Nonparametric EM Algorithms for estimating prior distributions

摘要

Consider a sequence of repetitive experiments E1, E2,..., EN. Each Ei is represented by a pair of random vectors (Yi, θi) such that Yi is observed, θi is not observed, and the conditional density of Yi given θi is known. The θi's are independent and identically distributed with common but unknown distribution function F*(θ). The problem is to estimate F* given the data Y1, Y2,..., YN. Two nonparametric maximum likelihood methods based on the EM algorithm are presented. Motivation for this problem comes from the analysis of the distribution of parameters in pharmacokinetic models based on population data.