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

23 Pages Posted: 23 Jan 2015

See all articles by Yogesh Malhotra

Yogesh Malhotra

Amazon Web Services Partner; Global Risk Management Network, LLC

Date Written: May 8, 2014

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

Suggested Citation

Malhotra, Yogesh, Markov Chain Monte Carlo Models, Gibbs Sampling, & Metropolis Algorithm for High-Dimensionality Complex Stochastic Problems (May 8, 2014). Available at SSRN: https://ssrn.com/abstract=2553537 or http://dx.doi.org/10.2139/ssrn.2553537

Yogesh Malhotra (Contact Author)

Amazon Web Services Partner ( email )

United States

HOME PAGE: http://YogeshMalhotra.com/

Global Risk Management Network, LLC ( email )

New Hartford, NY 13413
United States
+1-(646) 801-3644 (Phone)

HOME PAGE: http://YogeshMalhotra.com/bio.html

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