Is ABC-PRC truly PRC?

When 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 c>0 such that only identically zero weights are smaller than c” (p. 1764). This justification cannot hold as there is no such 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=0, 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…

One Response to “Is ABC-PRC truly PRC?”

  1. […] 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 […]

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