This paper describes a Markov chain Monte Carlo (MCMC) sampling approach for the estimation of not only the radio refractivity profiles from radar clutter but also the uncertainties in these estimates. This is done by treating the refractivity from clutter (RFC) problem in a Bayesian framework. It uses unbiased MCMC sampling techniques, such as Metropolis and Gibbs sampling algorithms, to gather more accurate information about the uncertainties. Application of these sampling techniques using an electromagnetic split-step fast Fourier transform parabolic equation propagation model within a Bayesian inversion framework can provide accurate posterior probability distributions of the estimated refractivity parameters. Then these distributions can be used to estimate the uncertainties in the parameters of interest. Two different MCMC samplers (Metropolis and Gibbs) are analyzed and the results compared not only with the exhaustive search results but also with the genetic algorithm results and helicopter refractivity profile measurements. Although it is slower than global optimizers, the probability densities obtained by this method are closer to the true distributions.

Quantifying uncertainty for parameter estimates obtained from matched-field geoacoustic inversions using a Bayesian approach requires estimation of the uncertainties in the data due to ambient noise as well as modeling errors. In this study, the variance parameter of the Gaussian error model, hereafter called error variance, is assumed to describe the data uncertainty. In practice, this parameter is not known a priori, and choosing a particular value is often difficult. Hence, to account for the uncertainty in error variance, several methods are introduced for implementing both the full and empirical Bayesian approaches. A full Bayesian approach that permits uncertainty of the error variance to propagate through the parameter estimation processes is a natural way of incorporating the uncertainty of error variance. Due to the large number of unknown parameters in the full Bayesian uncertainty analysis, an alternative, the empirical Bayesian approach is developed, in which the posterior distributions of model parameters are conditioned on a point estimate of the error variance. Comparisons between the full and empirical Bayesian inferences of model parameters are presented using both synthetic and experimental data. (c) 2006 Acoustical Society of America.