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Inference and monitoring convergence. (English) Zbl 0839.62020

Gilks, W. R. (ed.) et al., Markov chain Monte Carlo in practice. London: Chapman & Hall. 131-143 (1996).
This chapter presents an overview of methods for addressing two practical tasks: monitoring convergence of the simulation and summarizing inference about the target distribution using the output from the simulations.
The practical task in monitoring convergence is to estimate how much the inference based on Markov chain simulations differs from the desired target distribution. Our basic method, inspired by the analysis of variance, is to form an overestimate and an underestimate of the variance of the target distribution, with the property that the estimates will be roughly equal at convergence but not before.
For the entire collection see [Zbl 0832.00018].

MSC:

62F15 Bayesian inference
65C05 Monte Carlo methods
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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