Markov chain Monte Carlo (MCMC) methods allow exploration of intractable probability distributions by constructing a Markov chain whose stationary distribution equals the desired distribution. The output from the Markov chain is typically used to estimate several features of the stationary distribution such as mean and variance parameters along with quantiles and so on. Unfortunately, most reported MCMC estimates do not include a clear notion of the associated uncertainty. For expectations one can assess the uncertainty by estimating the variance in an asymptotic normal distribution of the Monte Carlo error. For general functionals there is no such clear path. This article studies the applicability of subsampling bootstrap methods to assess the uncertainty in estimating general functionals from MCMC simulations.
- Markov Chain
- Markov Chain Monte Carlo
- Coverage Probability
- Markov Chain Monte Carlo Method
- Quantile Function
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I am grateful to Galin L. Jones and two anonymous referees for their constructive comments in preparing this article.
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Flegal, J.M. (2012). Applicability of Subsampling Bootstrap Methods in Markov Chain Monte Carlo. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27439-8
Online ISBN: 978-3-642-27440-4