Options for temperature selection in maximum entropy approach to obtaining source levels and seabed porosity

Abstract

When analyzing acoustical data, the goal often is to find source strength and characteristics of the environment. Instead of finding point estimates, a more informative approach is to find probability distributions from either a Bayesian approach or a maximum entropy approach. The Bayesian approach relies on prior distributions and an estimate of the noise covariance, while the maximum entropy approach relies on an estimate of a “temperature” derived from analogies with statistical mechanics. Different representations of the temperature are appropriate in different situations. The best choice is related to confidence in the model being used and if the model captures all the relevant physics. Examples of how the choice of temperature impacts the posterior distributions are shown using a toy model and a real-world application. Specifically, the maximum entropy approach is applied to models of transiting ship noise to obtain posterior distributions of source level and porosity of the sediment layer. These examples show that the selection of temperature significantly impacts the posterior distributions. [Work supported by the Office of Naval Research.]