Presented at *Univ. Bretagne Occidentale*, Nov. 16, 2000, Brest, France

## Use of Markov Chain Monte Carlo to estimate uncertainties in Bayesian reconstructions based on deformable models

Kenneth M. Hanson

*Los Alamos National Laboratory*
### Abstract

The aim of the Markov Chain Monte Carlo technique is to produce a sequence of parameter vectors that represent random draws from a probability density function (pdf). The pdf of interest in Bayesian analysis is typically the posterior distribution. Because of its simplicity, the most often used MCMC technique is the Metropolis algorithm. Issues of burn in and convergence are introduced. The efficiency of the MCMC technique is determined by estimating the autocorrelation of each parameter. More advanced algorithms include the Metropolis-Hastings, Langevin, and Hamiltonian-hybrid algorithms. An example is given of using MCMC to assess the uncertainties in a tomographic reconstruction from two views. This difficult problem is solved in a Bayesian framework through the use of a deformable module to describe the boundary of the object, whose interior density is known to be uniform.

**Keywords:** Markov chain Monte Carlo, Metropolis algorithm, Metropolis-Hastings, Hamiltonian hybrid technique, MCMC convergence, burn in, MCMC efficiency, autocorrelation, Bayesian tomographic reconstruction, deformable model, uncertainty assessment

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Send e-mail to author at kmh@hansonhub.com