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March 2021 Dynamic Variable Selection with Spike-and-Slab Process Priors
Veronika Rockova, Kenichiro McAlinn
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Bayesian Anal. 16(1): 233-269 (March 2021). DOI: 10.1214/20-BA1199

Abstract

We address the problem of dynamic variable selection in time series regression with unknown residual variances, where the set of active predictors is allowed to evolve over time. To capture time-varying variable selection uncertainty, we introduce new dynamic shrinkage priors for the time series of regression coefficients. These priors are characterized by two main ingredients: smooth parameter evolutions and intermittent zeroes for modeling predictive breaks. More formally, our proposed Dynamic Spike-and-Slab (DSS) priors are constructed as mixtures of two processes: a spike process for the irrelevant coefficients and a slab autoregressive process for the active coefficients. The mixing weights are themselves time-varying and depend on lagged values of the series. Our DSS priors are probabilistically coherent in the sense that their stationary distribution is fully known and characterized by spike-and-slab marginals. For posterior sampling over dynamic regression coefficients, model selection indicators as well as unknown dynamic residual variances, we propose a Dynamic SSVS algorithm based on forward-filtering and backward-sampling. To scale our method to large data sets, we develop a Dynamic EMVS algorithm for MAP smoothing. We demonstrate, through simulation and a topical macroeconomic dataset, that DSS priors are very effective at separating active and noisy coefficients. Our fast implementation significantly extends the reach of spike-and-slab methods to big time series data.

Acknowledgments

The authors would like to thank the Reviewers and the Associate Editor for providing thorough and thoughtful feedback which lead to substantial improvements of our paper.

Citation

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Veronika Rockova. Kenichiro McAlinn. "Dynamic Variable Selection with Spike-and-Slab Process Priors." Bayesian Anal. 16 (1) 233 - 269, March 2021. https://doi.org/10.1214/20-BA1199

Information

Published: March 2021
First available in Project Euclid: 28 April 2020

MathSciNet: MR4194280
Digital Object Identifier: 10.1214/20-BA1199

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Vol.16 • No. 1 • March 2021
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