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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19 views

Does pairwise correlation and multicollinearity matter in dispersion and zeroinflation model of glmmTMB?

I'm using glmmTMB to calculate beta-binomial GLMMs with nested and crossed random intercepts. I have overdispersed, zero-inflated data (assessed with Dharma). I use continuous terms in the very ...
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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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Posterior Predictive distributions: beta-binomial models

I am trying to do some inference on binomial proportions and I'm having trouble understanding the posterior predictive distribution of my model. I am concerned that my model isn't learning anything, ...
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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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53 views

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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44 views

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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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 ...
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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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85 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 ...
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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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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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55 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 ...
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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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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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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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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 −...
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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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255 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 $...
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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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395 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 ...
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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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267 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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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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121 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 ...
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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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85 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 ...
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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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119 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 ...
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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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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 (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 ...
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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 ...
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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. ...
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68 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 ...
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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 ...
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455 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 ...
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532 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 ...
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329 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 <...
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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, ...