Gaussian process model selection for parameter estimation in ocean acoustics

Abstract

The dynamic nature of the ocean environment presents numerous challenges to parameter estimation in ocean acoustics. We present a variational Bayesian method which selects an optimal model for parameter estimation in ocean acoustics using Gaussian process (GP) regression. GP model selection is based on Bayesian model selection, which treats the parameters and kernel selection of the model as hyperparameters and uses Bayesian inference to compute a model’s likelihood with respect to its hyperparameters. However, in Bayesian model selection, the integrals over parameter space are often intractable and require approximation or sampling methods such as Markov chain Monte Carlo. GP renders these integrals tractable by treating hyperparameters as multivariate Gaussian distributions, which greatly speeds up the optimization. Furthermore, model selection using GPs allows for straightforward evaluation of uncertainty in the selected model’s likelihood. In this study, we compare results of acoustic parameter estimation from Bayesian and GP model selection using an ocean acoustic propagation model.