How to fit a beta-binomial model in python

Answer
To fit a beta-binomial model in Python, you can use the scipy.stats.betabinom function. The beta-binomial distribution is a binomial distribution with a probability of success that follows a beta distribution. Here's a step-by-step guide to fitting a beta-binomial model:
  1. Import the necessary libraries:
python
import numpy as np from scipy.stats import betabinom
  1. Define the number of trials (n), the number of successes (k), and the alpha and beta parameters (a and b).
python
n, k, a, b = 100, 60, 2.3, 0.63
  1. Calculate the probability mass function (PMF) for the given data:
python
pmf = betabinom.pmf(k, n, a, b)
  1. Calculate the negative log-likelihood function:
python
def bbll(parms, k, n): alpha, beta = parms ll = betabinom.logpmf(k, n, alpha, beta) return -ll.sum()
  1. Use the minimize function to find the maximum likelihood estimates for the alpha and beta parameters:
python
result = minimize(bbll, [1, 1], args=(pmf, n), method='Nelder-Mead')
  1. Print the results:
python
print(result.x)
This code will output the maximum likelihood estimates for the alpha and beta parameters of the beta-binomial model.
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