strong consistency of the variance estimator in steady state simulation output analysis in this paper we study the problem of variance estimation in steady state simulation output analysis a confidence interval for the mean of an output sequence may be constructed using a weakly consistent estimator of the time average variance constant of the process moreover a strongly consistent estimator of the variance constant is required for fixed width confidence interval estimation procedures to be asymptotically valid here we establish sufficient conditions to ensure strong consistency of the estimator of the variance constant obtained by several widely used methods of steady state simulation output analysis namely batch means overlapping batch means spaced batch means and standardized time series area estimator we also introduce the overlapping area estimator of the variance constant the established sufficient conditions provide qualitative insight into the relation between the correlation of the process and certain parameters e g batch size of the output method used

indifference zone free selection of the best many procedures have been proposed in the literature to select the simulated alternative with the best mean performance from a finite set of alternatives among these procedures frequentist procedures are typically designed under either the subset selection ss formulation or the indifference zone iz formulation both formulations may encounter problems when the goal is to select the unique best alternative for any configuration of the means in particular ss procedures may return a subset that contains more than one alternative and iz procedures hinge on the relationship between the chosen iz parameter and the true mean differences that is unknown to decision makers a priori in this paper we propose a new formulation that guarantees to select the unique best alternative with a user specified probability of correct selection pcs as long as the means of alternatives are unique and we design a class of fully sequential procedures under this formulation these procedures are parameterized by the

mean square consistency of the variance estimator in steady state simulation output analysis in steady state simulation output analysis mean square consistency of the process variance estimator is important for a number of reasons one way to construct an asymptotically valid confidence interval around a sample mean is via construction of a consistent estimator of the process variance and a central limit theorem also if an estimator is consistent in the mean square sense a mean square error analysis is theoretically justified finally batch size selection is an open research problem in steady state output analysis and a mean square error analysis approach has been proposed in the literature to be valid the process variance estimators constructed must be consistent in the mean square sense in this paper we prove mean square consistency of the process variance estimator for the methods of batch means overlapping batch means standardized time series area and spaced batch means by rigorously computing the rate of decay of the variance of the process variance estimators asymptotic results for third and higher centered moments of the batch means and area variance estimators are also given along with central limit theorems

multiple comparison procedures for steady state simulations suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance and unknown asymptotic variance we allow for the asymptotic variances to be unequal and for the distributions of the k systems to be different we consider the problem of running independent single stage simulations to make multiple comparisons of the steady state means of the different systems we derive asymptotically valid as the run lengths of the simulations of the systems tend to infinity simultaneous confidence intervals for each of the following problems all pairwise comparisons of means all contrasts multiple comparisons with a control and multiple comparisons with the best our confidence intervals are based on standardized time series methods and we establish the asymptotic validity of each under the sole assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem although simulation is the context of this paper the results naturally apply to asymptotically stationary time series

a sequential sampling procedure for stochastic programming we develop a sequential sampling procedure for a class of stochastic programs we assume that a sequence of feasible solutions with an optimal limit point is given as input to our procedure such a sequence can be generated by solving a series of sampling problems with increasing sample size or it can be found by any other viable method our procedure estimates the optimality gap of a candidate solution from this sequence if the point estimate of the optimality gap is sufficiently small according to our termination criterion then we stop otherwise we repeat with the next candidate solution from the sequence under an increased sample size we provide conditions under which this procedure i terminates with probability one and ii terminates with a solution that has a small optimality gap with a prespecified probability

fixed width sequential stopping rules for a class of stochastic programs monte carlo sampling based methods are frequently used in stochastic programming when exact solution is not possible a critical component of monte carlo sampling based methods is determining when to stop sampling to ensure the desired quality of the solutions in this paper we develop stopping rules for sequential sampling procedures that depend on the width of an optimality gap confidence interval estimator the procedures solve a sequence of sampling approximations with increasing sample size to generate solutions and stop when the width of the confidence interval on the current solution s optimality gap plus an inflation factor fall below a prespecified value epsilon we first present a method that takes the schedule of sample sizes as an input and provide guidelines on the growth of sample sizes then we present a method that increases the sample sizes according to the current estimates of the optimality gap the larger the estimates the larger the increases in sample sizes we provide conditi

a knowledge gradient policy for sequential information collection in a sequential bayesian ranking and selection problem with independent normal populations and common known variance we study a previously introduced measurement policy which we refer to as the knowledge gradient policy this policy myopically maximizes the expected increment in the value of information in each time period where the value is measured according to the terminal utility function we show that the knowledge gradient policy is optimal both when the horizon is a single time period and in the limit as the horizon extends to infinity we show furthermore that in some special cases the knowledge gradient policy is optimal regardless of the length of any given fixed total sampling horizon we bound the knowledge gradient policy s suboptimality in the remaining cases and show through simulations that it performs competitively with or significantly better than other policies

retrospective optimization of mixed integer stochastic systems using dynamic simplex linear interpolation abstract we propose a family of retrospective optimization ro algorithms for optimizing stochastic systems with both integer and continuous decision variables the algorithms are continuous search procedures embedded in a ro framework using dynamic simplex interpolation rodsi by decreasing dimensions corresponding to the continuous variables of simplex the retrospective solutions become closer to an optimizer of the objective function we present convergence results of rodsi algorithms for stochastic convex systems numerical results show that a simple implementation of rodsi algorithms significantly outperforms some random search algorithms such as genetic algorithm ga and particle swarm optimization pso

simulation output analysis using standardized time series the method of standardized time series sts was proposed by schruben as an approach for constructing asymptotic confidence intervals for the steady state mean from a single simulation run the sts method cancels out the variance constant while other methods attempt to consistently estimate the variance constant our goal in this paper is to generalize the sts method and to study some of its basic properties starting from a functional central limit theorem fclt for the sample mean of the simulated process a class of mappings of c 0 1 to is identified each of which leads to a sts confidence interval one of these mappings leads to the batch means method a lower bound is obtained for the expected length of the asymptotic as the run size becomes large sts confidence intervals this lower bound is not attained but can be approached arbitrarily closely by sts confidence intervals methods that consistently estimate the variance constant do realize this lower bound the variance of the length of a sts confidence interval is of larger order in the run length than is that for the regenerative method

an investigation of finite sample behavior of confidence interval estimators we investigate the small sample behavior and convergence properties of confidence interval estimators cies for the mean of a stationary discrete process we consider cies arising from nonoverlapping batch means overlapping batch means and standardized time series all of which are commonly used in discrete event simulation the performance measures of interest are the coverage probability and the expected value and variance of the half length we use empirical and analytical methods to make detailed comparisons regarding the behavior of the cies for a variety of stochastic processes all the cies under study are asymptotically valid however they are usually invalid for small sample sizes we find that for small samples the bias of the variance parameter estimator figures significantly in cie coverage performance the less bias the better a secondary role is played by the marginal distribution of the stationary process we also point out that some cies require fewer observations before manifesting

reducing the conservativeness of fully sequential indifference zone procedures in this technical note we study three sources of conservativeness in fully sequential indifference zone procedures and quantify by experiments the impact of each source in terms of the number of observations to identify which source is critical then we propose new asymptotically valid procedures that lessen conservativeness by mean update with or without variance update experimental results show that meaningful improvement on the efficiency is achieved with the new procedures

confidence interval estimation using standardized time series observations of a stationary stochastic process can be transformed into a standardized time series this paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions in particular the conditions are satisfied by stationary discrete event simulations confidence intervals can be constructed using this lemma for illustration we develop two easily computed interval estimators for the process mean when independent replications of the series are available such as in computer simulation experiments these interval estimators may be combined with the classical confidence interval estimator these interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known in an empirical study using three elementary simulated processes the interval estimators presented here compare favorably with the classical interval estimator in a recent paper goldsman and schruben goldsman d l schruben 1982 asymptotic properties of some confidence interval estimators tech rep 544 school of o r i e cornell university ithaca ny show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals

characterization of abelian varieties we prove that any smooth complex projective variety x with plurigenera p 1 x p 2 x 1 and irregularity q x dim x is birational to an abelian variety

large sample results for batch means in analyzing the output process generated by a steady state simulation we often seek to estimate the expected value of the output the sample mean based on a finite sample of size n is usually the estimator of choice for the steady state mean and a measure of the sample mean s precision is the variance parameter i e the limiting value of the sample size multiplied by the variance of the sample mean as n becomes large this paper establishes asymptotic properties of the conventional batch means bm estimator of the variance parameter as both the batch size and the number of batches become large in particular we show that the bm variance estimator is asymptotically unbiased and convergent in mean square we also provide asymptotic expressions for the variance of the bm variance estimator exact and empirical examples illustrate our findings

on the asymptotic validity of fully sequential selection procedures for steady state simulation we present fully sequential procedures for steady state simulation that are designed to select the best of a finite number of simulated systems when best is defined by the largest or smallest long run average performance we also provide a framework for establishing the asymptotic validity of such procedures and prove the validity of our procedures an example based on the m m 1 queue is given

deformation theory generic vanishing theorems and some conjectures of enriques catanese and beauville introduction 389 w notation and conventions 392 w deformations of cohomology groups 392 w generic vanishing criteria for topologically trivial line bundles 397 w a nakano type generic vanishing theorem 401 w an application to surfaces 405 references 407

fourier transforms generic vanishing theorems and polarizations of abelian varieties the purpose of this paper is to give two applications of fourier transforms and generic vanishing theorems

surfaces with pg q 3 we classify minimal complex surfaces of general type with p g q 3 more precisely we show that such a surface is either the symmetric product of a curve of genus 3 or a free z 2 quotient of the product of a curve of genus 2 and a curve of genus 3 our main tools are the generic vanishing theorems of green and lazarsfeld and the characterization of theta divisors given by hacon in corollary 3 4 of fourier transforms generic vanishing theorems and polarizations of abelian varieties

computing efforts allocation for ordinal optimization and discrete event simulation ordinal optimization has emerged as an efficient technique for simulation and optimization exponential convergence rates can be achieved in many cases in this paper we present a new approach that can further enhance the efficiency of ordinal optimization our approach intelligently determines the optimal number of simulation replications or samples and significantly reduces the total simulation cost numerical illustrations are included the results indicate that our approach can obtain an additional 74 computation time reduction above and beyond the reduction obtained through the use of ordinal optimization for a 10 design example

direct sampling method for diffusive optical tomography in this work we are concerned with the diffusive optical tomography dot problem in the case when only one or two pairs of cauchy data are available we propose a simple and efficient direct sampling method to locate inhomogeneities inside a homogeneous background and solve the dot problem in both full and limited aperture cases this new method is easy to implement and less expensive computationally numerical experiments demonstrate its effectiveness and robustness against noise in the data this provides a new promising numerical strategy for the dot problem