Bayesian Statistical Models: Optimized Python Implementations

This repository contains highly optimized Python implementations of three fundamental Bayesian statistical models. Each implementation focuses on computational efficiency, numerical stability, and vectorization, replacing standard iterative loops with linear algebra operations (NumPy/SciPy) and JIT compilation (Numba) where appropriate.

📂 Repository Structure

File	Model	Key Techniques
GP.py	Gaussian Process Regression	Cholesky Decomposition, SciPy cdist
BayesianFM.py	3D Bayesian Finite Mixture	Vectorized Gibbs Sampling, Log-Sum-Exp Trick
BayesianHMMGibbs.py	Bayesian Hidden Markov Model	FFBS Algorithm, Numba JIT Compilation

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🚀 Installation & Dependencies

To run these scripts, you will need a standard scientific Python environment.

pip install numpy scipy matplotlib numba