451,893 research outputs found
High Performance Financial Simulation Using Randomized Quasi-Monte Carlo Methods
GPU computing has become popular in computational finance and many financial
institutions are moving their CPU based applications to the GPU platform. Since
most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly
from parallel implementations, and consequently Monte Carlo has become a focal
point in GPU computing. GPU speed-up examples reported in the literature often
involve Monte Carlo algorithms, and there are software tools commercially
available that help migrate Monte Carlo financial pricing models to GPU.
We present a survey of Monte Carlo and randomized quasi-Monte Carlo methods,
and discuss existing (quasi) Monte Carlo sequences in GPU libraries. We discuss
specific features of GPU architecture relevant for developing efficient (quasi)
Monte Carlo methods. We introduce a recent randomized quasi-Monte Carlo method,
and compare it with some of the existing implementations on GPU, when they are
used in pricing caplets in the LIBOR market model and mortgage backed
securities
Metropolis Methods for Quantum Monte Carlo Simulations
Since its first description fifty years ago, the Metropolis Monte Carlo
method has been used in a variety of different ways for the simulation of
continuum quantum many-body systems. This paper will consider some of the
generalizations of the Metropolis algorithm employed in quantum Monte Carlo:
Variational Monte Carlo, dynamical methods for projector monte carlo ({\it
i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path
integral Monte Carlo, the sampling of permutations, cluster methods for lattice
models, the penalty method for coupled electron-ionic systems and the Bayesian
analysis of imaginary time correlation functions.Comment: Proceedings of "Monte Carlo Methods in the Physical Sciences"
Celebrating the 50th Anniversary of the Metropolis Algorith
Comparative Monte Carlo Efficiency by Monte Carlo Analysis
We propose a modified power method for computing the subdominant eigenvalue
of a matrix or continuous operator. Here we focus on defining
simple Monte Carlo methods for its application. The methods presented use
random walkers of mixed signs to represent the subdominant eigenfuction.
Accordingly, the methods must cancel these signs properly in order to sample
this eigenfunction faithfully. We present a simple procedure to solve this sign
problem and then test our Monte Carlo methods by computing the of
various Markov chain transition matrices. We first computed for
several one and two dimensional Ising models, which have a discrete phase
space, and compared the relative efficiencies of the Metropolis and heat-bath
algorithms as a function of temperature and applied magnetic field. Next, we
computed for a model of an interacting gas trapped by a harmonic
potential, which has a mutidimensional continuous phase space, and studied the
efficiency of the Metropolis algorithm as a function of temperature and the
maximum allowable step size . Based on the criterion, we
found for the Ising models that small lattices appear to give an adequate
picture of comparative efficiency and that the heat-bath algorithm is more
efficient than the Metropolis algorithm only at low temperatures where both
algorithms are inefficient. For the harmonic trap problem, we found that the
traditional rule-of-thumb of adjusting so the Metropolis acceptance
rate is around 50% range is often sub-optimal. In general, as a function of
temperature or , for this model displayed trends defining
optimal efficiency that the acceptance ratio does not. The cases studied also
suggested that Monte Carlo simulations for a continuum model are likely more
efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure
Hybrid Monte Carlo-Methods in Credit Risk Management
In this paper we analyze and compare the use of Monte Carlo, Quasi-Monte
Carlo and hybrid Monte Carlo-methods in the credit risk management system
Credit Metrics by J.P.Morgan. We show that hybrid sequences used for
simulations, in a suitable way, in many relevant situations, perform better
than pure Monte Carlo and pure Quasi-Monte Carlo methods, and they essentially
never perform worse than these methods.Comment: 18 pages, 18 figure
Population Monte Carlo algorithms
We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms.
In these algorithms, a set of ``walkers'' or ``particles'' is used as a
representation of a high-dimensional vector. The computation is carried out by
a random walk and split/deletion of these objects. The algorithms are developed
in various fields in physics and statistical sciences and called by lots of
different terms -- ``quantum Monte Carlo'', ``transfer-matrix Monte Carlo'',
``Monte Carlo filter (particle filter)'',``sequential Monte Carlo'' and
``PERM'' etc. Here we discuss them in a coherent framework. We also touch on
related algorithms -- genetic algorithms and annealed importance sampling.Comment: Title is changed (Population-based Monte Carlo -> Population Monte
Carlo). A number of small but important corrections and additions. References
are also added. Original Version is read at 2000 Workshop on
Information-Based Induction Sciences (July 17-18, 2000, Syuzenji, Shizuoka,
Japan). No figure
Off-diagonal Wave Function Monte Carlo Studies of Hubbard Model I
We propose a Monte Carlo method, which is a hybrid method of the quantum
Monte Carlo method and variational Monte Carlo theory, to study the Hubbard
model. The theory is based on the off-diagonal and the Gutzwiller type
correlation factors which are taken into account by a Monte Carlo algorithm. In
the 4x4 system our method is able to reproduce the exact results obtained by
the diagonalization. An application is given to investigate the half-filled
band case of two-dimensional square lattice. The energy is favorably compared
with quantum Monte Carlo data.Comment: 9 pages, 11 figure
General Construction of Irreversible Kernel in Markov Chain Monte Carlo
The Markov chain Monte Carlo update method to construct an irreversible
kernel has been reviewed and extended to general state spaces. The several
convergence conditions of the Markov chain were discussed. The alternative
methods to the Gibbs sampler and the Metropolis-Hastings algorithm were
proposed and assessed in some models. The distribution convergence and the
sampling efficiency are significantly improved in the Potts model, the
bivariate Gaussian model, and so on. This approach using the irreversible
kernel can be applied to any Markov chain Monte Carlo sampling and it is
expected to improve the efficiency in general.Comment: 16 pages, 8 figures; submitted to the proceedings of The Tenth
International Conference on Monte Carlo and Quasi-Monte Carlo Methods in
Scientific Computing (MCQMC 2012), which will be published by
Springer-Verlag, in a book entitled Monte Carlo and Quasi-Monte Carlo Methods
201
Introduction to Monte Carlo Methods
Monte Carlo methods play an important role in scientific computation,
especially when problems have a vast phase space. In this lecture an
introduction to the Monte Carlo method is given. Concepts such as Markov
chains, detailed balance, critical slowing down, and ergodicity, as well as the
Metropolis algorithm are explained. The Monte Carlo method is illustrated by
numerically studying the critical behavior of the two-dimensional Ising
ferromagnet using finite-size scaling methods. In addition, advanced Monte
Carlo methods are described (e.g., the Wolff cluster algorithm and parallel
tempering Monte Carlo) and illustrated with nontrivial models from the physics
of glassy systems. Finally, we outline an approach to study rare events using a
Monte Carlo sampling with a guiding function.Comment: lecture at the third international summer school "Modern Computation
Science", 15 - 26 August 2011, Oldenburg (Germany), see
http://www.mcs.uni-oldenburg.d
Fast orthogonal transforms for multi-level quasi-Monte Carlo integration
We combine a generic method for finding fast orthogonal transforms for a
given quasi-Monte Carlo integration problem with the multilevel Monte Carlo
method. It is shown by example that this combined method can vastly improve the
efficiency of quasi-Monte Carlo
Adaptive Tuning Of Hamiltonian Monte Carlo Within Sequential Monte Carlo
Sequential Monte Carlo (SMC) samplers form an attractive alternative to MCMC
for Bayesian computation. However, their performance depends strongly on the
Markov kernels used to rejuvenate particles. We discuss how to calibrate
automatically (using the current particles) Hamiltonian Monte Carlo kernels
within SMC. To do so, we build upon the adaptive SMC approach of Fearnhead and
Taylor (2013), and we also suggest alternative methods. We illustrate the
advantages of using HMC kernels within an SMC sampler via an extensive
numerical study
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