I'm using the abcpmc code:
Approximate Bayesian Computing (ABC) Population Monte Carlo (PMC) implementation based on Sequential Monte Carlo (SMC) with Particle Filtering techniques.
described in the Approximate Bayesian computation for forward modeling in cosmology, Akeret et al. (2015) article.
It seems to work rather well, but I'm not sure about the convergence/stopping criteria. Looking at the method's algorithm, it's easy to see that it can get stuck trying to find models below the given threshold ($\epsilon_t$):
where $N$ is the number of "particles" used. What I currently do is to stop the process if at any step it spends more than a fixed amount of time finding those $N$ particles below the current threshold value (say 30 sec per particle as the maximum allowed time for some 20 particles, ie: 10 min of max time at any step).
My questions are:
- is this a reasonable approach (not the particular values I use, but the general method)?
- As far as I understand, unlike the standard MCMC, with ABC one expects the acceptance rate to decrease as the process moves forward, ideally reaching a value as small as possible. Can this also be used as a stopping criteria (stop if acceptance rate is below some fixed value)?
- Are all the samples collected by an ABC sampler effective/independent samples (or are they correlated as with the usual MCMC)? Could this be used as another stopping criteria (stop at a given value of effective/independent samples)?