“…the chosen statistic needs to be a so-called sufficient statistic in that any information about the parameter of interest which is contained in the data, is also contained in the summary statistic.”
Elise Jenningsa and Maeve Madigan arXived a paper on a new Python code they developed for implementing ABC-SMC, towards astronomy or rather cosmology applications. They stress the parallelisation abilities of their approach which leads to “crucial speed enhancement” against the available competitors, abcpmc and cosmoabc. The version of ABC implemented there is “our” ABC PMC where particle clouds are shifted according to mixtures of random walks, based on each and every point of the current cloud, with a scale equal to twice the estimated posterior variance. (The paper curiously refers to non-astronomy papers through their arXiv version, even when they have been published. Like our 2008 Biometrika paper.) A large part of the paper is dedicated to computing aspects that escape me, like the constant reference to MPIs. The algorithm is partly automated, except for the choice of the summary statistics and of the distance. The tolerance is chosen as a (large) quantile of the previous set of simulated distances. Getting comments from the designers of abcpmc and cosmoabc would be great.
“It is clear that the simple Gaussian Likelihood assumption in this case, which neglects the effects of systematics yields biased cosmological constraints.”
The last part of the paper compares ABC and MCMC on a supernova simulated dataset. Which is somewhat a dubious comparison since the model used for producing the data and running ABC is not the same as the Gaussian version used with MCMC. Unsurprisingly, MCMC then misses the true value of the cosmological parameters and most likely and more importantly the true posterior HPD region. While ABC SMC (or PMC) proceeds to a concentration around the genuine parameter values. (There is no additional demonstration of how accelerated the approach is.)