ABCSMC

ABCSMC stands for Approximate Bayesian Computation Sequential Monte Carlo, a family of likelihood-free inference methods for Bayesian parameter estimation and model selection in complex stochastic models. In settings where the likelihood is analytically intractable but simulation from the model is feasible, ABC-SMC uses a sequence of increasingly stringent tolerance levels to approximate the posterior distribution of model parameters. The method generates a population of parameter–data simulations (particles), retaining those whose simulated data are close to the observed data under a predefined distance measure. In successive populations, particles are resampled according to their weights, perturbed through a proposal kernel, and re-evaluated with a decreasing tolerance, building a sequence of approximations from the prior toward the posterior.

Implementation notes: weights are updated to correct for the bias introduced by resampling and perturbation; common choices use summary statistics to reduce dimensionality. The algorithm ends with an approximate posterior from the last population. Extensions include adaptive tolerance schedules, adaptive perturbation kernels, and model choice within the ABC-SMC framework.

Applications span fields where simulators exist but likelihoods are difficult to compute, including population genetics, ecology, epidemiology, systems biology, and cosmology. Advantages include improved efficiency over basic ABC rejection samplers and the ability to incorporate prior information and conduct model comparison. Limitations include dependence on chosen summary statistics and distance measures, potential bias from information loss, and substantial computational cost for complex models.

History: ABC-SMC was developed in the late 2000s as an extension of approximate Bayesian computation to sequential Monte Carlo methods, enabling more scalable inference in simulation-based models.