Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nested $\hat R$: Assessing Convergence for Markov chain Monte Carlo when
  using many short chains   When using Markov chain Monte Carlo (MCMC) algorithms, we can increase the
number of samples either by running longer chains or by running more chains.
Practitioners often prefer the first approach because chains need an initial
``warmup'' phase to forget their initial states; the number of operations
needed for warmup is constant with respect to chain length but increases
linearly with the number of chains. However, highly parallel hardware
accelerators such as GPUs may allow us to run many chains in parallel almost as
quickly as a single chain. This makes it more attractive to run many chains
with a short sampling phase. Unfortunately, existing diagnostics are not
designed for the ``many short chains'' regime. This is notably the case for the
popular $\hat R$ statistic which claims convergence only if the effective
sample size \textit{per chain} is sufficiently large. We present $\mathfrak
n\hat R$, a generalization of $\hat R$, which does not conflate short chains
and poor mixing, and offers a useful diagnostic provided we run enough chains
and meet certain initialization conditions. We define what constitutes a proper
warmup in the many-chains regime and recommend a threshold for $\mathfrak n
\hat R$. Furthermore we use $\mathfrak n \hat R$ to construct a warmup scheme
with an adaptive length, allowing users to avoid running their MCMC algorithms
longer than necessary.

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The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph