Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting the Gelman-Rubin Diagnostic   Gelman and Rubin's (1992) convergence diagnostic is one of the most popular
methods for terminating a Markov chain Monte Carlo (MCMC) sampler. Since the
seminal paper, researchers have developed sophisticated methods for estimating
variance of Monte Carlo averages. We show that these estimators find immediate
use in the Gelman-Rubin statistic, a connection not previously established in
the literature. We incorporate these estimators to upgrade both the univariate
and multivariate Gelman-Rubin statistics, leading to improved stability in MCMC
termination time. An immediate advantage is that our new Gelman-Rubin statistic
can be calculated for a single chain. In addition, we establish a one-to-one
relationship between the Gelman-Rubin statistic and effective sample size.
Leveraging this relationship, we develop a principled termination criterion for
the Gelman-Rubin statistic. Finally, we demonstrate the utility of our improved
diagnostic via examples.

5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio