain the predictive power on a dependent variable (or even lead t
PCA is sometimes used to correct problems caused by collinear variables so that most of the variation in the X space is captured by the K principal components.
But this mathematical problem is of co |
8,773 | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? | As other has pointed out, there is no direct link between top k eigenvectors and the predictive power. By picking the top and using them as basis, you are retaining some top energy (or variance along those axis).
It can be that the axis explaining the most variance are actually useful for prediction but in general this... | How can top principal components retain the predictive power on a dependent variable (or even lead t | As other has pointed out, there is no direct link between top k eigenvectors and the predictive power. By picking the top and using them as basis, you are retaining some top energy (or variance along | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)?
As other has pointed out, there is no direct link between top k eigenvectors and the predictive power. By picking the top and using them as basis, you are retaining some top energy (or variance alo... | How can top principal components retain the predictive power on a dependent variable (or even lead t
As other has pointed out, there is no direct link between top k eigenvectors and the predictive power. By picking the top and using them as basis, you are retaining some top energy (or variance along |
8,774 | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? | Let me offer one simple explanation.
PCA amounts to removing certain features intuitively. This decreases chances of over-fitting. | How can top principal components retain the predictive power on a dependent variable (or even lead t | Let me offer one simple explanation.
PCA amounts to removing certain features intuitively. This decreases chances of over-fitting. | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)?
Let me offer one simple explanation.
PCA amounts to removing certain features intuitively. This decreases chances of over-fitting. | How can top principal components retain the predictive power on a dependent variable (or even lead t
Let me offer one simple explanation.
PCA amounts to removing certain features intuitively. This decreases chances of over-fitting. |
8,775 | When to avoid Random Forest? | Thinking about the specific language of the quotation, a leatherman is a multi-tool: a single piece of hardware with lots of little gizmos tucked into it. It's a pair of pliers, and a knife, and a screwdriver and more! Rather than having to carry each of these tools individually, the leatherman is a single item that yo... | When to avoid Random Forest? | Thinking about the specific language of the quotation, a leatherman is a multi-tool: a single piece of hardware with lots of little gizmos tucked into it. It's a pair of pliers, and a knife, and a scr | When to avoid Random Forest?
Thinking about the specific language of the quotation, a leatherman is a multi-tool: a single piece of hardware with lots of little gizmos tucked into it. It's a pair of pliers, and a knife, and a screwdriver and more! Rather than having to carry each of these tools individually, the leathe... | When to avoid Random Forest?
Thinking about the specific language of the quotation, a leatherman is a multi-tool: a single piece of hardware with lots of little gizmos tucked into it. It's a pair of pliers, and a knife, and a scr |
8,776 | When to avoid Random Forest? | Sharp corners. Exactness.
They use diffusion methods. They fit lumpy things well. They do not fit elaborate and highly detailed things well when the sample size is low. I would imagine that they do not do well on multivariate time-series data - when something over here depends on that one thing over there a distanc... | When to avoid Random Forest? | Sharp corners. Exactness.
They use diffusion methods. They fit lumpy things well. They do not fit elaborate and highly detailed things well when the sample size is low. I would imagine that they d | When to avoid Random Forest?
Sharp corners. Exactness.
They use diffusion methods. They fit lumpy things well. They do not fit elaborate and highly detailed things well when the sample size is low. I would imagine that they do not do well on multivariate time-series data - when something over here depends on that o... | When to avoid Random Forest?
Sharp corners. Exactness.
They use diffusion methods. They fit lumpy things well. They do not fit elaborate and highly detailed things well when the sample size is low. I would imagine that they d |
8,777 | When to avoid Random Forest? | This is the first time I actually answer a question, so do not pin me down on it .. but I do think I can answer your question:
If you are indeed only interested in model performance and not in thing like interpretability, random forest is indeed often a very good learning algorithm, but does perform slightly worse in t... | When to avoid Random Forest? | This is the first time I actually answer a question, so do not pin me down on it .. but I do think I can answer your question:
If you are indeed only interested in model performance and not in thing l | When to avoid Random Forest?
This is the first time I actually answer a question, so do not pin me down on it .. but I do think I can answer your question:
If you are indeed only interested in model performance and not in thing like interpretability, random forest is indeed often a very good learning algorithm, but doe... | When to avoid Random Forest?
This is the first time I actually answer a question, so do not pin me down on it .. but I do think I can answer your question:
If you are indeed only interested in model performance and not in thing l |
8,778 | When to avoid Random Forest? | Random forest fits multi-dimensional staircase to your data. It produces sharp edges in predictions. If your data are of continuous nature, then probably there are better methods to fit them. That doesn't mean however that "you should avoid random forest to fit them" :-) I don't think there is any kind of data where yo... | When to avoid Random Forest? | Random forest fits multi-dimensional staircase to your data. It produces sharp edges in predictions. If your data are of continuous nature, then probably there are better methods to fit them. That doe | When to avoid Random Forest?
Random forest fits multi-dimensional staircase to your data. It produces sharp edges in predictions. If your data are of continuous nature, then probably there are better methods to fit them. That doesn't mean however that "you should avoid random forest to fit them" :-) I don't think there... | When to avoid Random Forest?
Random forest fits multi-dimensional staircase to your data. It produces sharp edges in predictions. If your data are of continuous nature, then probably there are better methods to fit them. That doe |
8,779 | When to avoid Random Forest? | There's already many good points by others e.g. about sparse feature spaces, when we know a step-function will not work well/when you don't have a good representation of the data (some of these may of course be a matter of creating better features first), as well as non-tabular data types where other approaches are kno... | When to avoid Random Forest? | There's already many good points by others e.g. about sparse feature spaces, when we know a step-function will not work well/when you don't have a good representation of the data (some of these may of | When to avoid Random Forest?
There's already many good points by others e.g. about sparse feature spaces, when we know a step-function will not work well/when you don't have a good representation of the data (some of these may of course be a matter of creating better features first), as well as non-tabular data types w... | When to avoid Random Forest?
There's already many good points by others e.g. about sparse feature spaces, when we know a step-function will not work well/when you don't have a good representation of the data (some of these may of |
8,780 | When to avoid Random Forest? | RF is a static model and when it comes to dealing with dynamical systems and online learning, the cost of adapting to the data drift is the same as reconstructing the entire structure again. | When to avoid Random Forest? | RF is a static model and when it comes to dealing with dynamical systems and online learning, the cost of adapting to the data drift is the same as reconstructing the entire structure again. | When to avoid Random Forest?
RF is a static model and when it comes to dealing with dynamical systems and online learning, the cost of adapting to the data drift is the same as reconstructing the entire structure again. | When to avoid Random Forest?
RF is a static model and when it comes to dealing with dynamical systems and online learning, the cost of adapting to the data drift is the same as reconstructing the entire structure again. |
8,781 | When to avoid Random Forest? | First of all, the Random Forest cannot be applied to the following data types:
images
audio
text (after preprocessing data will be sparse and RF doesn't work well with sparse data)
For tabular data type, it is always good to check Random Forest because:
it requires less data preparation and preprocessing than Neural... | When to avoid Random Forest? | First of all, the Random Forest cannot be applied to the following data types:
images
audio
text (after preprocessing data will be sparse and RF doesn't work well with sparse data)
For tabular data | When to avoid Random Forest?
First of all, the Random Forest cannot be applied to the following data types:
images
audio
text (after preprocessing data will be sparse and RF doesn't work well with sparse data)
For tabular data type, it is always good to check Random Forest because:
it requires less data preparation ... | When to avoid Random Forest?
First of all, the Random Forest cannot be applied to the following data types:
images
audio
text (after preprocessing data will be sparse and RF doesn't work well with sparse data)
For tabular data |
8,782 | When to avoid Random Forest? | Random Forests are prone to exhausing memory and causing out-of-memory errors (as compared to an incremental / batch learning method that fixes memory usage. | When to avoid Random Forest? | Random Forests are prone to exhausing memory and causing out-of-memory errors (as compared to an incremental / batch learning method that fixes memory usage. | When to avoid Random Forest?
Random Forests are prone to exhausing memory and causing out-of-memory errors (as compared to an incremental / batch learning method that fixes memory usage. | When to avoid Random Forest?
Random Forests are prone to exhausing memory and causing out-of-memory errors (as compared to an incremental / batch learning method that fixes memory usage. |
8,783 | How to know if a time series is stationary or non-stationary? | Testing if a series is stationary versus non-stationary requires that you consider a sequence of alternative hypotheses . One for each listable Gaussian Assumption. One has to understand that the Gaussian Assumptions are all about the error process and have nothing to do with the observed series under evaluation. As co... | How to know if a time series is stationary or non-stationary? | Testing if a series is stationary versus non-stationary requires that you consider a sequence of alternative hypotheses . One for each listable Gaussian Assumption. One has to understand that the Gaus | How to know if a time series is stationary or non-stationary?
Testing if a series is stationary versus non-stationary requires that you consider a sequence of alternative hypotheses . One for each listable Gaussian Assumption. One has to understand that the Gaussian Assumptions are all about the error process and have ... | How to know if a time series is stationary or non-stationary?
Testing if a series is stationary versus non-stationary requires that you consider a sequence of alternative hypotheses . One for each listable Gaussian Assumption. One has to understand that the Gaus |
8,784 | How to know if a time series is stationary or non-stationary? | Stationarity means that the marginal distribution of the process does not change with time. A weaker forms states that the mean and the variance stay the same over time. So anything that violates it will be deemed non-stationary, for whatever silly reasons. For instance, a deterministic $y_t = \sin t$ is non-stationa... | How to know if a time series is stationary or non-stationary? | Stationarity means that the marginal distribution of the process does not change with time. A weaker forms states that the mean and the variance stay the same over time. So anything that violates it w | How to know if a time series is stationary or non-stationary?
Stationarity means that the marginal distribution of the process does not change with time. A weaker forms states that the mean and the variance stay the same over time. So anything that violates it will be deemed non-stationary, for whatever silly reasons. ... | How to know if a time series is stationary or non-stationary?
Stationarity means that the marginal distribution of the process does not change with time. A weaker forms states that the mean and the variance stay the same over time. So anything that violates it w |
8,785 | How to know if a time series is stationary or non-stationary? | Time series is stationary if its mean level and variance stay steady over time. You can read more on this topic (with specification of relevant tests in R), in our post..
http://www.statosphere.com.au/check-time-series-stationary-r/ | How to know if a time series is stationary or non-stationary? | Time series is stationary if its mean level and variance stay steady over time. You can read more on this topic (with specification of relevant tests in R), in our post..
http://www.statosphere.com.au | How to know if a time series is stationary or non-stationary?
Time series is stationary if its mean level and variance stay steady over time. You can read more on this topic (with specification of relevant tests in R), in our post..
http://www.statosphere.com.au/check-time-series-stationary-r/ | How to know if a time series is stationary or non-stationary?
Time series is stationary if its mean level and variance stay steady over time. You can read more on this topic (with specification of relevant tests in R), in our post..
http://www.statosphere.com.au |
8,786 | Cost function in OLS linear regression | As you seem to realize, we certainly don't need the $1/m$ factor to get linear regression. The minimizers will of course be exactly the same, with or without it. One typical reason to normalize by $m$ is so that we can view the cost function as an approximation to the "generalization error", which is the expected squ... | Cost function in OLS linear regression | As you seem to realize, we certainly don't need the $1/m$ factor to get linear regression. The minimizers will of course be exactly the same, with or without it. One typical reason to normalize by $ | Cost function in OLS linear regression
As you seem to realize, we certainly don't need the $1/m$ factor to get linear regression. The minimizers will of course be exactly the same, with or without it. One typical reason to normalize by $m$ is so that we can view the cost function as an approximation to the "generaliz... | Cost function in OLS linear regression
As you seem to realize, we certainly don't need the $1/m$ factor to get linear regression. The minimizers will of course be exactly the same, with or without it. One typical reason to normalize by $ |
8,787 | Cost function in OLS linear regression | You don't have to. The loss function has the same minimum whether you include the $\frac{1}{m}$ or suppress it. If you include it though, you get the nice interpretation of minimizing (one half) the average error per datapoint. Put another way, you are minimizing the error rate instead of the total error.
Consider c... | Cost function in OLS linear regression | You don't have to. The loss function has the same minimum whether you include the $\frac{1}{m}$ or suppress it. If you include it though, you get the nice interpretation of minimizing (one half) the | Cost function in OLS linear regression
You don't have to. The loss function has the same minimum whether you include the $\frac{1}{m}$ or suppress it. If you include it though, you get the nice interpretation of minimizing (one half) the average error per datapoint. Put another way, you are minimizing the error rate... | Cost function in OLS linear regression
You don't have to. The loss function has the same minimum whether you include the $\frac{1}{m}$ or suppress it. If you include it though, you get the nice interpretation of minimizing (one half) the |
8,788 | Cross-validation or bootstrapping to evaluate classification performance? | One important difference in the usual way cross validation and out-of-bootstrap methods are applied is that most people apply cross validation only once (i.e. each case is tested exactly once), while out-of-bootstrap validation is performed with a large number of repetitions/iterations.
In that situation, cross valida... | Cross-validation or bootstrapping to evaluate classification performance? | One important difference in the usual way cross validation and out-of-bootstrap methods are applied is that most people apply cross validation only once (i.e. each case is tested exactly once), while | Cross-validation or bootstrapping to evaluate classification performance?
One important difference in the usual way cross validation and out-of-bootstrap methods are applied is that most people apply cross validation only once (i.e. each case is tested exactly once), while out-of-bootstrap validation is performed with ... | Cross-validation or bootstrapping to evaluate classification performance?
One important difference in the usual way cross validation and out-of-bootstrap methods are applied is that most people apply cross validation only once (i.e. each case is tested exactly once), while |
8,789 | Cross-validation or bootstrapping to evaluate classification performance? | You need modifications to the bootstrap (.632, .632+) only because the original research used a discontinuous improper scoring rule (proportion classified correctly). For other accuracy scores the ordinary optimism bootstrap tends to work fine. For more information see this.
Improper scoring rules mislead you on the ... | Cross-validation or bootstrapping to evaluate classification performance? | You need modifications to the bootstrap (.632, .632+) only because the original research used a discontinuous improper scoring rule (proportion classified correctly). For other accuracy scores the or | Cross-validation or bootstrapping to evaluate classification performance?
You need modifications to the bootstrap (.632, .632+) only because the original research used a discontinuous improper scoring rule (proportion classified correctly). For other accuracy scores the ordinary optimism bootstrap tends to work fine. ... | Cross-validation or bootstrapping to evaluate classification performance?
You need modifications to the bootstrap (.632, .632+) only because the original research used a discontinuous improper scoring rule (proportion classified correctly). For other accuracy scores the or |
8,790 | Cross-validation or bootstrapping to evaluate classification performance? | From 'Applied Predictive Modeling., Khun. Johnson. p.78
"No resampling method is uniformly better than another; the choice should be made while considering several factors. If the sample size is small, we recommend using repeated 10-fold cross validation for several reasons; the bias and variance properties are good, ... | Cross-validation or bootstrapping to evaluate classification performance? | From 'Applied Predictive Modeling., Khun. Johnson. p.78
"No resampling method is uniformly better than another; the choice should be made while considering several factors. If the sample size is smal | Cross-validation or bootstrapping to evaluate classification performance?
From 'Applied Predictive Modeling., Khun. Johnson. p.78
"No resampling method is uniformly better than another; the choice should be made while considering several factors. If the sample size is small, we recommend using repeated 10-fold cross v... | Cross-validation or bootstrapping to evaluate classification performance?
From 'Applied Predictive Modeling., Khun. Johnson. p.78
"No resampling method is uniformly better than another; the choice should be made while considering several factors. If the sample size is smal |
8,791 | What is the difference between "limiting" and "stationary" distributions? | From An Introduction to Stochastic Modeling by Pinsky and Karlin (2011):
A limiting distribution, when it exists, is always a stationary distribution, but the converse is not true. There may exist a stationary distribution but no limiting distribution. For example, there is no limiting distribution for the periodic Ma... | What is the difference between "limiting" and "stationary" distributions? | From An Introduction to Stochastic Modeling by Pinsky and Karlin (2011):
A limiting distribution, when it exists, is always a stationary distribution, but the converse is not true. There may exist a | What is the difference between "limiting" and "stationary" distributions?
From An Introduction to Stochastic Modeling by Pinsky and Karlin (2011):
A limiting distribution, when it exists, is always a stationary distribution, but the converse is not true. There may exist a stationary distribution but no limiting distri... | What is the difference between "limiting" and "stationary" distributions?
From An Introduction to Stochastic Modeling by Pinsky and Karlin (2011):
A limiting distribution, when it exists, is always a stationary distribution, but the converse is not true. There may exist a |
8,792 | What is the difference between "limiting" and "stationary" distributions? | A stationary distribution is such a distribution $\pi$ that if the distribution over states at step $k$ is $\pi$, then also the distribution over states at step $k+1$ is $\pi$. That is,
\begin{equation}
\pi = \pi P.
\end{equation}
A limiting distribution is such a distribution $\pi$ that no matter what the initial dis... | What is the difference between "limiting" and "stationary" distributions? | A stationary distribution is such a distribution $\pi$ that if the distribution over states at step $k$ is $\pi$, then also the distribution over states at step $k+1$ is $\pi$. That is,
\begin{equati | What is the difference between "limiting" and "stationary" distributions?
A stationary distribution is such a distribution $\pi$ that if the distribution over states at step $k$ is $\pi$, then also the distribution over states at step $k+1$ is $\pi$. That is,
\begin{equation}
\pi = \pi P.
\end{equation}
A limiting dis... | What is the difference between "limiting" and "stationary" distributions?
A stationary distribution is such a distribution $\pi$ that if the distribution over states at step $k$ is $\pi$, then also the distribution over states at step $k+1$ is $\pi$. That is,
\begin{equati |
8,793 | What is the difference between "limiting" and "stationary" distributions? | Putting notation aside, the word "stationary" means "once you get there, you will stay there"; while the word "limiting" implies "you will eventually get there if you go far enough". Just thought this might be helpful. | What is the difference between "limiting" and "stationary" distributions? | Putting notation aside, the word "stationary" means "once you get there, you will stay there"; while the word "limiting" implies "you will eventually get there if you go far enough". Just thought this | What is the difference between "limiting" and "stationary" distributions?
Putting notation aside, the word "stationary" means "once you get there, you will stay there"; while the word "limiting" implies "you will eventually get there if you go far enough". Just thought this might be helpful. | What is the difference between "limiting" and "stationary" distributions?
Putting notation aside, the word "stationary" means "once you get there, you will stay there"; while the word "limiting" implies "you will eventually get there if you go far enough". Just thought this |
8,794 | What's the difference between a probability and a proportion? | I have hesitated to wade into this discussion, but because it seems to have gotten sidetracked over a trivial issue concerning how to express numbers, maybe it's worthwhile refocusing it. A point of departure for your consideration is this:
A probability is a hypothetical property. Proportions summarize observations... | What's the difference between a probability and a proportion? | I have hesitated to wade into this discussion, but because it seems to have gotten sidetracked over a trivial issue concerning how to express numbers, maybe it's worthwhile refocusing it. A point of | What's the difference between a probability and a proportion?
I have hesitated to wade into this discussion, but because it seems to have gotten sidetracked over a trivial issue concerning how to express numbers, maybe it's worthwhile refocusing it. A point of departure for your consideration is this:
A probability i... | What's the difference between a probability and a proportion?
I have hesitated to wade into this discussion, but because it seems to have gotten sidetracked over a trivial issue concerning how to express numbers, maybe it's worthwhile refocusing it. A point of |
8,795 | What's the difference between a probability and a proportion? | If you flip a fair coin 10 times and it comes up heads 3 times, the proportion of heads is .30 but the probability of a head on any one flip is .50. | What's the difference between a probability and a proportion? | If you flip a fair coin 10 times and it comes up heads 3 times, the proportion of heads is .30 but the probability of a head on any one flip is .50. | What's the difference between a probability and a proportion?
If you flip a fair coin 10 times and it comes up heads 3 times, the proportion of heads is .30 but the probability of a head on any one flip is .50. | What's the difference between a probability and a proportion?
If you flip a fair coin 10 times and it comes up heads 3 times, the proportion of heads is .30 but the probability of a head on any one flip is .50. |
8,796 | What's the difference between a probability and a proportion? | A proportion implies it is a guaranteed event, whereas a probability is not.
If you eat hamburgers 14% of the time, in a given (4-week) month (or over whatever interval you based your proportion on), you must have eaten 4 hamburgers; whereas with probability there is a possibility of having eaten no hamburgers at all o... | What's the difference between a probability and a proportion? | A proportion implies it is a guaranteed event, whereas a probability is not.
If you eat hamburgers 14% of the time, in a given (4-week) month (or over whatever interval you based your proportion on), | What's the difference between a probability and a proportion?
A proportion implies it is a guaranteed event, whereas a probability is not.
If you eat hamburgers 14% of the time, in a given (4-week) month (or over whatever interval you based your proportion on), you must have eaten 4 hamburgers; whereas with probability... | What's the difference between a probability and a proportion?
A proportion implies it is a guaranteed event, whereas a probability is not.
If you eat hamburgers 14% of the time, in a given (4-week) month (or over whatever interval you based your proportion on), |
8,797 | What's the difference between a probability and a proportion? | The difference is not in the calculation, but in the purpose to which the metric is put: Probability is a concept of time; proportionality is a concept of space.
If we want to know the probability of a future event, we can use the probability at which the event took place in the past to derive our best estimate for t... | What's the difference between a probability and a proportion? | The difference is not in the calculation, but in the purpose to which the metric is put: Probability is a concept of time; proportionality is a concept of space.
If we want to know the probability o | What's the difference between a probability and a proportion?
The difference is not in the calculation, but in the purpose to which the metric is put: Probability is a concept of time; proportionality is a concept of space.
If we want to know the probability of a future event, we can use the probability at which the ... | What's the difference between a probability and a proportion?
The difference is not in the calculation, but in the purpose to which the metric is put: Probability is a concept of time; proportionality is a concept of space.
If we want to know the probability o |
8,798 | What's the difference between a probability and a proportion? | Proportion and probability, both are calculated from the total but the value of proportion is certain while that of probability is no0t certain.. | What's the difference between a probability and a proportion? | Proportion and probability, both are calculated from the total but the value of proportion is certain while that of probability is no0t certain.. | What's the difference between a probability and a proportion?
Proportion and probability, both are calculated from the total but the value of proportion is certain while that of probability is no0t certain.. | What's the difference between a probability and a proportion?
Proportion and probability, both are calculated from the total but the value of proportion is certain while that of probability is no0t certain.. |
8,799 | What's the difference between a probability and a proportion? | From my point of view the main difference between proportion and probability is the three axioms of probability which proportions don't have. i.e.
(i) Probability always lies between 0 and 1.
(ii) Probability sure event is one.
(iii) P(A or B) = P(A) +P(B), A and B are mutually exclusive events | What's the difference between a probability and a proportion? | From my point of view the main difference between proportion and probability is the three axioms of probability which proportions don't have. i.e.
(i) Probability always lies between 0 and 1.
(ii) Pro | What's the difference between a probability and a proportion?
From my point of view the main difference between proportion and probability is the three axioms of probability which proportions don't have. i.e.
(i) Probability always lies between 0 and 1.
(ii) Probability sure event is one.
(iii) P(A or B) = P(A) +P(B), ... | What's the difference between a probability and a proportion?
From my point of view the main difference between proportion and probability is the three axioms of probability which proportions don't have. i.e.
(i) Probability always lies between 0 and 1.
(ii) Pro |
8,800 | What's the difference between a probability and a proportion? | In the Frequentist Interpretation of Probability, the probability is long-run relative frequency. That means, the proportion in a large number of observations.
If you toss a coin 10 times and you get 4 tails, the proportion of tails is 0.4. However, 10 is not a very large number. This is only a proportion, not a probab... | What's the difference between a probability and a proportion? | In the Frequentist Interpretation of Probability, the probability is long-run relative frequency. That means, the proportion in a large number of observations.
If you toss a coin 10 times and you get | What's the difference between a probability and a proportion?
In the Frequentist Interpretation of Probability, the probability is long-run relative frequency. That means, the proportion in a large number of observations.
If you toss a coin 10 times and you get 4 tails, the proportion of tails is 0.4. However, 10 is no... | What's the difference between a probability and a proportion?
In the Frequentist Interpretation of Probability, the probability is long-run relative frequency. That means, the proportion in a large number of observations.
If you toss a coin 10 times and you get |
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