Defining uncertainty with maximum entropy method.

Abstract

The maximum entropy (ME) method was strongly defended and advocated by E. T. Jaynes as a means to define uncertainty. Here, the ME method is applied to the estimation of ocean waveguide parameter probability distributions from measured acoustic data. An ME analysis produces a canonical distribution, well known from equilibrium statistical mechanics, which is the distribution that maximizes the entropy subject to constraints that reflect selected features of the measured data and a model. The ME method gives the most conservative distribution based only on the measured data and observed features. A Bayesian approach also has the goal of defining uncertainty, but starts from the specification of the likelihood function and the model priors. Data noise is naturally handled in the specification of the likelihood function. The discussion introduces simple examples, showing basic relationships between the constraints in ME and the maximum likelihood estimation. In special cases the form of the likelihood function used in Bayesian conditionalization can be derived from the ME approach. The form of the cost function is an important consideration in comparing ME and Bayesian methods of inferences. In general ME and Bayesian inferences lead to different results. [Work supported by ONR Code 321 OA.]