11.6.4.3. Checking for convergence with the Gelman–Rubin diagnostic

Once the trace and acceptance ratio plots have been analysed, and an initial burn-in value has been chosen, the Gelman–Rubin diagnostic can be used to verify the convergence of the chains. This diagnostic compares the intra- and inter-chain variances (see [Bla17] for more details).

The method diagGelmanRubin has the following prototype:

std::unordered_map<string, double> diagGelmanRubin();

This method takes no arguments, as it is called directly from the TCalibration object. For example, in Macro “calibrationMCMCFlowrate1D.C”, the Gelman–Rubin diagnostic is computed with:

std::unordered_map<string, double> GelmanRubin_values = cal->diagGelmanRubin();
GelmanRubin_values["hl"]; // To extract the Gelman-Rubin statistic for parameter hl

The returned object GelmanRubin_values is an unordered map where each parameter name (e.g., hl) is associated with its Gelman–Rubin statistic value. The results are also printed in the console (see Console), accompanied by a short generic commentary interpreting the statistic.

In this example, the Gelman–Rubin diagnostic confirms good convergence of the chains (and thus the suitability of the chosen burn-in value). In other cases, where the statistics indicate poorer convergence, it may be necessary to run additional iterations (see Running the estimate, exporting and loading chains, and continuing the calculation) or to adjust the burn-in value (see Investigating the quality of the samples through diagnostics and plots).