Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Stochastic Error and Computational Efficiency of the Markov Chain
  Monte Carlo Method   In Markov Chain Monte Carlo (MCMC) simulations, the thermal equilibria
quantities are estimated by ensemble average over a sample set containing a
large number of correlated samples. These samples are selected in accordance
with the probability distribution function, known from the partition function
of equilibrium state. As the stochastic error of the simulation results is
significant, it is desirable to understand the variance of the estimation by
ensemble average, which depends on the sample size (i.e., the total number of
samples in the set) and the sampling interval (i.e., cycle number between two
consecutive samples). Although large sample sizes reduce the variance, they
increase the computational cost of the simulation. For a given CPU time, the
sample size can be reduced greatly by increasing the sampling interval, while
having the corresponding increase in variance be negligible if the original
sampling interval is very small. In this work, we report a few general rules
that relate the variance with the sample size and the sampling interval. These
results are observed and confirmed numerically. These variance rules are
derived for the MCMC method but are also valid for the correlated samples
obtained using other Monte Carlo methods. The main contribution of this work
includes the theoretical proof of these numerical observations and the set of
assumptions that lead to them.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th