Abstract
One issue with any Monte Carlo sampling technique, and especially Markov chain Monte Carlo, is convergence. Before samples can be used for parameter estimation, the analyst must have reasonable assurance that the Markov chain(s) used to generate the samples has converged to the posterior distribution. This chapter presents qualitative and quantitative convergence checks that an analyst can use to obtain this assurance and avoid pitfalls caused by lack of convergence.
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- 1.
It is possible, especially with highly correlated parameters, that there will be difficulty in getting the chains to mix, despite convergence. Since we cannot readily distinguish between the two problems, we will refer to poor chain mixing as being a sign of failure to achieve convergence. Regardless of the source of the lack of mixing, the estimates should not be used until the problem is rectified, perhaps by reparameterizing the problem in terms of parameters that are less strongly correlated.
Reference
Robert CP, Casella G (2010) Monte Carlo statistical methods, 2nd edn. Springer, Berlin
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© 2011 Springer-Verlag London Limited
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Kelly, D., Smith, C. (2011). Checking Convergence to Posterior Distribution. In: Bayesian Inference for Probabilistic Risk Assessment. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-84996-187-5_6
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DOI: https://doi.org/10.1007/978-1-84996-187-5_6
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