Bayesian Analysis. II. Signal Detection and Model Selection

. In the preceding paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T 1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockham's razor: theorize about possible models, compare these to experiment; and select the simplest model that "best" fits the data. Introduction The parameter estimation problem discussed in the preceding paper [1] tells how to estimate the parameters given a model; but it does not tell how to sel..