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binomial GLM for proportion Vs Beta regression

Provided that there are enough cases so that the proportions can be considered to be sampled from continuous distributions, the choice depends on your understanding of the nature of the sampling. Beta ...
EdM's user avatar
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1 vote

Random Sampling from Distribution

The purpose of this form of the Pearson plot is that it can help identify a distribution from a class of distributions[1], but each sub-family is only identified in the diagram up to multiplication by ...
Glen_b's user avatar
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How to construct a multivariate Beta distribution?

There's a recent preprint that constructs a multivariate beta from the logistic-beta process. Its construction is highly flexible and comes with computational benefits, especially when modeling latent ...
clee's user avatar
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What is the posterior probability for flipping a coin, assuming a beta distribution as conjugate prior

The question is itself ambiguous, as many already claimed. Usually, we use bayesian analysis to find which values of $\theta$ can give as an output the observed result ($X$, or the simulations you ...
Oscar Flores's user avatar
5 votes
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How good is the Beta distribution as a conjugate for Binomial distribution?

The fact that there is an (arbitrary?) $c$ scaling up and down the posterior distribution makes me think that the Beta distribution ... may not be a good representation of the distribution of $\theta$,...
Sextus Empiricus's user avatar
6 votes

How good is the Beta distribution as a conjugate for Binomial distribution?

I don't have my textbook in front of me, but I recall the Bayes estimator with conjugate prior is Bayes optimal meaning the posterior mode minimizes the MSE. In other words, it is a biased estimator ...
AdamO's user avatar
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3 votes

Taking the limit of a Beta Distribution to yield the Gamma Distribution

Consider the integral over the Beta Distribution: $\int^1_0Beta(x;\alpha,\beta)dx = \int^1_0\frac{(\alpha + \beta -1)!}{(\alpha -1)!(\beta-1)!}x^{\alpha-1}(1-x)^{\beta-1}dx=1$ Transforming variables ...
SSD's user avatar
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5 votes
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Taking the limit of a Beta Distribution to yield the Gamma Distribution

Suppose $X\sim\operatorname{Beta}(\alpha,n).$ Consider the limit of the distribution of $nX$ as $n\to\infty.$ \begin{align} f_{nX}(x) = {} & \frac d{dx} \Pr(nX\le x) = \frac d{dx} \Pr\left( X\le\...
Michael Hardy's user avatar
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What's the intuition for a Beta Distribution with alpha and / or beta less than 1?

It makes the mean distance above $0$ equal to $\dfrac\alpha{\alpha+\beta}$ and the mean distance below $1$ equal to $\dfrac\beta{\alpha+\beta}.$
Michael Hardy's user avatar
6 votes
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Modelling a proportion/percentage which is left censored

Semiparametric ordinal regression models such as the proportional odds model handle detection limits automatically, as long as you don’t try to use the model to estimate the mean. You can use it to ...
Frank Harrell's user avatar

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