Bayesian Sequential Experimental Design for Binary Response Data with Application to Electromyographic Experiments

Abstract

We develop a sequential Monte Carlo approach for Bayesian analysis of the experimental design for binary response data. Our work is motivated by surface electromyographic (SEMG) experiments, which can be used to provide information about the functionality of subjects’ motor units. These experiments involve a series of stimuli being applied to a motor unit, with whether or not the motor unit fires for each stimulus being recorded. The aim is to learn about how the probability of firing depends on the applied stimulus (the so-called stimulus-response curve). One such excitability parameter is an estimate of the stimulus level for which the motor unit has a 50% chance of firing. Within such an experiment we are able to choose the next stimulus level based on the past observations. We show how sequential Monte Carlo can be used to analyse such data in an online manner. We then use the current estimate of the posterior distribution in order to choose the next stimulus level. The aim is to select a stimulus level that mimimises the expected loss of estimating a quantity, or quantities, of interest. We will apply this loss function to the estimates of target quantiles from the stimulus-response curve. Through simulation we show that this approach is more efficient than existing sequential design methods in terms of estimating the quantile(s) of interest. If applied in practice, it could reduce the length of SEMG experiments by a factor of three.