Bayesian Semiparametric Covariate Informed Multivariate Density Deconvolution

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