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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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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28 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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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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210 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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2answers
136 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 $\...
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245 views

Beta distribution

After studying about the beta distribution I understood that the beta density function is used to find the densities for the probabilities. Densities may range from 0 to inf. That is if the density of ...
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1answer
270 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 $...
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2k views

Estimate beta binomial distribution

I have a dataset as follows: ...
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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)}...
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Multi-armed bandit where you must pull N pulls in T timesteps

Multi-armed bandit where you must pull N pulls in T timesteps Consider the beta-Bernoulli multi-armed bandit, with the following wrinkle: We have a total of $T$ time steps. We must pull $N$ pulls ...
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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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1answer
267 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) ...
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1answer
141 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 ...
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Design of a triangular test (or 2-out-of-5) when there is intra-group variability of samples

I would like to submit to an expert group a set of images from two genetically different types of plants to see if they can find a difference. I have 20 images for each of the two types. Images are ...
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236 views

Posterior of Beta Distribution

Let $X$ be the number of packets that fail to reach their destination nodes from $n$ = 100 randomly selected packets. Use the Beta-binomial formulation to specify the posterior distribution $p(\theta|...
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230 views

Translating user-defined joint-distribution from PyMC to PyMC3

I'm attempting to set up a simple beta binomial hierarchical model with an uninformative prior in PyMC3. I've read that the uninformative prior for this model should have alpha and beta hyper-...
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1answer
791 views

Convert probabilities of “binomial events” into beta distribution for binomial parameter (theta)

I have three events that essentially arise from a binomial distribution with k=2, i.e., X~Binomial(theta,n=2). Given some model and data I obtained a conditional (pos distribution for a particular X_i,...
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68 views

Is it possible to validate very small p-values via bootstrap?

Suppose I want to see whether the p-values generated by a certain parametric method are close to the “true” p-values. To avoid relying on any parametric assumptions, the latter are produced via ...
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479 views

Calculate expected value from discrete beta distribution

I have a lookup table in 2 variables, $Z_l$ and $T_l$. So, $Z_l$ and $T_l$ are vectors with same length where $Z_l$ goes from 0 to 1 and $T_l$ varies between 300 and 2000. If you are curious, $Z_l$ ...
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107 views

Recursive Bayesian Estimation, $p(C_k|\mathbf{x})$ as (discrete) likelihood

I''ve been struggeling with this problem for the last couple of days. The main goal is to use the probabilistic classification output $p(C_k|\mathbf{x})$, from for example a logistic regression, to ...