Approximate Bayesian Computation via Population Monte Carlo and Classification
This addresses inefficiencies in likelihood-free inference for fields like biology, though it appears incremental as it builds on existing PMC and classification methods.
The paper tackles the problem of inefficient and subjective sampling in Approximate Bayesian Computation (ABC) for likelihood-free inference by proposing Classification-PMC, which blends adaptive proposals and classification to produce posterior samples without subjectivity. The result shows that Classification-PMC outperforms state-of-the-art methods like ratio estimation and SMC ABC when simulations from the likelihood are computationally difficult.
Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient particle proposals in high dimensions, and subjectivity in the choice of summary statistics, discrepancy measure, and error tolerance. Sequential Monte Carlo (SMC) methods have been combined with ABC to improve the efficiency of particle proposals, but suffer from subjectivity and require many simulations from the likelihood function. Likelihood-Free Inference by Ratio Estimation (LFIRE) leverages classification to estimate the posterior density directly but does not explore the parameter space efficiently. This work proposes a classification approach that approximates population Monte Carlo (PMC), where model class probabilities from classification are used to update particle weights. This approach, called Classification-PMC, blends adaptive proposals and classification, efficiently producing samples from the posterior without subjectivity. We show through a simulation study that Classification-PMC outperforms two state-of-the-art methods: ratio estimation and SMC ABC when it is computationally difficult to simulate from the likelihood.