Model selection using Bayesian samples: An introduction to the deviance information criterion

Abstract

This paper presents the deviance information criterion (DIC) as a metric for model selection based on Bayesian sampling approaches, with examples from seabed geoacoustic and/or scattering inversion. The DIC uses all samples of a distribution to approximate Bayesian evidence, unlike more common measures such as the Bayesian information criterion, which only use point estimates. The DIC uses distribution samples to approximate Bayesian evidence, unlike more common measures such as the Bayesian information criterion based on point estimates. Hence the DIC is more appropriate for non-linear Bayesian inversions utilizing posterior sampling. Two examples are considered: determining the dominant seabed scattering mechanism (interface and/or volume scattering), and choosing between seabed profile parameterizations based on smooth gradients (polynomial splines) or discontinuous homogeneous layers. In both cases, the DIC is applied to trans-dimensional inversions of simulated and measured data, utilizing reversible jump Markov chain Monte Carlo sampling. For the first case, the DIC is found to correctly select the true scattering mechanism for simulations, and its choice for the measured data inversion is consistent with sediment cores extracted at the experimental site. For the second case, the DIC selects the polynomial spline parameterization for soft seabeds with smooth gradients. [Work supported by ONR.]