Bayesian Semiparametric Covariate Informed Multivariate Density Deconvolution

TL;DR

This paper introduces a Bayesian semiparametric method for multivariate density deconvolution that accounts for covariates, enabling more accurate estimation of long-term dietary intake distributions in nutritional studies.

Contribution

It presents a novel covariate-informed multivariate deconvolution approach using copula and tensor factorization techniques, allowing flexible density modeling and predictor selection.

Findings

Method effectively captures covariate effects on densities.

Simulation studies demonstrate accurate density recovery.

Application to nutritional data shows practical utility.

Abstract

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes. The problem of estimating the density of the latent long-term average intakes from their observed but error contaminated recalls then becomes a problem of multivariate deconvolution of densities. The underlying densities could potentially vary with the subjects' demographic characteristics such as sex, ethnicity, age, etc. The problem of density deconvolution in the presence of associated precisely measured covariates has, however, never been considered before, not even in the univariate setting. We present a flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution. Building on recent advances in copula deconvolution and conditional tensor factorization techniques, our proposed method not only allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors. Importantly, the method also allows the density of interest and the density of the measurement errors to vary with potentially different sets of predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The empirical efficacy of the proposed method is illustrated through simulation experiments. Its practical utility is demonstrated in the afore-described nutritional epidemiology applications in estimating covariate-adjusted long term intakes of different dietary components. Supplementary materials include substantive additional details and R codes are also available online.