# 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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### 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 ...
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 ... 0answers 11 views ### Distribution with a parameter being function of another? The beta-binomial distribution has probability mass function given by: f(k\mid n,\alpha,\beta). Is there any theoretical problem in setting \beta=g(\alpha) for some linear function g? By doing ... 0answers 25 views ### 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 \... 1answer 49 views ### 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. ... 1answer 37 views ### 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 ... 0answers 9 views ### how to perform Beta binomial distribution for the count category in R language Dear friends I have a data-frame looking like this ... 2answers 111 views ### 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 ... 1answer 43 views ### 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 ... 0answers 13 views ### 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 ... 1answer 45 views ### 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 ... 1answer 89 views ### 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 ... 0answers 45 views ### 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, ... 0answers 18 views ### 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. ... 0answers 22 views ### 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... 1answer 174 views ### 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 ... 0answers 14 views ### Confidence interval bounds for BIN(1,p) Consider the confidence interval bounds (p L , p u ) for BIN(1, p). In this caseT =ΣXi ~ BIN(n, p) is sufficient for p. To apply the cdf pivoting method, solve pbinom(t; n, p U) = α/2 1 − pbinom(t −... 1answer 170 views ### 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 ... 0answers 54 views ### 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#... 0answers 27 views ### 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 ... 1answer 45 views ### 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.}{\... 1answer 176 views ### 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 ... 0answers 166 views ### 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 ... 1answer 277 views ### 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 ... 0answers 58 views ### 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 ... 2answers 161 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 ... 0answers 152 views ### 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 &... 0answers 100 views ### 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-... 1answer 111 views ### 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 ... 3answers 560 views ### 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 ... 1answer 76 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 ... 1answer 63 views ### 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. ... 1answer 102 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 ... 0answers 31 views ### 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 ... 2answers 270 views ### 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 ... 1answer 46 views ### Can (log-)likelihood be used to compare a binomial model to its beta-binomial equivalent? In this article the author talks about fitting beta-binomial models to data when the there data is over-dispersed relative to the assumptions of a model with binomial errors. Near the end they present ... 0answers 24 views ### How to fit a Beta-Binomial Distribution to a dataset [duplicate] I have a data set which is defined over positive integers and I have reasons to believe it follows a beta-binomial distribution. I am aware there is the ... 1answer 36 views ### 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. ... 1answer 65 views ### Beta-binomial Model with missing values I have read http://www.sumsar.net/blog/2018/12/visualizing-the-beta-binomial/ this simple explanation of how the posterior is changing while more data are added: in this visualization there are six ... 0answers 60 views ### Beta-binomial distribution for scaled and translated Beta Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ... 2answers 389 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 ... 1answer 473 views ### Poisson-binomial vs. Beta-binomial I have N distinct bernoulli trials with a distinct probability for each trial given by, P=(p1, p2, ..., pN). I want to know the distribution of the number of successes. Given that I know P, I can ... 0answers 283 views ### Hypothesis testing with beta binomial. Dealing with overdispersion To make the question more understandable I will use a reproducible example. I have count data, how many connections different groups share with a unique group. In my case I have an upper bound of <... 0answers 74 views ### How to infer a prior belief after observing a behavior My participant goes through a maze made of 32 T intersections. At each intersection he must choose whether to go either to the left or to the right: one option will lead to another T intersection, ... 2answers 292 views ### How to convert the parameters in a binomial distribution to those in a beta distribution? I know that the beta distribution is the generalized continuous case of the discrete binomial distribution. Let's say I have a binomial distribution, B(N,p). I would like to know the corresponding \... 0answers 21 views ### Sample from multiple urns - when to stop? I have a problem that hasn't yet been addressed, although follows similar lines of reasoning here and here. My problem is as follows: I have N urns, each with a different number of black and white ... 2answers 627 views ### 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 ... 1answer 884 views ### 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...
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 ...