Sequential Monte Carlo without likelihoods

Abstract

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

An adaptive sequential Monte Carlo method for approximate Bayesian computation

“…Conversely, if the { n } decrease too quickly, then, with high probability, all the weights W (i) n can equal zero; hence the SMC sampler approximation would have collapsed. To prevent such a collapse, the algorithms in [17] and [18] targeting π n (θ, x|y) generate particles…”

“…Some concerns have been raised about this algorithm [4]; this debate is not contributed to. It is just mentioned that [4,19,21] developed methods to improve the performance of the algorithm in [18] by using an approximation of the 'optimal' backward kernel in [8,Section 2.4]. This leads to algorithms of computational complexity that are quadratic in the number of particles and still requires a careful determination of the sequence of tolerance levels.…”

“…These MCMC schemes can still perform poorly if the tolerance level is small. Consequently various sequential Monte Carlo (SMC) methods have been recently constructed as an alternative to MCMC methods [4,17,18,21]. The key idea is to decompose the difficult problem of sampling from π (θ, x|y) into a series of simpler subproblems.…”

“…In the ABC context, [18] used the SMC samplers methodology developed in [8] coupled with a partial rejection proposal (PRC). Some concerns have been raised about this algorithm [4]; this debate is not contributed to.…”

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation

“…We therefore refer to this as the ABC-PMC algorithm. There is also a wider family of related ABC-SMC algorithms, including Sisson et al (2007) and Del Moral et al (2012), which update their particles in more complex ways based on MCMC moves, as described in Del Moral et al (2006). (c) Simulate dataset D * from the model using parameters θ * .…”