Discussion on the paper by Andrieu, Doucet and Holenstein
Nick Whiteley · 2004
I offer my thanks to the authors for an inspirational paper. Their approach to constructing extended target distributions is powerful, can be exploited further and applied elsewhere. A key ingredient is the elucidation of the probability model underlying a SMC algorithm and the genealogical tree structures it generates. Two further developments on this theme are described below. Firstly, at the end of one Conditional SMC run in the PG algorithm, the authors suggest sampling K from its full conditional under ˜π N, then deterministically tracing back the ancestral lineage of X K T, to yield X K 1:T: = (X BK