  The exact estimation of latent variable models with big data is known to be
challenging. The latents have to be integrated out numerically, and the
dimension of the latent variables increases with the sample size. This paper
develops a novel approximate Bayesian method based on the Langevin diffusion
process. The method employs the Fisher identity to integrate out the latent
variables, which makes it accurate and computationally feasible when applied to
big data. In contrast to other approximate estimation methods, it does not
require the choice of a parametric distribution for the unknowns, which often
leads to inaccuracies. In an empirical discrete choice example with a million
observations, the proposed method accurately estimates the posterior choice
probabilities using only 2% of the computation time of exact MCMC.
