Abstract
For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel \(P_{\mu} = \sum_k \mu(k)P^k.\) In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker’s and Metropolis algorithms in terms of asymptotic variance.
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Supported by EPSRC grants EP/G026521/1 and EP/D002060/1 and by CRiSM.
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Łatuszyński, K., Roberts, G.O. CLTs and Asymptotic Variance of Time-Sampled Markov Chains. Methodol Comput Appl Probab 15, 237–247 (2013). https://doi.org/10.1007/s11009-011-9237-8
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DOI: https://doi.org/10.1007/s11009-011-9237-8
Keywords
- Time-sampled Markov chains
- Barker’s algorithm
- Metropolis algorithm
- Central Limit Theorem
- Asymptotic variance
- Variance bounding Markov chains
- MCMC estimation