Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model

TL;DR

This paper develops efficient estimation methods for joint probabilities of two correlated traits in group testing, introducing an EM algorithm for the MLE and closed-form estimators, with application to plant virus transmission.

Contribution

It introduces a novel EM algorithm for the MLE in two-trait group testing and proposes closed-form estimators to improve bias and mean square error.

Findings

EM algorithm guarantees convergence to the global maximum

Closed-form estimators reduce bias and MSE

Application to Potato virus Y transmission estimation

Abstract

Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of situations routinely encountered in applications. More recently, there has been growing interest in using group testing to simultaneously estimate the joint probabilities of two correlated traits using a multinomial model. Unfortunately, basic estimation results, such as the maximum likelihood estimator (MLE), have not been adequately addressed in the literature for such cases. In this paper, we show that finding the MLE for this problem is equivalent to maximizing a multinomial likelihood with a restricted parameter space. A solution using the EM algorithm is presented which is guaranteed to converge to the global maximizer, even on the boundary of the parameter space. Two additional closed form estimators are presented with the goal of minimizing the bias and/or mean square error. The methods are illustrated by considering an application to the joint estimation of transmission prevalence for two strains of the Potato virus Y by the aphid myzus persicae.