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.

The beta-binomial disribution is a discrete distribution on 0, 1, ..., n.

It arises as a mixture distribution, where the probability of success in a binomial distribution (p) is itself drawn from a beta distribution. Because of this it is sometimes used as a model for heterogeneous mixtures of binomials or more generally for situations where the variance of a discrete distribution on 0, 1, ..., n has a larger variance than the binomial.

It also commonly occurs in Bayesian applications.

Reference: Wikipedia - Beta-binomial distribution

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What is the intuition behind beta distribution?

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Relationship between Binomial and Beta distributions

I'm more of a programmer than a statistician, so I hope this question isn't too naive. It happens in sampling program executions at random times. If I take N=10 random-time samples of the program's state, I could see function Foo being executed on,…
Mike Dunlavey
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Why is there -1 in beta distribution density function?

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Tim
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Minimizing symmetric mean absolute percentage error (SMAPE)

I am working on a forecasting application in which forecast errors are measured using the symmetric mean absolute percentage error : $$ SMAPE = \frac{1}{n} \sum\limits_{t=1}^n{\frac{|F_t - A_t|}{F_t + A_t}} $$ After creating my ML model and applying…
Rui Gonçalves
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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 based solely on the probability of some…
Bogdan Kulynych
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What is the distribution of a sum of identically distributed Bernoulli random varibles if each pair has the same correlation?

What is the distribution of a sum of $n$ Bernoulli random variables, each having success probability $p$, where each pair is correlated with correlation coefficient $\rho$? $$Y = \sum_{i=1}^n X_i$$ $$ X_i \sim…
amoeba
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Estimating beta-binomial distribution

Suppose that I culture cancer cells in n different dishes g₁ , g₂ , … , g n and observe the number of cells n i in each dish that look different than normal. The total number of cells in dish g i is t i . There is individual differences between…
Vebjorn Ljosa
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Hyperprior Noninformative Beta Binomial Model

I've been working through Gelman's Bayesian Data Analysis 3 text and have been trying to understand one of the hierarchical models revolving around rat tumors (Chapter 5). He uses a binomial model with p assigned a beta distribution. The Beta…
aarmstrong
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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 failures (tails) ", which also made sense when…
Yehoshaphat Schellekens
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Limit of beta-binomial distribution is binomial

I am trying to understand the relationship between the beta-binomial and the binomial distribution. More specifically, I am trying to show that the limit of the beta-binomial distribution, with $p=a/(a+b)$ is binomial as $a+b$ goes to infinity. I am…
DanRoDuq
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Taking into account the uncertainty of p when estimating the mean of a binomial distribution

I have a binomial distribution with parameters $N$ and $p$, and the estimate for the mean of my distribution is N$\times p$. The values of $N$ and $p$ are such that we can use the Gaussian approximation to estimate the $\sigma$ of the mean as…
Helga Holmestad
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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 successes in a future experiment, $p$, but I need a CI…
James
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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: Item Count Total -------------------- 1 1 30 2 10 340 3 0 0 4 1 10 ... I want to calculate the posterior of the success probability $p_i$ for…
Kiudee
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Which distributions on [0,1] other than the beta distribution form nice compounds with the binomial distribution?

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Hyper-parameter estimation for Beta-Binomial Empirical Bayes

I am reading a paper Illustrating empirical Bayes methods and in the paper the author uses method of moments to derive the value of an estimate. In equation 17 the author gives the following marginal distribution $$m(y_i\vert \lambda) = {n\choose…
Alex
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