The Bayesian information criterion (BIC) is widely used for variable selection. We focus on the regression setting for which variations of the BIC have been proposed. A version that includes the Fisher Information matrix of the predictor variables performed best in one published study. In this article, we extend the evaluation, introduce a performance measure involving how closely posterior probabilities are approximated, and conclude that the version that includes the Fisher Information often favors regression models having more predictors, depending on the scale and correlation structure of the predictor matrix. In the image analysis application that we describe, we therefore prefer the standard BIC approximation because of its relative simplicity and competitive performance at approximating the true posterior probabilities.

A flexible and effective set of procedures has been developed to reconstruct the temporal variation occurring during a geomagnetic survey. These procedures use regression techniques and the field measurements made at survey track intersections. They have been applied to both ship and aircraft survey data collected in open ocean areas to remove from 60 to 80 percent of the temporal variation. This paper presents these procedures and the results for one ship and one aircraft survey.