Bayesian Nonparametric Estimation of Simpson's Index

Abstract

Simpson’s index is one of the oldest and most popular diversity indices. Traditionally, Simpson’s index has been estimated using frequentist methods, although Bayesian nonparametric estimation has been explored in recent years. Bayesian nonparametric estimation is an attractive alternative to frequentist estimation because it provides a theoretical framework for incorporating prior information while overcoming some of the limitations of parametric Bayesian approaches. Specifically, nonparametric priors do not require that we make an assumption about the true number of types in the population, something that is often unknown. This thesis introduces expressions for the bias, variance, and mean squared error for some existing Bayesian nonparametric estimators of Simpson’s index. These estimators of Simpson’s index require the specification of a concentration parameter and/or a discount parameter, and so we discuss various strategies for selecting these parameters. We also illustrate how these Bayesian nonparametric estimators compare to the standard frequentist estimators in an empirical study. The findings of this study indicate that the Bayesian nonparametric estimators with well-specified parameters outperform the frequentist estimators in terms of mean squared error.