# Questions tagged [beta-binomial-distribution]

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 distribution for uncertain binary trials

I have a larger problem but have presented what I believe is a minimal example. Imagine that you are trying to determine the true probability of a potentially-biased coin landing on heads, and want to ...
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### Bayesian A/B test - using an updated prior based on collected data

I have a question about whether I would be adding bias to an A/B test by updating my prior based on combined A & B data, and then running the A/B test on that prior. My A/B test is click through ...
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### Entropy of the beta-binomial compound distribution

I have a generative process as follows: $$x \mid \alpha \sim \textsf{Beta}\left (\alpha,\beta \right) \\ y \mid x \sim \textsf{Bernoulli}(x).$$ How does one go about calculating the Entropy of ...
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### How to estimate beta distribution parameters using a beta binomial with empirical bayes

I would like to estimate parameters for a beta distribution using a maximum likelihood approach in python (as mentioned here). I can do this for a beta: ...
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### Discrete Probability Density that is Monotonically Decreasing as K Increases and is 0 at K=N+1

My knowledge of distributions is limited, so I apologize beforehand for what may be a silly question. I am looking for a discrete probability distribution with domain $\{1,2,...,N\}$ that satisfies ...
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### Calculating the tail bounds for a beta-binomial regression

I have a beta-binomial regression model that depends on a probability $p$ and a given over-dispersion $\beta$ and is used to parametrise the distribution of $Y$ in the following way  Y(x) \sim ...
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### What is the intuition behind beta distribution?

Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
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### Distribution with a parameter being function of another?

The beta-binomial distribution has probability mass function given by: $f(k\mid n,\alpha,\beta)$. Is there any theoretical problem in setting $\beta=g(\alpha)$ for some linear function $g$? By doing ...
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### How can I understand if my Beta Distribution is converging?

I am evaluating a Bayes AB Test on 2 variants, A and B. I then plotted a graph which shows the Probability of B is better than A on a daily basis. My worry comes in on the topic of 'peeking'. Let's ...
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### In a Beta-Binomial 'Bayesian' A/B test, is it possible to add a third, fourth, etc. recipe?

For context: How to define prior for beta-binomial A/B test For P(A > B), you can draw samples from A's posterior and B's posterior and then count the number of times the sample from A is greater ...
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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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### How to model qualitative body condition scores? Ordinal logistic regression?

I am after some advice on how to model qualitative animal body condition scores? My overarching research question relates to comparing the body condition of animals across seasons, locations, age ...
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### Confidence interval for beta-binomial distribution with restricted range

Based on guidance provided below I have revised my question. How would I calculate a 95% CI for the mean of a beta-binomial distribution that ranges between 0 and 5 and can only have values that are ...
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### Visually compare binomial and beta-binomial appropriateness in R

I'm trying to choose the best distribution family for generalized linear regression. My outcome is cross-sectional, over-dispersed proportion data (# of behaviors/20-22 possible behaviors). I used the ...