AbstractMarkov Chain Monte Carlo (MCMC) sampling from a posterior distribution corresponding to a massive data set can be computationally prohibitive as producing one sample requires a number of operations that is linear in the data size. In this article we introduce a new communication‐free parallel method, the “Likelihood Inflating Sampling Algorithm (LISA),” that significantly reduces computational costs by randomly splitting the data set into smaller subsets and running MCMC methods “independently” in parallel on each subset using different processors. Each processor will be used to run an MCMC chain that samples sub‐posterior distributions which are defined using an “inflated” likelihood function. We develop a strategy for combining the draws from different sub‐posteriors to study the full posterior of the Bayesian Additive Regression Trees (BART) model. The performance of the method is tested using simulated data and a large socio‐economic study. The Canadian Journal of Statistics 46: 147–175; 2018 © 2017 Statistical Society of Canada