821,411 research outputs found
Simulation in Statistics
Simulation has become a standard tool in statistics because it may be the
only tool available for analysing some classes of probabilistic models. We
review in this paper simulation tools that have been specifically derived to
address statistical challenges and, in particular, recent advances in the areas
of adaptive Markov chain Monte Carlo (MCMC) algorithms, and approximate
Bayesian calculation (ABC) algorithms.Comment: Draft of an advanced tutorial paper for the Proceedings of the 2011
Winter Simulation Conferenc
Quantum Monte Carlo simulation
Contemporary scientific studies often rely on the understanding of complex
quantum systems via computer simulation. This paper initiates the statistical
study of quantum simulation and proposes a Monte Carlo method for estimating
analytically intractable quantities. We derive the bias and variance for the
proposed Monte Carlo quantum simulation estimator and establish the asymptotic
theory for the estimator. The theory is used to design a computational scheme
for minimizing the mean square error of the estimator.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS406 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stochastic simulations for the time evolution of systems which obey generalized statistics: Fractional exclusion statistics and Gentile's statistics
We present a stochastic method for the simulation of the time evolution in
systems which obey generalized statistics, namely fractional exclusion
statistics and Gentile's statistics. The transition rates are derived in the
framework of canonical ensembles. This approach introduces a tool for
describing interacting fermionic and bosonic systems in non-equilibrium as
ideal FES systems, in a computationally efficient manner. The two types of
statistics are analyzed comparatively, indicating their intrinsic thermodynamic
differences and revealing key aspects related to the species size.Comment: 14 pages, 5 figures, IOP forma
Nonparametric tests based on area-statistics
Area statistics are sample versions of areas occuring in a probability plot of two distribution functions F and G. This paper gives a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations such as testing equality of distributions against inequality or testing stochastic dominance in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distribution of these statistics can be calculated via recursion formulae. Two tables with critical values of the new statistics are added. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian Bridge. The distribution functions and quantiles thereof are obtained by Monte-Carlo-Simulation. Finally, the power of two new tests based on area statistics is compared to the power of tests based on corresponding supremum statistics, i.e. statistics of the Kolmogorov-Smirnov type. --Area Statistics,P-P-Plot,Functionals of Brownian Bridge,Monte Carlo Simulation,Nonparametric Tests,Recursion Formulae
Numerical simulation of random paths with a curvature dependent action
We study an ensemble of closed random paths, embedded in R^3, with a
curvature dependent action. Previous analytical results indicate that there is
no crumpling transition for any finite value of the curvature coupling.
Nevertheless, in a high statistics numerical simulation, we observe two
different regimes for the specific heat separated by a rather smooth structure.
The analysis of this fact warns us about the difficulties in the interpretation
of numerical results obtained in cases where theoretical results are absent and
a high statistics simulation is unreachable. This may be the case of random
surfaces.Comment: 9 pages, LaTeX, 4 eps figures. Final version to appear in Mod. Phys.
Lett.
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