Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo
By Dootika Vats, James M. Flegal, Galin L. Jones. Bernoulli, 2015
51 citations recorded by the source corpus.
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We also show strong consistency of the eigenvalues of the estimator. Finally, we examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6df6358be807f2d3b1a11b930a89b57fcb42e29c
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In Statistics and Probability
- Dootika Vats
- Christina Knudson
- James M. Flegal
- Galin L. Jones
- Rémi Bardenet
- James P. Hobert
- Murali Haran
- Jeffrey S. Rosenthal
Citations in the corpus
- Revisiting the Gelman–Rubin Diagnostic (2018, background): “A theoretically-justified lower bound on the number of effective samples required to obtain a certain level of precision has been determined for the univariate case (Gong and Flegal, 2016) and for the general multivariate problem (Vats et al., 2018a).”
- Multivariate output analysis for Markov chain Monte Carlo (2015, background): “The concept of generalized variance was first introduced by Wilks (1932) as a univariate measure of spread for a multivariate distribution.”