2017/10/26 by Abhirup Mallik, Galin L. Jones, Mallik, Abhirup +1
Computer Science · Mathematics · #65C40 (Secondary) #65C60 (Primary) 65C05 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1710.09759
openalex publication_date 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new kernel for Metropolis Hastings called Directional Metropolis Hastings (DMH) with multivariate update where the proposal kernel has state dependent covariance matrix. We use the derivative of the target distribution at the current state to change the orientation of the proposal distribution, therefore producing a more plausible proposal. We study the conditions for geometric ergodicity of our algorithm and provide necessary and sufficient conditions for convergence. We also suggest a scheme for adaptively update the variance parameter and study the conditions of ergodicity of the adaptive algorithm. We demonstrate the performance of our algorithm in a Bayesian generalized linear model problem.