# Tagged Questions

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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### Multiple binomial variables: probability they are all 1

We have observed four phone booths by recording, at a given time point, whether each phone booth is occupied (0 or 1). We have approximately 50 such observations (i.e. at 50 different time points, so ...
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### Prediction interval for a future proportion of successes under Binomial setting

Suppose I fit a Binomial regression and obtain the point estimates and variance-covariance matrix of the regression coefficients. That will allow me to get a CI for the expected proportion of ...
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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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### Maximum Likelihood Estimation on Zero-Inflated data using Constraint

I have written a function that evaluates the log-likelihood of Zero-inflated Beta Binomial data: ...
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### How to combine two beta-binomial distributions

Say I have the following situation. I have two weighted coins: Coin 1: In the past I've seen this coin flipped 10 times, 8 of which it came up heads. So I can model the probability of $n$ heads out ...
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### Generating data from a Beta-Binomial distribution by inverting CDF in R [closed]

I am trying to generate data from a beta-binomial distribution by inverting its cdf in R. The code I have written to calculate the cdf seems to be working fine for most cases, but gives me values ...
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### Properly interpret the alpha / beta parameters in the Beta Distribution

For quite a while I believed that the proper interpretation of a Beta distribution with $\alpha$ and $\beta$ is: "what is the most likely $P$ given $\alpha -1$ success (heads), and $\beta -1$ of ...
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### Beta Distribution with Random Shape Parameters (Binomial or Poisson Binomial)

I've run into an interesting model into some of my research and I was hoping somebody with more mileage can point me to any resources or other applications. I'm familiar with the Beta-Binomial, but ...
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### Should I use a beta-binomial or binomial glmm?

I have several data sets on wildlife disease incidence. One of the issues with my dependent variable is that it represents only current infection status, therefore 0 (no disease) can represent either ...
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### How to specify a Bayesian binomial model with shrinkage to the population?

Problem I’m currently working on a problem where I have count data for $n$ items in the following form: ...
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### When to terminate the Bayesian A/B test?

I'm trying to do A/B testing the Bayesian way, as in Probabilistic Programming for Hackers and Bayesian A/B tests. Both articles assume that the decision maker decides which of the variants is better ...
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### Is the beta-binomial distribution a conjugate prior for some distribution?

The beta distribution is conjugate prior for the binomial distribution. Is the beta-binomial distribution a conjugate prior for some sampling distribution?
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### How to know dispersion if $\mu$ is close to or below 0 (chance-corrected beta-binomial model)

Background In sensory science, "replication" means having a panelist in a taste panel do multiple rounds of the same test. You cannot just count those additional rounds as additional panelists, ...
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### Beta distribution and beta binomial distribution

What is the difference or relation between beta distribution, beta binomial distribution and binomial distribution?
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### Distribution of the sum of two independent Beta-Binomial variables

Consider two independent discrete random variables $y_1$ and $y_2$, both distributed with a Beta-Binomial distribution, with different number of successes $n_1$ and $n_2$ but the same parameters $a$ ...
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### What is the appropriate model for underdispersed count data?

I am trying to model count data in R that is apparently underdispersed (Dispersion Parameter ~ .40). This is probably why a glm with ...
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### Understanding the multilevel / random-effects beta-binomial regression model

Suppose we have an outcome variable $y_{ji}$ which is a count of behaviors performed by group $j$ in round $i$, for $j = 1,...,n$ and $i = 1,...,8$. The outcome $y_{ji}$ counts are non-independent ...
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### Update rule for beta distribution with fixed K/confidence/sample size

Normally you have a beta distribution with shape parameters $a$ and $b$. The mean of this distribution is $a / (a + b)$ and the sample size, or the confidence (or K) is $a + b$. Now, if you do some ...
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### Use Bayesian hierarchical model to predict new data points

I have a data set $(n_i,y_i),i=0,...,10$. I modeled it as a Bayesian hierarchical beta-binomial model. $y_i∼Binomial(n_i,p_i)$ and $p_i∼Beta(\alpha,\beta)$. I have used MCMC to estimate $\alpha$ and ...
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### Estimate beta binomial distribution

I have a dataset as follows: ni-xi 76 48 38 19 20 14 26 29 39 45 38 36 32 34 26 21 23 12 24 18 14 61 35 21 32 20 89 30 34 35 xi 0 0 16 26 1 8 23 19 24 16 16 19 0 0 0 6 8 3 5 9 5 0 34 ...
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### prior distribution to the binomial distribution probability distributions urn model

I have an infinite population with unknown mean of successes and failures. I'm drawing 400 times from the population and get 400 successes. Now I want to generate random estimates for the true mean of ...
For a model with a binomial proportion as response variable, which is fitted with according to a binomial distribution, a dispersion parameter $\phi$ can be calculated, which is equal to the sum of ...