On a Multiplicative Algorithm for Computing Bayesian D-optimal Designs

TL;DR

This paper proves the monotonicity of a multiplicative algorithm for Bayesian D-optimal design computation using the minorization-maximization principle, confirming a previous conjecture.

Contribution

It establishes the monotonicity of the algorithm, providing theoretical validation for its use in Bayesian D-optimal design.

Findings

Proves the monotonicity of the algorithm.

Confirms a conjecture by Dette, Pepelyshev, and Zhigljavsky.

Uses the minorization-maximization principle for the proof.

Abstract

We use the minorization-maximization principle (Lange, Hunter and Yang 2000) to establish the monotonicity of a multiplicative algorithm for computing Bayesian D-optimal designs. This proves a conjecture of Dette, Pepelyshev and Zhigljavsky (2008).