The goal of every MCMC analysis is to evaluate integrals of the form There are other convergence diagnostics like the Gelman–Rubin statistic ( Note: you should not compute the G–R statistic using multiple chains in the same emcee ensemble because the chains are not independent!) but, since the integrated autocorrelation time directly quantifies the Monte Carlo error (and hence the efficiency of the sampler) on any integrals computed using the MCMC results, it is the natural quantity of interest when judging the robustness of an MCMC analysis. The basic idea is that the samples in your chain are not independent and you must estimate the effective number of independent samples. With emcee, we follow Goodman & Weare (2010) and recommend using the integrated autocorrelation time to quantify the effects of sampling error on your results. However, some discussion of autocorrelation analysis is (or should be!) a necessary part of any publication using MCMC. This can be a difficult subject to discuss because it isn’t formally possible to guarantee convergence for any but the simplest models, and therefore any argument that you make will be circular and heuristic. In this tutorial, we will discuss a method for convincing yourself that your chains are sufficiently converged. This is a cross post from the new emcee documentation. Launch an executable version of this post on. This post is implemented as a Jupyter notebook Please open an issue or pull request on that repository if you have questions, comments, or suggestions. The source for this post can be found here. Autocorrelation time estimation Oct 16 2017
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