B0944
Title: Generalized Bayes for compositional data
Authors: Abhi Datta - Johns Hopkins Bloomberg School of Public Health (United States) [presenting]
Abstract: Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited, and the existing models are often difficult to interpret in the compositional space, due to their use of complex log-ratio transformations. A transformation-free linear regression model is developed where the expected value of the compositional outcome is expressed as a single Markov transition from the compositional predictor. Generalized Bayesian inference, with Kullback-Leibler loss functions, is used based only on a first-moment assumption. The method is robust to different generating mechanisms for compositional data and allows 0s and 1s in the compositional outputs thereby including categorical outputs as a special case. A fast and efficient Gibbs sampler is outlined using a rounding and coarsening approximation to the loss functions. Posterior consistency, asymptotic normality and valid coverage of interval estimates are established. The method is used for calibrating compositional (probabilistic) outputs on causes of death to improve cause-specific mortality estimates in low- and middle-income countries.
