Estimating Parameter Uncertainties Using Hybrid Monte Carlo-Least Squares Support Vector Machine Method

Estimating parameters uncertainties is an important issue in geoacoustic inversion. From the Bayesian rule, the geoacoustic parameters uncertainties are characterized by their posterior probability distributions (PPDs). In present, Grid Searchching (GS), Monte Carlo integration (MCI) and a hybrid SA(Simulated Annealing) MCMC(Markov Chain Monte Carlo) method has been developed to estimate the PPD. However, these methods require a large amount of computation time and become impractical. The hybrid Monte Carlo (MC)-Least Squares Support Vector Machine (LSSVM) method is presented in this paper. The LSSVM algorithm is first applied to approximate the functional relations between the PPDs and the geoacoustic parameters. Then the PPDs may be approximated by a LSSVM model, which is trained using fewer forward model samples than GS, MCI and SA-MCMC. Finally, comparison of GS, MCI, SAMCMC and MC-LSSVM for a noisy synthetic benchmark test case indicates that the MC-LSSVM provides reasonable estimates of the parameters PPDs while requiring less computation time.