# Questions tagged [beta-binomial]

The beta-binomial is a discrete distribution on 0, 1, ..., *n* where the probability of success in a binomial distribution (*p*) is itself drawn from a beta distribution.

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### Beta-binomial distribution for scaled and translated Beta

Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
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### How to infer a prior belief after observing a behavior

My participant goes through a maze made of 32 T intersections. At each intersection he must choose whether to go either to the left or to the right: one option will lead to another T intersection, ...
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### Can (log-)likelihood be used to compare a binomial model to its beta-binomial equivalent?

In this article the author talks about fitting beta-binomial models to data when the there data is over-dispersed relative to the assumptions of a model with binomial errors. Near the end they present ...
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### Hypothesis testing with beta binomial. Dealing with overdispersion

To make the question more understandable I will use a reproducible example. I have count data, how many connections different groups share with a unique group. In my case I have an upper bound of <...
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### Sample from multiple urns - when to stop?

I have a problem that hasn't yet been addressed, although follows similar lines of reasoning here and here. My problem is as follows: I have $N$ urns, each with a different number of black and white ...
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### Differential effect of parents quality on sons and daughters: how to test it

Suppose you have n broods followed up during x years. In each brood there are a varying number of sons and daughters that sum up to a varying number of offspring in each brood. You dispose of this ...
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### Bayesian a posteriori law of bernouilli law, from observed correlated bernouilli law

Suppose that you have $N$ people passing an exam having 2 yes/no questions. After seeing the results of $N-1$ people and the result of the first question of the $Nth$ person, I want to know what I can ...
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### Intuition of Beta-Binomial Distribution

I am given $$Q \sim\mathrm{Beta} (2,3)$$ $$[X|Q=q]\sim\mathrm{Bin} (3,q)$$ I am asked to find (1) $E[X]$, (2) $\operatorname{Var}[X]$, (3) $E[Q|X]$, (4) $\operatorname{Var}[Q|X]$, (5) $v(q|X=x)$. I ...
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### Beta binomial GLMM dispersion statistic issue

I am analyzing proportion data with GLMM in which the number of occurrence a behaviour of interest has been displayed and has not been displayed are concatenated and fitted as a single response ...
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### Translating user-defined joint-distribution from PyMC to PyMC3

I'm attempting to set up a simple beta binomial hierarchical model with an uninformative prior in PyMC3. I've read that the uninformative prior for this model should have alpha and beta hyper-...
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### Is it possible to validate very small p-values via bootstrap?

Suppose I want to see whether the p-values generated by a certain parametric method are close to the “true” p-values. To avoid relying on any parametric assumptions, the latter are produced via ...
I have a lookup table in 2 variables, $Z_l$ and $T_l$. So, $Z_l$ and $T_l$ are vectors with same length where $Z_l$ goes from 0 to 1 and $T_l$ varies between 300 and 2000. If you are curious, $Z_l$ ...
### Recursive Bayesian Estimation, $p(C_k|\mathbf{x})$ as (discrete) likelihood
I''ve been struggeling with this problem for the last couple of days. The main goal is to use the probabilistic classification output $p(C_k|\mathbf{x})$, from for example a logistic regression, to ...