# 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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### Selecting between a zero-inflated binomial, OLRE and beta-binomial model

I need some help in deciding which of the following models fits best the data that I have. This was a survey where participants reported proportions of successes (defined as n/m) in condition A and B. ...
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### Significant dispersion test

I used DHARMa for my residual diagnostics. For two models, the dispersion test is significant even though the rest of the diagnostic output looks good. I am wondering if both my models are correct ...
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### Bayesian A/B test - using an updated prior based on collected data

I have a question about whether I would be adding bias to an A/B test by updating my prior based on combined A & B data, and then running the A/B test on that prior. My A/B test is click through ...
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### how to perform Beta binomial distribution for the count category in R language

Dear friends I have a data-frame looking like this ...
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### Discrepancy between binomial and beta in R?

I'm getting a result I cannot explain when using beta distribution. I've got a result which came from a binomial distribution: 2 successes in 6 trials. I would think the maximum likelihood estimator ...
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### Reverse engineering Beta prior parameters from Binomial likelihood and posterior beta parameters

Suppose a friend has calculated a posterior distribution from a Beta prior and binomial likelihood, and you are interested in the prior parameters they used, but they won't give them to you. They only ...
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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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### 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 ...
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### What is the meaning of Marginal Density of Beta_binomial Distribution

Given an Experiment with a fair coins and 20 trials prior distribution defined as Beta(5,5) likelihood defined as Binomial(20,p) as a result it give a Beta Binomial distribution The Question is if I ...
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### Beta vs beta-binomial why beta has higher AIC

I am working with proportion data (very limited ~20 data points) for a response variable (RV), i.e. proportion of mature females out of total number of females sampled. The maturity is assessed by 6 ...
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### Help me understand how to apply a beta-binomial model in order to estimate a parameter when there are several Bernoulli trials?

So, I have been presented with this question: A sample of 100 people were asked how many days they drove their car during the last week (inc. the weekend). The resulting frequency of response is shown ...
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### Using a beta-binomial model to estimate the average for a uniform prior [duplicate]

Say we had a sample of 100 people who were asked how many days during the last week they drove their car. Let's say the resulting frequency table is as follows: Days, frequency 0, 1 1, 5 2, 3 3, 15 4, ...
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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 ...
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### Analytical power analysis of a binomial RCT

I have a certain population of users of my free app, with new ones installing every day. I want to run an RCT on them, specifically measuring the impact of some change on their conversion rate (i.e. ...
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### Estimate binomials given monotonic probabilities

I am given $N$ ordered coins and for each coin $i=1,..,N$ some trials $X_i \sim Bin(n_i, p_i)$. The coins are ordered in the sense that I know a priori that $0\leq p_1\leq p_2 \leq ... \leq p_N \leq 1$...
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### Comparing two groups with binomially distributed data

Below (in R), I have two independent groups of scores that are binomially distributed. These two groups of scores are known to have different probability of success (i,e., $p_1 \neq p_2$). Let's now ...
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### Bayesian Estimation, What is Equivalent Sample Size or Imaginary Sample Size?

I am trying to understand the formula given in the book Bayesian Networks, With Examples in R, by Marco Scutari & Jean-Baptiste Denis. The formula estimates the parameters of a categorical ...
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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 ...
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### Types of dispersion parameter for binomial data

For a model with a binomial proportion as response variable, which is fitted with according to a binomial distribution, a dispersion parameter $\phi$ can be calculated, which is equal to the sum of ...
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### Number of parameters mixture model

In order to do a LRT between two mixture models with different numbers of components, I need to know the number of parameters. I would like to know the answer both for: a) Gaussian mixture model b) ...
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### Binomial distribution for randomly drawn probabilities

Setting Probability theory can be a weird place sometimes. Here I was, confident in my insane math skills, trying to solve the following problem: Let $N, \alpha$ and $\beta$ be given. ...
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### Confidence interval bounds for BIN(1,p)

Consider the confidence interval bounds (p L , p u ) for BIN(1, p). In this caseT =Ī£Xi ~ BIN(n, p) is sufficient for p. To apply the cdf pivoting method, solve pbinom(t; n, p U) = Ī±/2 1 ā pbinom(t ā...
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### Relationship between Binomial distribution and the Beta distribution [duplicate]

I have been investigating the details of the Beta distribution and the Binomial distribution and have 2 questions to ask, but first a slight preamble to explain the background to my questions. In the ...
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### 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 ...
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### Estimating prior sd for the parameter p of a beta binomial regression

I am trying to implement model checks for a Bayesian beta binomial model using the workflow suggested by Betancourt (https://betanalpha.github.io/assets/case_studies/principled_bayesian_workflow.html#...
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### OLRE's vs. Beta Binomial Model for Overdispersed Mixed Effect logistic regression with proportion data?

this is a long post, as I wanted to be sure to provide all relevant information regarding my data, model, the methods that I have tried so far, and my diagnostic plots. If there are ways I should ...
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### Beta-Binomial regression or Poisson-Gamma model to account for uncertainty in (empricial Bayesian) prior? Explained in simple terms?

I have a dataset of $m$ individuals. For each individual $m$ I have $n_m$ (binomial ) observations with $s_m$ corresponding to the number of 'successes'. I use this data to fit a beta-binomial ...
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### How to model qualitative body condition scores? Ordinal logistic regression?

I am after some advice on how to model qualitative animal body condition scores? My overarching research question relates to comparing the body condition of animals across seasons, locations, age ...
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### Confidence interval for beta-binomial distribution with restricted range

Based on guidance provided below I have revised my question. How would I calculate a 95% CI for the mean of a beta-binomial distribution that ranges between 0 and 5 and can only have values that are ...
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### 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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### How do I carry out a significance test with Tarone's Z-statistic?

Context In this blog the author suggests using Tarone's Z-statistic to test for overdispersion in a binomial model to determine whether or not it is necessary to use a beta-binomial model instead. In ...
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### Can I construct a GAM in R for beta binomial data where the response is aggregated?

I have beta-binomial data pi = ri/ni and wish to construct a GAM using R. My data has columns {Case, X1...Xn, R, N} Initial thought Stack Successes(1) & Fail(0) use mgcv:gam with weights ri &...
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### Binomial Logistic-Normal Updating

I've been considering how sports with binary outcomes might be modelled e.g. the probability of a tennis player winning a point on serve. In text books the usual Bayesian approach uses the beta-...
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### Bayes prior and posterior distribution

Let's assume we have prior distribution beta with parameters 2,50. Let's just say it's prior knowledge of sign up rates for our product. Then we have two binomial models A and B, which both samples ...
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### Prior distribution to the binomial distribution probability distributions urn model

I have an infinite population with unknown mean of successes and failures. I'm drawing 400 times from the population and get 400 successes. Now I want to generate random estimates for the true mean of ...