Latent Bayesian melding for integrating individual and population models
This addresses the challenge of combining coarse-grained and detailed models in statistical inference, though it appears incremental as an extension of existing melding methods.
The paper tackles the problem of integrating individual-level and population-level statistical models by proposing latent Bayesian melding, which averages distributions under a logarithmic opinion pool framework. In a case study on electricity disaggregation, it shows significantly more accurate predictions compared to generalized moment matching.
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.