## Is ABC-PRC truly PRC?

**W**hen re-reading the supplementary material in the Appendix of Sisson et al. (2007b) yesterday, I found I have an additional difficulty with the ABC-PRC algorithm that is related with the partial rejection control (PRC) perspective. Indeed, the PRC idea as described in Jun Liu’s 2001 book is to resample from a population of weighted particles by randomly pruning particles with weights below a certain threshold ** c**, replacing them by new particles obtained by propagating an existing particle by an SMC step and modifying the weights accordinly. The PRC justification in ABC-PRC is however to “

*suppose we then implement the PRC algorithm for some*” (p. 1764). This justification cannot hold as there is no such

**c>0**such that only identically zero weights are smaller than**c****. If one picks a**

*c***lesser than all the realised weights, it becomes a function of the particles and modifies the distribution of the weighted particles. If**

*c***, which is the only constant possible for keeping all non-zero weights, the algorithm is no longer of the PRC form. So the validation of the ABC-PRC algorithm cannot proceed from a partial rejection principle, but rather from a regular rejection principle as earlier ABC algorithms…**

*c=0*
July 24, 2010 at 6:15 am

[…] and Pettitt mistakenly consider the method to include partial rejection control, as argued in this earlier post—, to Beaumont et al.’s ABC-PMC (2009). The paper also advances the idea of adapting the […]