# Tag Info

### Deriving predicted probabilities from gologit2 (proportional odds models) output

The Williams approach uses the Brant test for proportional odds. That this test is invalid has been pointed out since 1991 (Peterson & Harrell J Royal Stat Soc C). For related information see ...
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### How to show that many functions (a hundred, a thousand) have the same shape an distribution of values over an interval?

Based on your description 0.4 +ve derivative from zero to 0.4 and around zero or slightly negative derivative up to 1. You could fit $y = a_0 + a_1 x + a_2 (x-0.4)^+$, which is a piecewise linear ...
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Accepted

### How to show that many functions (a hundred, a thousand) have the same shape an distribution of values over an interval?

A Q-Q plot approach would not be appropriate for your objective. Not only that, it would give you misleading results. This is because a Q-Q plot changes the order of the data, arranging it in ...
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### Equivalence of first/second choice with naive probability - I don't buy it

Let $b_1, \dots, b_r$ be the $r$ red balls and let $b_{r+1}, \dots, b_{r+g}$ be the $g$ green balls. Let $\mathcal{B_1}, \mathcal{B_2}$ denote the first and the second drawn ball, respectively. If we ...
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### How to show that many functions (a hundred, a thousand) have the same shape an distribution of values over an interval?

To show that several functions are more or less the same you could just superimpose them graphically. I don't think quantile plots of any flavour are directly relevant or likely to be helpful. The ...
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1 vote

### Calculating the joint pdf of linearly dependent random variables $X$ and $Y=X$

As already explained in comments, there is no joint density in the plane, because all the probability mass of $(X, X)$ is concentrated on the diagonal $y=x$. There is a density on that diagonal, but ...
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### Are all random variables estimators?

FWIW you define yourself random variable and estimator as different functions, performing mapping between at least three different spaces: domain of possible outcomes a sample space to a measurable ...
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### Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

The misinterpretation of confidence intervals is related to what Blitzstein and Hwang (in their probability textbook) call "sympathetic magic". Sympathetic magic is an anthropology term for ...

### Equivalence of first/second choice with naive probability - I don't buy it

Imagine there are only two balls, one of each color. If the first ball is red, the probability of the second one being green is $100\%$. If the first ball is green, the probability of the second one ...
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### Equivalence of first/second choice with naive probability - I don't buy it

The abstract mathematical machinery is intuitive for many people provided it is clearly set up in a way that parallels the original probability problem. Before reading any more of this post, though, ...
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### Equivalence of first/second choice with naive probability - I don't buy it

What's "intuitive" to one may be less so to another. I find @Flounderer's answer to be quite intuitive, but here is an alternative if that didn't do it for you: An equivalent process is to ...
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### Comparability of classifier probabiliy estimates

Maybe not the answer you are looking for, but I agree comparing the outputs of the models without having a lot of testing to be confident in their probability calculations is problematic. You should ...
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### Equivalence of first/second choice with naive probability - I don't buy it

The solutions for exercises marked with the circled S symbol are available from this page: https://projects.iq.harvard.edu/stat110/strategic-practice-problems The intended solution is: This is true ...
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