Bayesian Inference in Common Microeconometric Models With Massive Datasets by Double Marginalized Subsampling

Bayesian inference with a large dataset is computationally intensive, as Markov chain Monte Carlo simulation requires a complete scan of the dataset for each proposed parameter update. To reduce the number of data points evaluated at each iteration of posterior simulation, we develop a double marginalized subsampling method, which is applicable to a wide array of microeconometric models including Tobit, Probit, regressions with non-Gaussian errors, heteroscedasticity and stochastic volatility, hierarchical longitudinal models, time-varying-parameter regressions, Gaussian mixtures, etc. We also provide an extension to double pseudo-marginalized subsampling, which has more applications beyond conditionally conjugate models. With rank-one update of the cumulative statistics, both methods target the exact posterior distribution, from which a parameter draw can be obtained with every single observation. Simulation studies demonstrate the statistical and computational efficiency of the marginalized sampler. The methods are also applied to a real-world massive dataset on the incidentally truncated mortgage rates.