Bayesian Semiparametric Multivariate Density Deconvolution

TL;DR

This paper introduces robust Bayesian semiparametric methods for multivariate density deconvolution when measurement error distributions are unknown, using replicated proxies and modeling error variability related to the unobserved variables.

Contribution

It develops novel Bayesian approaches that handle unknown measurement error distributions and their dependence on unobserved variables, extending existing methods to more realistic scenarios.

Findings

Methods effectively recover true density in simulations

Approach handles unknown error distributions with replicated proxies

Application successfully estimates dietary consumption patterns

Abstract

We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations being contaminated with additive measurement errors. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density is not known but replicated proxies are available for each unobserved value of the random vector. Additionally, we allow the variability of the measurement errors to depend on the associated unobserved value of the vector of interest through unknown relationships which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in many novel ways to meet the modeling and computational challenges. Theoretical results that show the flexibility of the proposed methods are provided. We illustrate the efficiency of the proposed methods in recovering the true density of interest through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls.