Abstract: Approximate Bayesian computation (ABC) has become a standard tool to conduct Bayesian inference for models with intractable likelihoods. However, most existing ABC methods suffer from the curse of dimensionality when the number of parameters is large. To solve this problem, we introduce a Gibbs Sequential Monte Carlo (SMC) method that utilizes a Gibbs kernel to update parameters within the SMC framework and approximate the conditional distribution of the parameters using a variety of regression adjustment methods. We discuss the computational advantage of our method over existing approaches and establish the theoretical property of the Gibbs kernel. We further demonstrate the superior numerical performance of our method using simulation studies and an application to cell motility example.

Key words and phrases: Approximate Bayesian computation, cell motility, Markov chain Monte Carlo, random forest, regression adjustment.