Firefly Monte Carlo: Exact MCMC with Subsets of Data

Understand

Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference.

• However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration.
• Here we present Firefly Monte Carlo (FlyMC) an auxiliary variable MCMC algorithm that only queries the likelihoods of a potentially small subset of the data at each iteration yet simulates from the exact posterior distribution, in contrast to recent proposals that are approximate even in the asymptotic limit.
• FlyMC is compatible with a wide variety of modern MCMC algorithms, and only requires a lower bound on the per-datum likelihood factors.