On Particle Learning

This document is the aggregation of six discussions of Lopes et al. (2010) that we submitted to the proceedings of the Ninth Valencia Meeting, held in Benidorm, Spain, on June 3-8, 2010, in conjunction with Hedibert Lopes' talk at this meeting, and of a further discussion of the rejoinder by Lopes et al. (2010). The main point in those discussions is the potential for degeneracy in the particle learning methodology, related with the exponential forgetting of the past simulations. We illustrate in particular the resulting difficulties in the case of mixtures.