# Questions tagged [beta-binomial]

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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166 views

### Correct usage/understanding of Bayes Factor when comparing two proportions

I'm just starting to learn R and explore Bayesian statistics, but I keep getting tripped on using Bayes Factor and (honestly), I'd love a little confirmation if my process is correct in interpreting ...
158 views

### Entropy of the beta-binomial compound distribution

I have a generative process as follows: $$x \mid \alpha \sim \textsf{Beta}\left (\alpha,\beta \right) \\ y \mid x \sim \textsf{Bernoulli}(x).$$ How does one go about calculating the Entropy of ...
667 views

### How to combine two beta-binomial distributions

Say I have the following situation. I have two weighted coins: Coin 1: In the past I've seen this coin flipped 10 times, 8 of which it came up heads. So I can model the probability of $n$ heads out ...
228 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 ...
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### Updating posterior distribution in online fashion [duplicate]

First, I am sorry if this is an obvious question, I am starting to study bayesian statistics (mainly for machine learning) and I was seeing the classic coin flip example using a Bernoulli distribution ...
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### Marginal probability of beta distribution

The problem: Suppose you have 10 voters and 2 candidates. Each voter has a probability $p$ of voting for a Candidate 1, and a probability $1-p$ of voting for Candidate 2. What is the probability that ...
2k views

### 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 ...
2k views

### Distribution of the sum of two independent Beta-Binomial variables

Consider two independent discrete random variables $y_1$ and $y_2$, both distributed with a Beta-Binomial distribution, with different number of successes $n_1$ and $n_2$ but the same parameters $a$ ...
193 views

### Aggregation of propensity scores with varying reliability

When trying to estimate the number of sampling units with an attribute, is there a good algebraic way to aggregate over propensity scores for that attribute which each have their own error? For ...
272 views

### Visually compare binomial and beta-binomial appropriateness in R

I'm trying to choose the best distribution family for generalized linear regression. My outcome is cross-sectional, over-dispersed proportion data (# of behaviors/20-22 possible behaviors). I used the ...
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### Beta Binomial Encryption

For the sake of example, suppose we have a list of advertisements $\{A_i\}_{i=1}^n$, each of which have parameters $I_i$: the number of impressions, and $C_i$ the number of clicks. Then $C_i/I_i$ ...
160 views

### Aggregated Count Data-Days in the last 30- Negative Binomial vs Beta Binomial vs Binomial Regression

I need help choosing between the binomial, negative binomial, and beta-binomial distributions and understanding the rationale of why I would choose one over the other, as well as understanding how it ...
109 views

### In a Beta-Binomial 'Bayesian' A/B test, is it possible to add a third, fourth, etc. recipe?

For context: How to define prior for beta-binomial A/B test For P(A > B), you can draw samples from A's posterior and B's posterior and then count the number of times the sample from A is greater ...
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### 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....
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### 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 ...
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### 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 $\mu_1 = \frac{\alpha_1}{\alpha_1 + \beta_1}$, $\phi_1 = \alpha_1 +\beta_1$...
646 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-...
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### Given an observed sample from a binomial distribution and a known prior, how can I update the probability distribution of possible 'p' values?

Let's say that I have an 'unfair' coin, for which I'm interested in estimating the 'heads' likelihood or 'p' value. I've been told that the 'heads' likelihood for my 'unfair' coin is normally ...
166 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 ...
217 views

### Beta-Binomial Derivation

I was looking on wikipedia and seemed to be not follow how the beta-binomial is derived. I was hoping I could provide an example I found in a paper and someone could explain the steps. Given the ...
64 views

### Conditional probability of tossing coins with uncertain head probability

Suppose there are two coins A and B. When tossing a coin $i$, "head" happens with probability $p_i$. The problem is that $p_i$ itself is a random variable. Say that the associated probability ...
221 views

### how to analyze overdispersed binary data

In my substantive research, I often use dichotomous scoring (1 correct, 0 wrong) for my tests (tests with $15~yes/no$ items). My goal is often to compare the the proportion of correct answers to all ...
1k views

### How do I specify a Bayesian Beta binomial model, with predictor variables, for R2jags?

I want to have a beta-binomial Bayesian model, with R2jags. I understand I need something like this: ...
44 views

### Interdependence of hyperparameters of bernouilli laws [closed]

Suppose that you have $N$ people passing an exam having 2 type of questions (type A and type B) which all have correct/uncorrect outcomes. After seeing the results, I want to modelize the probability ...
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### 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 ...
247 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 ...
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### How to know dispersion if $\mu$ is close to or below 0 (chance-corrected beta-binomial model)

Background In sensory science, "replication" means having a panelist in a taste panel do multiple rounds of the same test. You cannot just count those additional rounds as additional panelists, ...
59 views

### Calculating the parameters of a Beta-Binomial distribution using the mean and variance

I'm trying to do the same thing that was done in this question: Calculating the parameters of a Beta distribution using the mean and variance for the Beta-Binomial distribution for which the mean is ...
100 views

### How to model on rate (percentage) outcome, but with consideration of number of total counts?

I would like to model on a rate outcome, with a number of covariates. I also have the number of counts which generate the rate outcome. Like below: ...
I'm simplifying my research question and want to know whether the question can be properly modeled or not. Suppose we have two coins $X_1,X_2$ and assume that the outcomes are possibly correlated. ...