Ergodicity of Combocontinuous Adaptive MCMC Algorithms

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Abstract

This paper proves convergence to stationarity of certain adaptive MCMC algorithms, under certain assumptions including easily-verifiable upper and lower bounds on the transition densities and a continuous target density. In particular, the transition and proposal densities are not required to be continuous, thus improving on the previous ergodicity results of Craiu et al. (Ann Appl Probab 25(6):3592–3623, 2015).

Keywords

Markov chain Monte Carlo Adaptive MCMC Ergodicity Dini’s theorem Piecewise continuous Combocontinuous 

Mathematics Subject Classifications (2010)

60J22 60J05 62M05 

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Notes

Acknowledgements

We thank the anonymous reviewer for very helpful comments, which led to many improvements.

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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Statistical SciencesUniversity of TorontoTorontoCanada

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