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Approximation Properties of Variational Bayes for Vector Autoregressions

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Document pages: 16 pages

Abstract: Variational Bayes (VB) is a recent approximate method for Bayesian inference.It has the merit of being a fast and scalable alternative to Markov Chain MonteCarlo (MCMC) but its approximation error is often unknown. In this paper, wederive the approximation error of VB in terms of mean, mode, variance,predictive density and KL divergence for the linear Gaussian multi-equationregression. Our results indicate that VB approximates the posterior meanperfectly. Factors affecting the magnitude of underestimation in posteriorvariance and mode are revealed. Importantly, We demonstrate that VB estimatespredictive densities accurately.

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