Gelman-Rubin statistic

The Gelman-Rubin statistic allows a statement about the convergence of Monte [Carlo simulations].

Definition

Monte Carlo simulations are started with different initial values. The samples from the respective burn-in phases are discarded.
From the samples, the variance between the chains and the variance in the chains is estimated:
An estimate of the Gelman-Rubin statistic then results as
When L tends to infinity and B tends to zero, R tends to 1.
A different formula is given by Vats & Knudson.

Alternatives

The Geweke Diagnostic compares whether the mean of the first x percent of a chain and the mean of the last y percent of a chain match.

Literature

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