This repository contains Python code used to compute resultants for the Beta-Binomial Maximum Likelihood Estimation (MLE) problem in the special case where each item receives exactly two ratings (n = 2). The code supports the derivation of the closed-form solution presented in Theorem 2 of our paper:
On the MLE for the Beta-Binomial Distribution
Daniel Berend, Yuri Chernyavsky, Luba Sapir
The likelihood equations for the Beta-Binomial model can be transformed into a system of two polynomial equations in two variables (α and β). Using elimination theory and resultants, we reduce this system to a single equation in one variable, enabling a closed-form solution.
This script:
- Defines the polynomial system for n = 2.
- Computes the resultant with respect to α and β using SymPy.
- Simplifies and factors the resultants for clarity.
- Python 3.8+
- https://www.sympy.org/
Install with:
pip install sympy