In these notes we discuss the efficiency of a Monte-Carlo estimator. This naturally leads to the search for more efficient estimators and towards this end we describe some simple variance reduction techniques. In particular, we describe common random numbers, control variates, antithetic Variates and conditional Monte-Carlo, all of which are designed to reduce the variance of our Monte-Carlo es...

This paper presents an analytical view of variance reduction by control variate technique for pricing arithmetic Asian options as a financial derivatives. In this paper, the effect of correlation between two random variables is shown. We propose an efficient method for choose suitable control in pricing arithmetic Asian options based on the control variates (CV). The numerical experiment shows ...

We use simulation to estimate the steady-state performance of a stable multiclass queueing network. Standard estimators have been seen to perform poorly when the network is heavily loaded. We introduce two new simulation estimators. The first provides substantial variance reductions in moderately-loaded networks at very little additional computational cost. The second estimator provides substan...

We use simulation to estimate the steady-state performance of a stable multiclass queueing network. Standard estimators have been seen to perform poorly when the network is heavily loaded. We introduce two new simulation estimators. The first provides substantial variance reductions in moderately-loaded networks at very little additional computational cost. The second estimator provides substan...

Simulation is an essential tool for performance evaluation of communication networks. We are interested in the waiting timeW of packets. The Control Variates method takes profit of the knowledge about another stochastic process strongly correlated withW to reduce the uncertainty in the estimation of its mean. We analyze the usefulness of the cycle time as a control stochastic process for Medium...

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by substantial computational cost. This paper considers control based on Stein operators, presenting framework that encompasses generalizes existing approaches use polynomials, ke...

Numerical simulations in cosmology require trade-offs between volume, resolution and run-time that limit the volume of Universe can be simulated, leading to sample variance predictions ensemble-average quantities such as power spectrum or correlation function(s). Sample is particularly acute at large scales, which also where analytic techniques highly reliable. This provides an opportunity comb...

The central computational problem in Bayesian analysis is that of computing the posterior expectation of one or more quantities of interest|a ratio of two often-intractable integrals. The method of Laplace gives an approximation to this ratio that depends only on asymptotic features of the function of interest and the posterior density function, in a neighborhood of the posterior mode. Monte Ca...