Paper:
Latent Bayesian melding for integrating individual and population models
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 singlechannel 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.

Review:
This paper proposes a method to integrate two prior belief under different views and applies it to a specific engineering problem called energy disaggregation. The method is based on an approach called Bayesian melding proposed previously. The authors replace a fixed prior in Bayesian melding with a prior having latent variables, and MAP-estimate the latent variables. The result shows the proposed method may improve the separation of energy consumption timeseries of individual appliances from total energy.The energy disaggregation problem is interesting in its own right and it is understandable that the integration of different types of prior belief should be important for this kind of problem. However, the proposed method is seen just an application of Bayesian melding once the latent variables in the prior have been fixed, so the method is quite trivial from general point of view. On the other hand, the method might contribute to the specific field where the energy disaggregation problem is relevant, while it was unclear to me from the manuscript.Although the paper is well written overall, the presentation of the background and the explanation of Bayesian melding (Sections 1 and 2) should be improved. The introduction is not very specific so it was difficult at the first reading to see what those methods mentioned here (posterior regularization, learning with measurements, etc. and also Bayesian melding) will actually do. Section 2 is quite problematic as it only gives the formula of Bayesian melding. The authors should introduce when and why having two different priors should be reasonable, and how it is related to the notion of individual and population mentioned in Introduction. Some more justification about the form of \tilde{p}_S(S) should also be necessary.Minor comments: - Sec.2: usuall -> usually, invertable -> invertible - Give the definition of c_\alpha - Is there any reasonable method to select alpha?