Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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?

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 for other people here. So I would be very thankful…
ffriend
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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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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 family = poisson or a negative binomial (glm.nb) model are not significant. When I look at the descriptives of my…
Sil
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Why is there -1 in beta distribution density function?

Beta distribution appears under two parametrizations (or here) $$ f(x) \propto x^{\alpha} (1-x)^{\beta} \tag{1} $$ or the one that seems to be used more commonly $$ f(x) \propto x^{\alpha-1} (1-x)^{\beta-1} \tag{2} $$ But why exactly is there "$-1$"…
Tim
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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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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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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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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 …
Kiudee
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Which distributions on [0,1] other than the beta distribution form nice compounds with the binomial distribution?

For which distributions x, other than beta, is the x-binomial distribution nice? The beta and binomial distributions are famously conjugate but I am curious if other non-conjugate distributions will give comparably simple compound pmfs. By nice I…
gam
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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…
DanRoDuq
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How to implement generalized hypergeometric function to use in beta-binomial cdf, sf, ppf?

I'm writing a subclass of scipy.stats._distn_infrastructure.rv_discrete for the beta binomial distribution whose PMF is $$P(X=k \mid N, \alpha, \beta){N \choose k} \frac{\mathrm{B}(k+\alpha,N-k+\beta)}{\mathrm{B}(\alpha,\beta)},$$ where $\mathrm{B}$…
Scott Norton
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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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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, … , gn and observe the number of cells ni in each dish that look different than normal. The total number of cells in dish gi is ti. There is individual differences between…
Vebjorn Ljosa
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