Metropolis Hasting and Choleski Approach: A case of Simulating Bivariate Normal Distribution
Sachin Kafle, Prakash Parajuli · 2025
Several methods had been proposed to simulate Bivariate Normal distribution, including Choleski Decompostion method, LU decomposition method, Power method, and Markov Chain Monte Carlo method etc. This report primarily focuses on the shortcomings of Choleski approach and demonstrates the advantage of using Metropolis Hasting (MCMC) method to obtain stationary distribution faster than comparatively Choleski approach. Just as any MCMC methods, Metropolis Hasting comes with its drawbacks which stems it from the faster convergence. Thus, Reparameterization of the target and proposal distribution is done for faster convergence. This report examines an reparameterized MCMC approach which shows significant improvement over Choleski approach.