# 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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Let $m,n,l$ be three integers, and, for $i=1,\dots,N$, let $C_i\sim\frac{1}{m}\text{Binom}(m,\mu)$ where $\mu\sim\text{Beta}(n+1-l,l)$ be i.i.d. beta-binomial random variables. Let $\bar{C}=\frac1N\... 0 votes 0 answers 40 views ### Can I use a Prior with Simulated data? I have a prior about some proportion that follows a Beta distribution. Unfortunately, I do not have (yet) observed data but I was offered a thousand simulated datasets. Each dataset comes from ... 0 votes 1 answer 177 views ### Beta-Binomial Gibbs Sampler I am self-studying Bayesian statistics from the book Computational Bayesian Statistics by Turkman et al, but I am stuck on Problem 6.3 from the book: Suppose we want to consider a Binomial (unknown$\... 1 vote
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### Am I wanting to perform a random walk?

I am trying to determine the best method to obtain a probability distribution that describes the likelihood of flipping only heads for a number of successive coin tosses with a coin that has an ...
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### Histogram of the MLE of the probability in binomial distribution and the plot of beta distributions

I have data with columns "y" and "n", which for this example can be "y" count of heads out of "n" coin flips. There are "i" rows ie "i" ...
1 vote
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### help computing the beta likelihood when we only observe the number of successes and failures (not the latent probability of success)

Imagine we have a biased coin that generates heads with unknown probability $\theta$ where $\theta$ is drawn from a beta distribution with known parameters $(\alpha, \beta)$. Next imagine that we flip ...
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### Betabinomial (BB) regression in the gamlss package (R)

I'd be grateful for any help with beta-binomial (BB) regression in the gamlss package: predictions from the fitted model of "mu" values for each observation in my data seem reasonable. But ...
1 vote
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### Change shape parameters in a beta distribution based in each datapoint [closed]

I am new to Bayesian statistics and I have been trying to implement a Beta Binomial model from a PhD thesis in rjags. The thesis describes prior distribution for the variables but I am stuck in how to ...
1 vote
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### Comparing performance of Quasi-binomial model and Beta-binomial model

I read some books in biostatistics about fitting binary date with Beta-Binomial regression model and Quasi-Binomial regression model. It proposes a setting: Setting: Assuming we have a sequence of ...
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### Marginal Distribution in Beta-Binomial Model with Overdispersion Parameters

Problem Setting: We assume there is a sequence of binomial trials of size $N_i$, $Y_i$ is the number of events of interest, $x_i$ is the predictor associated with trial $i$, and $\pi_i$ is the ...
1 vote
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### Inconsistent posterior estimates in Beta-Binomial likelihood vs Binomial in Bayesian, multilevel models?

In this Google Colab, I've simulated Binomial count data and compared the performance of Binomial-likelihood and Beta-Binomial-likelihood models. Both models have the same Beta prior on theta, the ...
1 vote
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### Beta-Binomial mixture vs Beta-Binomial multilevel model?

I first read about the Beta PDF in the context that it was conjugate to the Binomial distribution; a Beta prior with a Binomial likelihood returns a Beta posterior. So this sounds to me like a ...
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### Simulations: why is "1 by 1" much more efficient than "many by 1"?

Note: I am not familiar with discussions of this particular issue of simulation studies, so I may use wrong terms or oversee obvious aspect. My apologies for that. I want to simulate a two-step ...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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