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.

Filter by
Sorted by
Tagged with
3
votes
1answer
20 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. ...
0
votes
1answer
26 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 ...
0
votes
1answer
156 views

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 ...
3
votes
2answers
110 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 ...
-1
votes
1answer
37 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 ...
3
votes
1answer
94 views

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....
481
votes
14answers
191k views

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 ...
0
votes
0answers
10 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 ...
0
votes
1answer
32 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 ...
-2
votes
1answer
65 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 ...
0
votes
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, ...
1
vote
1answer
134 views

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 ...
0
votes
0answers
17 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. ...
0
votes
0answers
20 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 $0\leq p_1\leq p_2 \leq ... \leq p_N \leq 1$...
6
votes
1answer
549 views

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 ...
2
votes
1answer
110 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 ...
35
votes
7answers
29k views

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 ...
4
votes
1answer
3k views

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 ...
0
votes
1answer
454 views

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) ...
0
votes
1answer
35 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. ...
0
votes
0answers
11 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 −...
2
votes
1answer
115 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 ...
2
votes
2answers
334 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 ...
0
votes
0answers
34 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#...
0
votes
1answer
39 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.}{\...
1
vote
0answers
25 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 ...
2
votes
1answer
122 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 ...
2
votes
1answer
40 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 ...
0
votes
1answer
129 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 $...
2
votes
0answers
137 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 ...
2
votes
1answer
209 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 ...
3
votes
0answers
57 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 ...
0
votes
2answers
111 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 ...
2
votes
0answers
376 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 ...
2
votes
2answers
234 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 ...
2
votes
0answers
119 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 &...
0
votes
0answers
87 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-...
1
vote
1answer
102 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 ...
0
votes
0answers
24 views

Bayesian updating via priors

Currently learning about using the Beta distribution and the Beta-Binomial distribution in Bayesian inference. I am confused regarding the following statement: $f(p | X=k)=\frac{P(X=k|p)f(p)}{P(X=k)}...
19
votes
3answers
558 views

Why is there -1 in beta distribution density function?

Beta distribution appears under two parametrizations (or here) $$ f(x) \propto x^{\alpha} (1-x)^{\beta} \tag{1} $$ or the one that seems to be used more commonly $$ f(x) \propto x^{\alpha-1} (1-x)^{...
2
votes
2answers
163 views

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 ...
1
vote
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 ...
5
votes
3answers
473 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 ...
0
votes
1answer
60 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. ...
0
votes
1answer
93 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 ...
0
votes
1answer
380 views

Beta Binomial Inverse CDF

There are p groups of size $n_1, n_2, ... , n_p$ each with number of successes $x_1, x_2, ... x_p$ and number of failures $n_1 - x_1, n_2 - x_2, ... , n_p - x_p$. $X_i$ ~ $Binom( n_i, p_i)$, where $...
1
vote
1answer
413 views

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 ...
0
votes
0answers
27 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 ...
9
votes
1answer
922 views

Prediction interval for a future proportion of successes under Binomial setting

Suppose I fit a Binomial regression and obtain the point estimates and variance-covariance matrix of the regression coefficients. That will allow me to get a CI for the expected proportion of ...