Markov Chain Monte Carlo in a Dynamical System of Information Theoretic Particles

Tokunbo Ogunfunmi and Manas Deb

A chapter in The Monte Carlo Methods - Recent Advances, New Perspectives and Applications from IntechOpen

Abstract: In Bayesian learning, the posterior probability density of a model parameter is estimated from the likelihood function and the prior probability of the parameter. The posterior probability density estimate is refined as more evidence becomes available. However, any non-trivial Bayesian model requires the computation of an intractable integral to obtain the probability density function (PDF) of the evidence. Markov Chain Monte Carlo (MCMC) is a well-known algorithm that solves this problem by directly generating the samples of the posterior distribution without computing this intractable integral. We present a novel perspective of the MCMC algorithm which views the samples of a probability distribution as a dynamical system of Information Theoretic particles in an Information Theoretic field. As our algorithm probes this field with a test particle, it is subjected to Information Forces from other Information Theoretic particles in this field. We use Information Theoretic Learning (ITL) techniques based on Rényi's ?-Entropy function to derive an equation for the gradient of the Information Potential energy of the dynamical system of Information Theoretic particles. Using this equation, we compute the Hamiltonian of the dynamical system from the Information Potential energy and the kinetic energy. The Hamiltonian is used to generate the Markovian state trajectories of the system.

Keywords: Hamiltonian Monte Carlo (HMC); information theoretic learning; Kernel density estimator (KDE); Markov chain Monte Carlo; Parzen window; Rényi's entropy; information potential (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.intechopen.com/chapters/79141 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:244766

DOI: 10.5772/intechopen.100428

Access Statistics for this chapter

More chapters in Chapters from IntechOpen
Bibliographic data for series maintained by Slobodan Momcilovic (ai@intechopen.com).