# 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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### Optimization fails to converge on known parameters for zero-inflated beta binomial distribution [closed]

I am trying to fit to simulated zero-inflated beta binomial data using the distributions provided by VGAM in R. When using optim on a likelihood function I wrote, ...
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### Beta-binomial relationship between dispersion and correlation parameters

Context: I have created a beta-binomial model using glmmTMB() from the glmmTMB package and I am now trying to simulate a beta-...
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### What are the assumptions of beta-binomial models, and how do I test for them in r?

I want to model the effects of dispersal distance (disp) and reproductive rate (rep) on colonization rate, quantified as the ...
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### Inference for Binomial proportion with estimated p but unknown N

Let's say I own a bakery that, among other desserts, sells one really tasty chocolate cake. It's so good that I've estimated that I've estimated 80% of my daily customers will buy a piece of cake, ...
1 vote
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### Distributional choices for sparse 0,1 data

I am using GAMs to model the relationship between a binary response variable (0 or 1) and several continuous fixed and random explanatory variables. It seems that a binomial distribution is the ...
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### Estimating variance of Poisson Binomial random variable

Let's say I have a weighted coin, with probability $p_i$ of being heads. I flip $N_i$ times, and estimate $P_i$ and the variance on $p_i$ using the relevant formulas for a Binomial distribution. Call ...
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### Overdispersion Mixed generalized linear model

I am running a mixed generalized linear model to analyze insect capture in a baited trap. The experiment consisted of 3 separate cages, in each one one treatment (C+, C- or T) and 10 insects were ...
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### What is the correct implementation of MCMC

I am learning Markov Chain Monte Carlo (MCMC) simulation as of the moment. My background is civil engineering and please excuse my ignorance if some of the questions are quite obvious. I want to learn ...
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### prior and posterior predictive distributions, Bayes Theory

Consider the binomial sampling model with a Beta prior on $\theta$ and the prior predictive distribution. Let $n$ be the binomial sample size. \begin{align} p(y^{new}) &= \int_{\theta}f(y^{new}|\...
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### Posterior of binomial and mixed prior

I'm currently studying posterior distribution with likelihood $y|\theta \sim B(n,\theta)$ and mixture of prior distribution $\theta \sim \pi Beta(\alpha_1, \beta_1) + (1-\pi)Beta(\alpha_2, \beta_2)$. ...
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### Inference of Beta-Bernoulli Distribution

Assume $x_1, x_2, \cdots, x_n$ follows a $Bern(\pi_0)$, Let $y_{ik}$ follows $Beta(\alpha,\beta)$, $i\in \{1,\cdots, n\}$, and $k\in \{1,\cdots, K\}$. Let $z_k$ follows a Bernoulli Distribution with a ...
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### Interpreting predict() with gamlss() and beta-binomial family=BB

Note after answer is posted: The issue here was actually about formatting the data of the dependent variables in the formula when using (beta-)binomial families. Not about ...
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### Laplace's law of succession for ordinal variables

this is just a little curiosity of mine, but has anyone heard of some simple model like Laplace's law of succession, however for ordinal RVs instead of a binomial? Specifically, I'm thinking about ...
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### Significance of outliers with multiple weighted coins

tl;dr: I have N weighted coins, each of which has been flipped some number of times (n_i), and for which I've measured the ...
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### Express infinite serie in terms of a shape parameters of beta distribution

Player A and B participate in a match where the probability that A will win each point is $p$, for B its $1-p$ and a player wins when he reach $11$ points by a margin of $\ge2$ The outcome of the ...
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### For a binary outcome, is the distribution necessarily Bernoulli? Could, for instance, "beta-Bernoulli be in play?

When a variable is binary, it sure seems like its distribution is totally characterized by the probability of being in one group: the variable takes one value with probability $p$ and the other value ...
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### Parameterization of the beta-binomial family Glmmtmb

I have trouble understanding the documentation for the glmmtmb package (https://cran.r-project.org/web/packages/glmmTMB/glmmTMB.pdf) On page 26, in the details on the beta-binomial distribution, it ...
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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" ...
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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 ...
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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 ...
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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 ...
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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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1 vote
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I have three different random variables $\theta_1, \theta_2, \theta_3$ . These random variables are actually parameters of binomial likelihood Assume that I have prior distribution of $\theta_2 \sim ... 2 votes 1 answer 875 views ### Calculate the posterior probability in two groups, Pr(p1>p2 | Data)? Assume the prior distribution of p1 and p2: p1~beta(1,1) p2~beta(2,3) Assume the data in group1 and group2 follows bernouli distribution: y1~Binom(10,0.3) y2~Binom(10,0.6) How can I calculate the ... • 21 5 votes 0 answers 236 views ### Calculating ICC for a beta-binomial GLMM I understand that ICC in binomial GLMMs with a logit link can be calculated via R, where the residual deviance is (pi ^ 2) / 3. However, this is assuming that the ... • 51 3 votes 2 answers 209 views ### 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 ... • 41 1 vote 0 answers 25 views ### Can I use posterior beta parameters from a previous experiment to use as priors for my current experiment? I am doing a Bayesian comparison between two proportions, H0 being Proportion(Protein)> Proportion(Mixed). Here the Proportion is of no. of times a free-ranging dog(s) ate from a box(Protein, Mixed)... 4 votes 0 answers 168 views ### How does Pfizer justify it's Beta-Binomial model? [closed] This is a bit of a hodge podge of different clinical trial related questions, but starting with some basics. It seems like they're defining vaccine efficacy differently depending on where you look. At ... • 271 2 votes 1 answer 1k views ### Beta-binomial vs updating a prior beta distribution Bear with me, as I've just recently been learning about conjugate priors, prior and posterior distributions, and such material. My understanding of the beta-binomial distribution is that it basically ... • 325 2 votes 1 answer 86 views ### How to estimate the effects of vaccines with Beta- Bernoulli inference The original Tutorial comes from toward data science Given the following description: "Moderna: The vaccine is being tested in 30,000 people. Half received two doses of the vaccine, and half ... 1 vote 1 answer 1k views ### Beta-Binomial parameter estimation The MLE or method of moments estimation of parameters of a beta-binomial distribution makes use of (c, y) -- total number and positive counts. However, if we only have one such pair, then$\frac{\...
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 ...