Spectral Subsampling MCMC for Stationary Time Series

Robert Salomone · Matias Quiroz · Robert kohn · Mattias Villani · Minh-Ngoc Tran

Keywords: [ Bayesian Methods ] [ Monte Carlo Methods ] [ Spectral Methods ] [ Probabilistic Inference - Approximate, Monte Carlo, and Spectral Methods ]

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Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of independence. We propose a novel technique for speeding up MCMC for time series data by efficient data subsampling in the frequency domain. For several challenging time series models, we demonstrate a speedup of up to two orders of magnitude while incurring negligible bias compared to MCMC on the full dataset. We also propose alternative control variates for variance reduction based on data grouping and coreset constructions.

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