  Environmental health researchers may aim to identify exposure patterns that
represent sources, product use, or behaviors that give rise to mixtures of
potentially harmful environmental chemical exposures. We present Bayesian
non-parametric non-negative matrix factorization (BN^2MF) as a novel method to
identify patterns of chemical exposures when the number of patterns is not
known a priori. We placed non-negative continuous priors on pattern loadings
and individual scores to enhance interpretability and used a clever
non-parametric sparse prior to estimate the pattern number. We further derived
variational confidence intervals around estimates; this is a critical
development because it quantifies the model's confidence in estimated patterns.
These unique features contrast with existing pattern recognition methods
employed in this field which are limited by user-specified pattern number, lack
of interpretability of patterns in terms of human understanding, and lack of
uncertainty quantification.
