The use of a single pseudo-sample in approximate Bayesian computation

Abstract

We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that multiple pseudo-samples cannot substantially increase (and can substantially decrease) the efficiency of the algorithm as compared to employing a high-variance estimate based on a single pseudo-sample. We show that this conclusion also holds for a Markov chain Monte Carlo version of ABC, implying that it is unnecessary to tune the number of pseudo-samples used in ABC-MCMC. This conclusion is in contrast to particle MCMC methods, for which increasing the number of particles can provide large gains in computational efficiency.

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

“…McKinley et al (2009) demonstrated that repeating simulations of the data given θ does not seem to contribute (much) to an improved approximation of the posterior by the ABC sample. This observation appears to be consistent with the findings of Bornn et al (2016) who proved that K = 1 is usually very close to optimal. A review of ABC-MCMC algorithms can be found in Sisson and Fan (2011).…”

Improving Approximate Bayesian Computation via Quasi-Monte Carlo

“…Del Moral et al (2012). Bornn et al (2015) showed that M = 1 usually represents the best variance vs CPU time trade-off when using Monte Carlo sampling, however we shall see that this result does not hold when using QMC. Later on in the paper, we shall consider an alternative unbiased estimator, based on properties of the negative binomial distribution.…”

Approximate Bayesian Computation and Simulation-Based Inference for Complex Stochastic Epidemic Models

“…Mixing can generally be improved by increasing the tolerance(s), but at the cost of further information loss in the approximate posterior. Under the same assumptions as above, Bornn et al [2017] show that for a simple rejection sampling ABC algorithm, n = 1 is indeed optimal. In practice ABC-SMC samplers, such as described in Algorithm 1.1b seem to perform better for low n [see e.g.…”

“…Pitt et al, 2012, Sherlock et al, 2015, Doucet et al, 2015. In the specific case of ABC-MCMC with uniform matching, Bornn et al [2017] show that setting n = 1 results in run times that are at most a factor of 2 away from the optimum choice (obtained for some n > 1). However, their results also make the assumption that simulation run times are approximately constant, which is often not true for epidemic systems, where run times for individual simulations can often vary greatly even for fixed parameter inputs.…”