Bayesian semiparametric multivariate density deconvolution via stochastic rotation of replicates

In multivariate density deconvolution, the distribution of a random vector needs to be estimated from replicates contaminated with measurement errors. A novel approach to multivariate deconvolution is proposed by stochastically rotating and stretching or contracting the replicates toward the corresponding true latent values. The method further accommodates conditionally heteroscedastic measurement errors commonly observed in many real data applications. The estimation and inference schemes are developed within a Bayesian framework implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of the analysis. The method's efficacy is demonstrated empirically through simulation experiments and practically in estimating the long-term joint average intakes of different dietary components from their measurement error-contaminated 24-hour dietary recalls.