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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Valid confidence interval for the mean of the average of N iid beta-binomial random variables

Let $m,n,l$ be three integers, and, for $i=1,\dots,N$, let $C_i\sim\frac{1}{m}\text{Binom}(m,\mu)$ where $\mu\sim\text{Beta}(n+1-l,l)$ be i.i.d. beta-binomial random variables. Let $\bar{C}=\frac1N\...
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Can I use a Prior with Simulated data?

I have a prior about some proportion that follows a Beta distribution. Unfortunately, I do not have (yet) observed data but I was offered a thousand simulated datasets. Each dataset comes from ...
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Beta-Binomial Gibbs Sampler

I am self-studying Bayesian statistics from the book Computational Bayesian Statistics by Turkman et al, but I am stuck on Problem 6.3 from the book: Suppose we want to consider a Binomial (unknown $\...
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Am I wanting to perform a random walk?

I am trying to determine the best method to obtain a probability distribution that describes the likelihood of flipping only heads for a number of successive coin tosses with a coin that has an ...
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Histogram of the MLE of the probability in binomial distribution and the plot of beta distributions

I have data with columns "y" and "n", which for this example can be "y" count of heads out of "n" coin flips. There are "i" rows ie "i" ...
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help computing the beta likelihood when we only observe the number of successes and failures (not the latent probability of success)

Imagine we have a biased coin that generates heads with unknown probability $\theta$ where $\theta$ is drawn from a beta distribution with known parameters $(\alpha, \beta)$. Next imagine that we flip ...
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Betabinomial (BB) regression in the gamlss package (R)

I'd be grateful for any help with beta-binomial (BB) regression in the gamlss package: predictions from the fitted model of "mu" values for each observation in my data seem reasonable. But ...
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Change shape parameters in a beta distribution based in each datapoint [closed]

I am new to Bayesian statistics and I have been trying to implement a Beta Binomial model from a PhD thesis in rjags. The thesis describes prior distribution for the variables but I am stuck in how to ...
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Comparing performance of Quasi-binomial model and Beta-binomial model

I read some books in biostatistics about fitting binary date with Beta-Binomial regression model and Quasi-Binomial regression model. It proposes a setting: Setting: Assuming we have a sequence of ...
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Marginal Distribution in Beta-Binomial Model with Overdispersion Parameters

Problem Setting: We assume there is a sequence of binomial trials of size $N_i$, $Y_i$ is the number of events of interest, $x_i$ is the predictor associated with trial $i$, and $\pi_i$ is the ...
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Inconsistent posterior estimates in Beta-Binomial likelihood vs Binomial in Bayesian, multilevel models?

In this Google Colab, I've simulated Binomial count data and compared the performance of Binomial-likelihood and Beta-Binomial-likelihood models. Both models have the same Beta prior on theta, the ...
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Beta-Binomial mixture vs Beta-Binomial multilevel model?

I first read about the Beta PDF in the context that it was conjugate to the Binomial distribution; a Beta prior with a Binomial likelihood returns a Beta posterior. So this sounds to me like a ...
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Simulations: why is "1 by 1" much more efficient than "many by 1"?

Note: I am not familiar with discussions of this particular issue of simulation studies, so I may use wrong terms or oversee obvious aspect. My apologies for that. I want to simulate a two-step ...
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Conditional beta posterior for uniform priors

I have three different random variables $\theta_1, \theta_2, \theta_3$ . These random variables are actually parameters of binomial likelihood Assume that I have prior distribution of $\theta_2 \sim ...
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Success rate in BetaBinomial given weighted samples

I need advice on modeling my use case. Lets assume you have a population of X items and you have N trials. Each item $i$ from the overall population is selected/sampled to be evaluated with ...
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Calculate the posterior probability in two groups, Pr(p1>p2 | Data)?

Assume the prior distribution of p1 and p2: p1~beta(1,1) p2~beta(2,3) Assume the data in group1 and group2 follows bernouli distribution: y1~Binom(10,0.3) y2~Binom(10,0.6) How can I calculate the ...
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Calculating ICC for a beta-binomial GLMM

I understand that ICC in binomial GLMMs with a logit link can be calculated via R, where the residual deviance is (pi ^ 2) / 3. However, this is assuming that the ...
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Beta distribution for uncertain binary trials

I have a larger problem but have presented what I believe is a minimal example. Imagine that you are trying to determine the true probability of a potentially-biased coin landing on heads, and want to ...
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Can I use posterior beta parameters from a previous experiment to use as priors for my current experiment?

I am doing a Bayesian comparison between two proportions, H0 being Proportion(Protein)> Proportion(Mixed). Here the Proportion is of no. of times a free-ranging dog(s) ate from a box(Protein, Mixed)...
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Beta-binomial vs updating a prior beta distribution

Bear with me, as I've just recently been learning about conjugate priors, prior and posterior distributions, and such material. My understanding of the beta-binomial distribution is that it basically ...
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How to estimate the effects of vaccines with Beta- Bernoulli inference

The original Tutorial comes from toward data science Given the following description: "Moderna: The vaccine is being tested in 30,000 people. Half received two doses of the vaccine, and half ...
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Beta-Binomial parameter estimation

The MLE or method of moments estimation of parameters of a beta-binomial distribution makes use of (c, y) -- total number and positive counts. However, if we only have one such pair, then $\frac{\...
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How to estimate beta distribution parameters using a beta binomial with empirical bayes

I would like to estimate parameters for a beta distribution using a maximum likelihood approach in python (as mentioned here). I can do this for a beta: ...
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Discrete Probability Density that is Monotonically Decreasing as K Increases and is 0 at K=N+1

My knowledge of distributions is limited, so I apologize beforehand for what may be a silly question. I am looking for a discrete probability distribution with domain $\{1,2,...,N\}$ that satisfies ...
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Calculating the tail bounds for a beta-binomial regression

I have a beta-binomial regression model that depends on a probability $p$ and a given over-dispersion $\beta$ and is used to parametrise the distribution of $Y$ in the following way $$ Y(x) \sim ...
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Compound beta-binomial and beta distribution

I have a process that is modelled by a beta-binomial, parametrised by mean $\mu$ and correlation $\rho = 1/(\alpha+\beta+1)$ (as per dbetabinom in the R VGAM package). I know $\rho$, but the mean $\...
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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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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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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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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 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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How can I understand if my Beta Distribution is converging?

I am evaluating a Bayes AB Test on 2 variants, A and B. I then plotted a graph which shows the Probability of B is better than A on a daily basis. My worry comes in on the topic of 'peeking'. Let's ...
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Probability that the same r.v. generates the rth order statistic in one noise-added set, and the sth order statistic in another noise-added set

(Note: The title is confusing, as I have no idea if a name / short description exists for the setting below. I'm open to pointers and/or suggestions.) Setting Let $X_1, ..., X_N \overset{i.i.d.}{\...
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PyMC's treatment of shape versus deterministic data, when a random variable's parameter is vector-valued

I'm working on a problem with PyMC3 that makes me think I need to better understand how it deals with random variables whose parameters are vector-valued. Data description and problem setup I have $...
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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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3 votes
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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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1 vote
2 answers
487 views

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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2 votes
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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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6 votes
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Does order of events matter in Bayesian update?

I'm wondering whether the order of events can lead to different Bayesian update. For example, consider a coin-tossing problem with unknown $p$, the probability of Head. Initially, $p$ is known to ...
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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 ...
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Bayesian inference for a conditional probability

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. ...
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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 ...
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Bayesian estimation of weighted proportion

Having bayesian estimates of a proportion is relatively easy. You model that proportion as a binomial variable, you choose a beta-binomial prior and by using the likelihood you obtain a beta-binomial ...
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