Divide-and-conquer with sequential Monte Carlo

This document contains supplementary material for the paper ’Divide-and-Conquer with Sequential Monte Carlo’. In Section A we prove Propositions 1 and 2 and provide additional details on how these propositions can be extended to the more advanced D&C-SMC implementations discussed in Section 4 of the main paper. Section B provides detailed algorithmic descriptions of the (lightweight) mixture sampling method (Section 4.1 of the main paper) and tempering method (Section 4.2 of the main paper) in the context of the proposed D&C-SMC sampler. Sections C and D contain additional details and results for the two numerical examples presented in Sections 5.1 and 5.2 of the main paper, respectively. Finally, Section E provides an overview of the implementation used in Sections 5.2 and 5.3 of the main paper