Combines Importance Sampling Research Articles

Bayesian inference for circular distributions with unknown normalising constants

Very often, the likelihoods for circular data sets are of quite complicated forms, and the functional forms of the normalising constants, which depend upon the unknown parameters, are unknown. This latter problem generally precludes rigorous, exact inference (both classical and Bayesian) for circular data. Noting the paucity of literature on Bayesian circular data analysis, and also because realistic data analysis is naturally permitted by the Bayesian paradigm, we address the above problem taking a Bayesian perspective. In particular, we propose a methodology that combines importance sampling and Markov chain Monte Carlo (MCMC) in a very effective manner to sample from the posterior distribution of the parameters, given the circular data. With simulation study and real data analysis, we demonstrate the considerable reliability and flexibility of our proposed methodology in analysing circular data.

Combining importance sampling and temporal difference control variates to simulate Markov Chains

It is well known that in estimating performance measures associated with a stochastic system a good importance sampling distribution (IS) can give orders of magnitude of variance reduction while a bad one may lead to large, even infinite, variance. In this paper we study how this sensitivity of the estimator variance to the importance sampling change of measure may be "dampened" by combining importance sampling with stochastic approximation based temporal difference (TD) method. We consider a finite state space discrete time Markov chain (DTMC) with one-step transition rewards and an absorbing set of states and focus on estimating the cumulative expected reward to absorption starting from any state. In this setting we develop sufficient conditions under which the estimate resulting from the combined approach has a mean square error that asymptotically equals zero even when the estimate formed by using only importance sampling change of measure has infinite variance. In particular, we consider the problem of estimating the small buffer overflow probability in a queuing network, where the change of measure suggested in literature is shown to have infinite variance under certain parameters and where the appropriate combination of IS and TD method can be empirically seen to have a much faster convergence rate compared to naive simulation.

A sequential particle filter method for static models

SUMMARY Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes in order to explore consistently a sequence of multiple distributions of interest. We show that such methods can also offer an efficient estimation

SIMULATION OF MAXIMUM FLOW IN MULTISTATE NETWORKS

ABSTRACT This paper describes an efficient simulation method for estimating the probability function of maximum flow in a multistate network. A multistate network contains components that have random capacity range among different levels. We propose using importance sampling and choosing the binomial distribution as a biasing distribution to estimate the probability of maximum flow. The experimental result shows that the efficiency of the proposed method is high. This paper also combines importance sampling with the simulation that condition on the capacity of some cuts. The experimental result shows that such a combination will improve the importance sampling further.

Following a Moving Target—Monte Carlo Inference for Dynamic Bayesian Models

Summary Markov chain Monte Carlo (MCMC) sampling is a numerically intensive simulation technique which has greatly improved the practicality of Bayesian inference and prediction. However, MCMC sampling is too slow to be of practical use in problems involving a large number of posterior (target) distributions, as in dynamic modelling and predictive model selection. Alternative simulation techniques for tracking moving target distributions, known as particle filters, which combine importance sampling, importance resampling and MCMC sampling, tend to suffer from a progressive degeneration as the target sequence evolves. We propose a new technique, based on these same simulation methodologies, which does not suffer from this progressive degeneration.

Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options

This paper develops a variance reduction technique for Monte Carlo simulations of path‐dependent options driven by high‐dimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables which maximizes the product of probability and payoff—the most important path. The directions used for stratified sampling are optimal for a quadratic approximation to the integrand or payoff function. Indeed, under differentiability assumptions our importance sampling method eliminates variability due to the linear part of the payoff function, and stratification eliminates much of the variability due to the quadratic part of the payoff. The two parts of the method are linked because the asymptotically optimal drift vector frequently provides a particularly effective direction for stratification. We illustrate the use of the method with path‐dependent options, a stochastic volatility model, and interest rate derivatives. The method reveals novel features of the structure of their payoffs.

Measurement and performance evaluation of NFS traffic in ATM network

This article has three parts. At first, we explore traffic characterization of an ATM local area network and find the traffic presents both long and short range dependence in nature. Secondly, one long range dependent traffic model (fast fractional Gaussian noise) is constructed to explore influence of long-range dependence on the queuing performance of an infinite buffer-size queue. At last, we combine importance sampling scheme and long range dependent traffic models to simulate a finite buffer-size queue. The results show that both LRD and SRD play an important role in the queuing systems. Especially when LRD is strong, the more buffer solution is almost useless to improve the queuing performance. Multiplexing and enough capacity are better solutions for queuing performance.

Classical Variational Transition State Theory Study of Hydrogen Atom Diffusion Dynamics in Imperfect Xenon Matrices

Thermal diffusion rates of hydrogen atoms in imperfect face-centered-cubic (fcc) xenon lattices containing up to 4.12% vacant sites have been computed using classical Monte Carlo variational transition state theory with a pairwise Xe/H interaction potential obtained from the results of ab initio calculations at the MP4(SDTQ) level of theory. Convergence of the required integrals is achieved by combining importance sampling and a damped trajectory procedure with the standard Markov walk. The variational flux through spherical dividing surfaces is minimized as a function of radius of the dividing surface. The results show that the presence of 1.4% vacant lattice sites lowers the diffusion barrier by about 0.006 eV relative to the perfect fcc crystal system. The computed values of the hydrogen atom diffusion coefficients at 40 K indicate that, over the range of vacancies considered, the diffusion coefficients increase exponentially with the percentage of the lattice vacancies. The calculations also show that the lattice vacancies are mobile. The studies reveal that the propensity for vacant site mobility increases as the total number of lattice vacancies increases. Since this effect decreases the potential barrier to diffusion, the diffusion coefficients obtained from the variational transition state theory calculation are lower limits for a system with the present interaction potential. The calculated diffusion coefficients indicate that experimental matrices vapor-deposited at 10 and 28 K contain about 1.8 and 1.2% vacant sites, respectively. Since the calculated diffusion rates are lower limits, these percentages are upper limits for the potential surface used in the present investigation.

Fast simulation of highly dependable systems with general failure and repair processes

An approach for simulating models of highly dependable systems with general failure and repair time distribution is described. The approach combines importance sampling with event rescheduling in order to obtain variance reductions in such rare event simulations. The approach is general in nature and allows a variety of features commonly arising in dependability modeling to be simulated effectively. It is shown how the technique can be applied to systems with redundant components and/or periodic maintenance. For different failure time distributions, the effect of the maintenance period on the steady-state availability is explored. The amount of component redundancy needed to achieve a certain reliability level is determined. >