Bayesian inference for low count time series models with intractable likelihoods

Last evening, I read a nice paper with the above title by Drovandi, Pettitt and McCutchan, from QUT, Brisbane. Low count refers to observation with a small number of integer values. The idea is to mix ABC with the unbiased estimators of the likelihood proposed by Andrieu and Roberts (2009) and with particle MCMC… And even with a RJMCMC version. The special feature that makes the proposal work is that the low count features allows for a simulation of pseudo-observations (and auxiliary variables) that may sometimes authorise an exact constraint (that the simulated observation equals the true observation). And which otherwise borrows from Jasra et al. (2013) “alive particle” trick that turns a negative binomial draw into an unbiased estimation of the ABC target… The current paper helped me realise how powerful this trick is. (The original paper was arXived at a time I was off, so I completely missed it…) The examples studied in the paper may sound a wee bit formal, but they could lead to a better understanding of the method since alternatives could be available (?). Note that all those examples are not ABC per se in that the tolerance is always equal to zero.

The paper also includes reversible jump implementations. While it is interesting to see that ABC (in the authors’ sense) can be mixed with RJMCMC, it is delicate to get a feeling about the precision of the results, without a benchmark to compare to. I am also wondering about less costly alternatives like empirical likelihood and other ABC alternatives. Since Chris is visiting Warwick at the moment, I am sure we can discuss this issue next week there.