Markov Chain Monte Carlo Models, Gibbs Sampling, & Metropolis Algorithm for High-Dimensionality Complex Stochastic Problems

Abstract

Markov chain Monte Carlo (MCMC) methods have an important role in solving high dimensionality stochastic problems characterized by computational complexity. Given their critical importance, there is need for network and security risk management research to relate the MCMC quantitative methodological concerns with network and security risk applications. This article contributes to that research stream. The core quantitative methodological focus of the article is on Monte Carlo Models and MCMC Algorithms, Gibbs Sampling and Metropolis-Hastings Algorithm. Network and security risk management application focus is on how MCMC methods help solve previously unsolvable problems in computational statistical modeling of cryptography, cryptanalytics, and penetration testing; intrusion detection & prevention and anomaly detection; and, privacy in anonymity systems and social networks. Future quantitative methods applied research and development in MCMC and computational statistical computing to address systemic risk and model risk management is recommended.

Keywords: Bayesian Inference, Markov chain, Monte Carlo, High Dimensional Problems, High Dimensional Stochastics, Statistical Computing Algorithms, Metropolis-Hastings algorithm, Gibbs Sampling algorithm

JEL Classification: C10, C11, C13, C14, C15, C60, C61, C63