Ergodicity of Combocontinuous Adaptive MCMC Algorithms
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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).
KeywordsMarkov chain Monte Carlo Adaptive MCMC Ergodicity Dini’s theorem Piecewise continuous Combocontinuous
Mathematics Subject Classifications (2010)60J22 60J05 62M05
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We thank the anonymous reviewer for very helpful comments, which led to many improvements.
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