Compute multivariate effective sample size (mESS) of Markov chain, using the multivariate dependence structure of the process.
This is a MATLAB implementation of the mESS estimation method described in Vats et al. (2015), with some minor tweaks for the choice of batch size b for the computation of the Monte Carlo covariance matrix. Digit help multiESS to display the documentation.
See also the R package mcmcse for a separate implementation.
Disclaimer: This is a working version in need of some additional testing. The interface may change in the future.
The effective sample size of a Markov chain is the size of an i.i.d. sample with the same covariance structure as the current chain. mESS is given by mESS = n |Λ|^{1/p}/ |Σ|^{1/p}, where n is the current sample size, Λ is the sample covariance matrix, p is the number of parameters and Σ is an estimate of the Monte Carlo covariance matrix for the Markov chain (here obtained by batch estimation).
Vats, D., Flegal, J. M., & Jones, G. L. "Multivariate Output Analysis for Markov chain Monte Carlo", arXiv preprint arXiv:1512.07713 (2015). (link)
This is free, open source software released under the GPL-3 License. See LICENSE.txt for details.
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