Gelman, Andrew 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]. Cited in 49 Documents 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.) Keywords:Markov chain simulation; Bayesian posterior distributions; overview of methods; monitoring convergence; summarizing inference; Markov chain simulations; target distribution; overestimate; underestimate PDFBibTeX XMLCite \textit{A. Gelman}, in: Markov chain Monte Carlo in practice. London: Chapman \& Hall. 131--143 (1996; Zbl 0839.62020)