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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Test for Equality of Parameters in Beta-Binomial Distribution

With binomially distributed data, it's straightforward to test the null hypothesis of equiprobable responses, $H_0: p=0.5$, but say you want to test the analogue in a Beta-Binomial model fit to over-...
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Using poisson distribution to model proportions

I have recently came across a number of articles that have used Poisson GLMs when modelling proportion data. For instance, one study modelled the proportion of pig mortality for each sow using a ...
253 views

How do you compute the beta-binomial probability of “at least one”?

When working with the binomial distribution, it's sometimes useful to compute the probability of "at least one", which is 1 - P(none) or, after setting x to 0 in the formula for the PDF of the ...
105 views

How do I compute the estimated values of x for a beta-binomial distribution?

I understand how to set up a binomial probability distribution. I'm trying to extend my understanding to the beta-binomial. On Wikipedia, there is a beta-binomial example given at https://en....
257 views

Estimating beta parameters in truncated beta-binomial distribution

$\newcommand{\Beta}{\operatorname{Beta}}$I'm sampling a bunch of probabilities, $\theta_i \sim \Beta(a,b)$, from a common beta distribution, and then using each $\theta_i$ to sample a value $x_i$ out ...
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How to define prior for beta-binomial A/B test

I would like to run an A/B test using a Bayesian beta-binomial model whereby I would state probabilities such as $P(p_B>p_A)$ in place of using a traditional T-test. I've read that the prior should ...
422 views

Beta prior on (a,b) [duplicate]

Is it possible to rescale a beta prior to range from, say, $(0.5,1.0)$? For example, say that your likelihood function for some parameter $p$ is binomial and you know that $p \in (0.5,1.0)$ due to ...
940 views

Convert probabilities of “binomial events” into beta distribution for binomial parameter (theta)

I have three events that essentially arise from a binomial distribution with k=2, i.e., X~Binomial(theta,n=2). Given some model and data I obtained a conditional (pos distribution for a particular X_i,...
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Multi Armed Bandit for Continuous Rewards - Extended Question

This question is an extension to A continuous generalization of the binary bandit The Multi-Armed Bandit (MAB) Problem in general is described here: https://en.wikipedia.org/wiki/Multi-armed_bandit ...
188 views

Inferential statistics for vector of percentages

I'm getting confused by this and was wondering if someone can enlighten me: I have a random sample consisting of 50 percentages. Each percentage can take on any value between 0% and 100% inclusive ...
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Probability distribution for a binomial proportion 'derived' from serially dependent data

Consider the following type of data: This is data from a single-case experiment: an experiment in which one entity (i.e. one person) is observed repeatedly over time (cf. measurement times 1 to 20)...
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VGAM fitting a betabinomial model

I have a small question, given this: fit <- vglm(cbind(R, N-R) ~ 1, betabinomial, lirat, trace=TRUE, subset=(N > 1)) Why should I do ...
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Estimate accuracy of an estimation on Poisson binomial distribution

I manage a website that charges its customers using payment cards. Some transactions area approved, others are declined. I compute the approval rate of transactions for a interval (a calendar day) as ...
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Hyperprior Noninformative Beta Binomial Model [closed]

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 ...
150 views

Impact of conjugate priors on mutual information for Naive Bayes

I am currently thinking about the following problem. Suppose you have a simple Naive Bayes model for binary classification based on binary random variables. For example, suppose you want to predict ...
298 views

Beta-binomial logistic regression model for binomial data with small samples

I have fitted a nonlinear beta-binomial logistic regression model on data y_i: y_i ~ beta-binom(n_i,mu_i,\Phi) where mu_i = exp(\eta_i)/(1+exp(\eta_i)) , and \eta_i=\beta_0+\beta_1/(1+exp(\beta_2x_i ...
355 views

Bivariate distribution: beta and binomial

Consider a pair of RVs $X$ and $Y$, with the following conditional distributions: $$X | Y=y \sim Binom(L, y)$$ $$Y | X=x \sim Beta(\alpha + x, \nu)$$ where $L$, $\alpha$, and $\nu$; are all ...
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beta-binomial distribution with R

I am studying an experiment of the kind: Let $n_{ij}$ be the number of fetuses, $X_{ij}$ the number of responses i.e. the number of fetuses with a malformation in the jth litter of the ith dose level ...
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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 + ...
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A continuous generalization of the binary bandit

There is plenty of reading out there about Bayesian (beta-binomial) multiarm bandits for 0/1 data, but I would like to extend this slightly. To give some context, suppose I have two webpages, A and ...
188 views

Beta binomial mean different from actual mean

I have data that I am fitting a beta binomial distribution to. The VGAM package for R is being used to do this. However, the the mean of the fitting beta binomial distribution is vastly different from ...
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Beta distribution vs beta binomial distribution: alpha and beta

I have been attempting to estimate alpha and beta from a beta binomial distribution given my data. There are R packages like VGAM to do this. I am wondering if there is a difference between estimating ...
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Is it possible to validate very small p-values via bootstrap?

Suppose I want to see whether the p-values generated by a certain parametric method are close to the “true” p-values. To avoid relying on any parametric assumptions, the latter are produced via ...
494 views

Calculate expected value from discrete beta distribution

I have a lookup table in 2 variables, $Z_l$ and $T_l$. So, $Z_l$ and $T_l$ are vectors with same length where $Z_l$ goes from 0 to 1 and $T_l$ varies between 300 and 2000. If you are curious, $Z_l$ ...
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Recursive Bayesian Estimation, $p(C_k|\mathbf{x})$ as (discrete) likelihood

I''ve been struggeling with this problem for the last couple of days. The main goal is to use the probabilistic classification output $p(C_k|\mathbf{x})$, from for example a logistic regression, to ...
148 views

Difference test for beta–binomial variables

Let $X \sim \textrm{Beta–Binomial}(\alpha_1, \beta_1, n)$ and $Y \sim \textrm{Beta–Binomial}(\alpha_2, \beta_2, n)$ and write $\mu_1 = \frac{\alpha_1}{\alpha_1 + \beta_1}$, $\phi_1 = \alpha_1 +\beta_1$...
686 views

log-likelihood for a beta-binomial in R

Although I may ask a question that is already solved (but I found none that would explicitly refer to this), I would like to know, if (and I am no statistician) I am right with programming the log-...