A Note on the Evidence Approximation in Bayesian Experimental Design Models Based on an Orthonormal System

Abstract

In this paper, we first present a theorem on the relationship between the traditional model and a model based on an orthonormal system in experimental design. Using the theorem, the former model can be converted to the latter, and vice versa. Next, we introduce prior distributions over the hyperparameters for experimental design models to consider fully Bayesian predictions. Combining the conversion and a previous result, we show that we can make an approximation in which we set the hyperparameters to specific values determined by maximizing the evidence function.