Markov chain Monte Carlo posterior sampling with the Hamiltonian method.
A major advantage of Bayesian data analysis is that provides a characterization of the uncertainty in the model parameters estimated from a given set of measurements in the form of a posterior probability distribution. When the analysis involves a complicated physical phenomenon, the posterior may not be available in analytic form, but only calculable by means of a simulation code. In such cases, the uncertainty in inferred model parameters requires characterization of a calculated functional. An appealing way to explore the posterior, and hence characterize the uncertainty, is to employ the Markov Chain Monte Carlo technique. The goal of MCMC is to generate a sequence random of parameter x samples from a target pdf (probability density function), {pi}(x). In Bayesian analysis, this sequence corresponds to a set of model realizations that follow the posterior distribution. There are two basic MCMC techniques. In Gibbs sampling, typically one parameter is drawn from the conditional pdf at a time, holding all others fixed. In the Metropolis algorithm, all the parameters can be varied at once. The parameter vector is perturbed from the current sequence point by adding a trial step drawn randomly from a symmetric pdf. The trial position is either accepted or rejected on the basis of the probability at the trial position relative to the current one. The Metropolis algorithm is often employed because of its simplicity. The aim of this work is to develop MCMC methods that are useful for large numbers of parameters, n, say hundreds or more. In this regime the Metropolis algorithm can be unsuitable, because its efficiency drops as 0.3/n. The efficiency is defined as the reciprocal of the number of steps in the sequence needed to effectively provide a statistically independent sample from {pi}.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 975267
- Report Number(s):
- LA-UR-01-1410; TRN: US201008%%24
- Resource Relation:
- Conference: "Submitted to: Sensitivity Analysis of Model Output, Madrid, Spain, June 18-20, 2001"
- Country of Publication:
- United States
- Language:
- English
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