Bayesian Adaptive Estimation with Theoretical Bound: An Exploration-Exploitation Approach

Abstract

This paper investigates the theoretical bound to reduce the parameter uncertainty in Bayesian adaptive estimation for psychometric functions and proposes an exploration-exploitation (E-E) approach to improve the computation efficiency for parameter estimations. When the experimental trial goes on, the uncertainty of the parameters decreases dramatically and the space between the maximal mutual information and the theoretical bound gets narrower, so the advantage of classical Bayesian adaptive estimation algorithm diminishes. This approach tries to trade off the exploration (parameter posterior uncertainty) and the exploitation (parameter mean estimation). The experimental results show that the proposed E-E approach estimates parameters for psychometric functions with same convergence and reduces the computation time by more than 34.27%, compared with the classical Bayesian adaptive estimation.