  In many statistical problems, a more coarse-grained model may be suitable for
population-level behaviour, whereas a more detailed model is appropriate for
accurate modelling of individual behaviour. This raises the question of how to
integrate both types of models. Methods such as posterior regularization follow
the idea of generalized moment matching, in that they allow matching
expectations between two models, but sometimes both models are most
conveniently expressed as latent variable models. We propose latent Bayesian
melding, which is motivated by averaging the distributions over populations
statistics of both the individual-level and the population-level models under a
logarithmic opinion pool framework. In a case study on electricity
disaggregation, which is a type of single-channel blind source separation
problem, we show that latent Bayesian melding leads to significantly more
accurate predictions than an approach based solely on generalized moment
matching.
