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

the knowledge gradient algorithm for a general class of online learning problems we derive a one period look ahead policy for finite and infinite horizon online optimal learning problems with gaussian rewards our approach is able to handle the case where our prior beliefs about the rewards are correlated which is not handled by traditional multiarmed bandit methods experiments show that our kg policy performs competitively against the best known approximation to the optimal policy in the classic bandit problem and it outperforms many learning policies in the correlated case

subdiffusive master equation with space dependent anomalous exponent and structural instability we derive the fractional master equation with space dependent anomalous exponent we analyze the asymptotic behavior of the corresponding lattice model both analytically and by monte carlo simulation we show that the subdiffusive fractional equations with constant anomalous exponent in a bounded domain 0 l are not structurally stable with respect to the nonhomogeneous variations of parameter in particular the gibbs boltzmann distribution is no longer the stationary solution of the fractional fokker planck equation whatever the space variation of the exponent might be we analyze the random distribution of in space and find that in the long time limit the probability distribution is highly intermediate in space and the behavior is completely dominated by very unlikely events we show that subdiffusive fractional equations with the nonuniform random distribution of anomalous exponent is an illustration of a black swan the low probability event of the small value of the anomalous exponent that completely dominates the long time behavior of subdiffusive systems

statistical properties of functionals of the paths of a particle diffusing in a one dimensional random potential we present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one dimensional quenched random potential we demonstrate the implementation of the formalism in two specific examples 1 where the functional corresponds to the local time spent by the particle around the origin and 2 where the functional corresponds to the occupation time spent by the particle on the positive side of the origin within an observation time window of size t we compute the disorder average distributions of the local time the inverse local time the occupation time and the inverse occupation time and show that in many cases disorder modifies the behavior drastically

myopic allocation policy with asymptotically optimal sampling rate in this note we consider the statistical ranking and selection problem of finding the best alternative when the performances of each alternative must be estimated by sampling we provide a myopic allocation policy that asymptotically achieves the sampling ratios given by the optimal computing budget allocation an approximate solution of the optimal large deviations rate for the decreasing probability of false selection we analyze the asymptotic sampling ratio for both known variances and unknown variances under a bayesian framework numerical results substantiate the theoretical results

asymptotic optimality of invariant sequential probability ratio tests it is well known that wald s sprt for testing simple hypotheses based on i i d observations minimizes the expected sample size both under the null and under the alternative hypotheses among all tests with the same or smaller error probabilities and with finite expected sample sizes under the two hypotheses in this paper it is shown that this optimum property can be extended at least asymptotically as the error probabilities tend to 0 to invariant sprts like the sequential t test the savage sethuraman sequential rank order test etc in fact not only do these invariant sprts asymptotically minimize the expected sample size but they also asymptotically minimize all the moments of the sample size distribution among all invariant tests with the same or smaller error probabilities modifications of these invariant sprts to asymptotically minimize the moments of the sample size at an intermediate parameter are also considered

learning to optimize via information directed sampling we propose information directed sampling a new approach to online optimization problems in which a decision maker must balance between exploration and exploitation while learning from partial feedback each action is sampled in a manner that minimizes the ratio between squared expected single period regret and a measure of information gain the mutual information between the optimal action and the next observation we establish an expected regret bound for information directed sampling that applies across a very general class of models and scales with the entropy of the optimal action distribution we illustrate through simple analytic examples how information directed sampling accounts for kinds of information that alternative approaches do not adequately address and that this can lead to dramatic performance gains for the widely studied bernoulli gaussian and linear bandit problems we demonstrate state of the art simulation performance the electronic companion is available at https doi org 10 128

optimal information blending with measurements in the l2 sphere a sequential information collection problem where a risk averse decision maker updates a bayesian belief about the unknown objective function of a linear program is used to investigate the informational value of measurements performed to refine a robust optimization model the information is collected in the form of a linear combination of the objective coefficients subject to random noise we have the ability to choose the weights in the linear combination creating a new nonconvex continuous optimization problem which we refer to as information blending we develop two optimal blending strategies 1 an active learning method that maximizes uncertainty reduction and 2 an economic approach that maximizes an expected improvement criterion semidefinite programming relaxations are used to create efficient convex approximations to the nonconvex blending problem

a fully sequential elimination procedure for indifference zone ranking and selection with tight bounds on probability of correct selection we consider the indifference zone iz formulation of the ranking and selection problem with independent normal samples in this problem we must use stochastic simulation to select the best among several noisy simulated systems with a statistical guarantee on solution quality existing iz procedures sample excessively in problems with many alternatives in part because loose bounds on probability of correct selection lead them to deliver solution quality much higher than requested consequently existing iz procedures are seldom considered practical for problems with more than a few hundred alternatives to overcome this we present a new sequential elimination iz procedure called biz bayes inspired indifference zone whose lower bound on worst case probability of correct selection in the preference zone is tight in continuous time and nearly tight in discrete time to the author s knowledge this is the first sequential elimination procedure with tight bounds on worst case preference zone probability of correct selection for more than two alternatives theoretical results for the discrete time case assume that variances are known and have an integer multiple structure but the biz procedure itself can be used when these assumptions are not met in numerical experiments the sampling effort used by biz is significantly smaller than that of another leading iz procedure the kn procedure especially on the largest problems tested 214 16 384 alternatives

information bounds and quick detection of parameter changes in stochastic systems by using information theoretic bounds and sequential hypothesis testing theory this paper provides a new approach to optimal detection of abrupt changes in stochastic systems this approach not only generalizes previous work in the literature on optimal detection far beyond the relatively simple models treated but also suggests alternative performance criteria which are more tractable and more appropriate for general stochastic systems in addition it leads to detection rules which have manageable computational complexity for on line implementation and yet are nearly optimal under the different performance criteria considered

sequential detection of markov targets with trajectory estimation the problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered assuming a markov evolution of the system in particular the pair signal observation forms a hidden markov model hmm a sequential procedure is proposed wherein the detection part is a sequential probability ratio test sprt and the estimation part relies upon a maximum a posteriori probability map criterion gated by the detection stage the parameter to be estimated is the trajectory of the state evolution of the system itself a thorough analysis of the asymptotic behavior of the test in this new scenario is given and sufficient conditions for its asymptotic optimality are stated i e for almost sure minimization of the stopping time and for first order minimization of any moment of its distribution an application to radar surveillance problems is also examined

comparison of the sprt and the sequential linear detector in autoregressive noise corresp the sequential probability ratio test sprt with constant thresholds and the sequential linear detector sld are compared under an autoregressive noise assumption in terms of the average sample number asn when both detectors have the same error probabilities for small asn their performances are evaluated numerically results show that the sld is better when rho the parameter in the autoregressive noise is positive and the sprt is better when rho is negative however their asymptotic efficiencies as the signal approaches zero are found to be the same

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

hierarchical knowledge gradient for sequential sampling we propose a sequential sampling policy for noisy discrete global optimization and ranking and selection in which we aim to efficiently explore a finite set of alternatives before selecting an alternative as best when exploration stops each alternative may be characterized by a multi dimensional vector of categorical and numerical attributes and has independent normal rewards we use a bayesian probability model for the unknown reward of each alternative and follow a fully sequential sampling policy called the knowledge gradient policy this policy myopically optimizes the expected increment in the value of sampling information in each time period we propose a hierarchical aggregation technique that uses the common features shared by alternatives to learn about many alternatives from even a single measurement this approach greatly reduces the measurement effort required but it requires some prior knowledge on the smoothness of the function in the form of an aggregation function and computational issues limit the number of alternatives that can be easily considered to the thousands we prove that our policy is consistent finding a globally optimal alternative when given enough measurements and show through simulations that it performs competitively with or significantly better than other policies

constrained optimization in expensive simulation novel approach this article presents a novel heuristic for constrained optimization of computationally expensive random simulation models one output is selected as objective to be minimized while other outputs must satisfy given threshold values moreover the simulation inputs must be integer and satisfy linear or nonlinear constraints the heuristic combines i sequentialized experimental designs to specify the simulation input combinations ii kriging or gaussian process or spatial correlation modeling to analyze the global simulation input output data resulting from these designs and iii integer nonlinear programming to estimate the optimal solution from the kriging metamodels the heuristic is applied to an s s inventory system and a call center simulation and compared with the popular commercial heuristic optquest embedded in the arena versions 11 and 12 in these two applications the novel heuristic outperforms optquest in terms of number of simulated input combinations and quality of the estimated optimum

omitting meaningless digits in point estimates the probability guarantee of leading digit rules motivated by the question of which point estimator digits to report in a statistical experiment we study the probabilistic behavior of the digits as a function of the true performance measure and the point estimator s standard error we investigate the family of leading digit rules which guarantees that every unreported digit has correctness probability below a given threshold choosing the threshold to be about 0 198 yields yoneda s rule the easy to implement rule that reports the point estimate through the leading digit of the standard error has threshold approximately 0 117 which is not much larger than the one in ten probability of a uniformly distributed random digit being correct

bayesian optimization via simulation with pairwise sampling and correlated prior beliefs this paper addresses discrete optimization via simulation we show that allowing for both a correlated prior distribution on the means e g with discrete kriging models and sampling correlation e g with common random numbers or crn can significantly improve the ability to quickly identify the best alternative these two correlations are brought together for the first time in a highly sequential knowledge gradient sampling algorithm which chooses points to sample using a bayesian value of information voi criterion we provide almost sure convergence guarantees as the number of samples grows without bound when parameters are known and provide approximations that allow practical implementation including a novel use of the voi s gradient rather than the response surface s gradient we demonstrate that crn leads to improved optimization performance for voi based algorithms in sequential sampling environments with a combinatorial number of alternatives and costly samples

boundary conditions of normal and anomalous diffusion from thermal equilibrium infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomenon starting with an underlying continuous time random walk model we derive the boundary conditions for the diffusion equations describing this problem we discuss a simple method showing how the boundary conditions can be determined from equilibrium experiments when the diffusion processes are close to thermal equilibrium the boundary conditions are determined by a thermal boltzmann factor which in turn controls the solution of the problem

bisection search with noisy responses bisection search is the most efficient algorithm for locating a unique point x 0 1 when we are able to query an oracle only about whether x lies to the left or right of a point x of our choosing we study a noisy version of this classic problem where the oracle s response is correct only with probability p the probabilistic bisection algorithm pba introduced by horstein ieee trans inform theory 9 1963 pp 136 143 can be used to locate x in this setting while the method works extremely well in practice very little is known about its theoretical properties in this paper we provide several key findings about the pba which lead to the main conclusion that the expected absolute residuals of successive search results i e e x xn converge to 0 at a geometric rate

a multiple attribute utility theory approach to ranking and selection managers of large industrial projects often measure performance by multiple attributes for example our paper is motivated by the simulation of a large industrial project called a land seismic survey in which project performance is based on duration cost and resource utilization to address these types of problems we develop a ranking and selection procedure for making comparisons of systems e g project configurations that have multiple performance measures the procedure combines multiple attribute utility theory with statistical ranking and selection to select the best configuration from a set of possible configurations using the indifference zone approach we apply our procedure to results generated by the simulator for a land seismic survey that has six performance measures and describe a particular type of sensitivity analysis that can be used as a robustness check

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

sequential selection procedures using sample means to improve efficiency abstract two stage selection procedures have been widely studied and applied to determine appropriate sample sizes for selecting the best of k designs however standard indifference zone procedures are derived with a statistically conservative least favorable configuration assumption the enhanced two stage selection etss is a procedure that takes into account not only the variance of samples but also the difference between sample means when determining the sample sizes this paper discusses an implementation of sequential ranking and selection procedures due to the etss procedure to avoid relying too much on information obtained in just one stage we show that the needed ratios of sample sizes to maximize the probability of correct selection is approximately maintained at all iterations an experimental performance evaluation demonstrates the efficiency of our sequential procedures

continuous optimization via simulation using golden region search simulation optimization so is a class of mathematical optimization techniques in which the objective function can only be numerically evaluated through simulation in this paper a new so approach called golden region gr search is developed for continuous problems gr divides the feasible region into a number of sub regions and selects one region in each iteration for further search based on the quality and distribution of simulated points in the feasible region and the result of scanning the response surface through a metamodel monte carlo experiments show that the gr method is efficient compared to three well established approaches in the literature we also prove the asymptotic convergence in probability to a global optimum for a large class of random search methods in general and gr in particular

statistics of natural populations iii sequential sampling plans for the estimation of gene frequencies in previous work several models have been developed for genetic surveys of natural populations parents of unknown genotype are collected from a natural population polymorphic at a single genetic locus from each of these n cryptic parents a number of offspring are identified for their genotype our problem is to select an efficient offspring sampling plan for estimating the frequency of an allele in the cryptic adult population based on the n family profiles of juvenile genotypes a criterion called the information per unit cost of observation is introduced to evaluate sequential sampling plans in which the number of offspring per family examined is random some simple practical schemes for stopping the sampling of offspring from a collected parent are introduced one example is stopping when i the offspring are definitive about the parental genotype s for the first time ii a fixed number of one genotype only is seen or iii a fixed maximum feasible number of offspring have been genotyped this sampling scheme is recommended for each sampling scheme the best linear unbiased estimator and the sequential maximum likelihood estimator of the allele frequency are characterized from the moments of these estimators it is then possible to tabulate efficient sequential sampling plans which are better in the sense of information per unit cost just as simple and less costly than corresponding fixed sampling plans in use

selection procedures with frequentist expected opportunity cost bounds selection procedures help identify the best of a finite set of simulated alternatives most work has measured the quality of a selection with the probability of correct selection p cs but the expected opportunity cost of a potentially incorrect decision makes more sense in business contexts this paper analyzes the first selection procedures that guarantee an upper bound for the expected opportunity cost in a frequentist sense of a potentially incorrect selection the paper therefore bridges a gap between the indifference zone approach with frequentist guarantees but for the p cs and the bayesian approach to selection procedures which has considered the opportunity cost we also provide unexpected expected opportunity cost guarantees for several existing indifference zone selection procedures that were originally designed to provide p cs guarantees

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

bayesian decision process for cost efficient dynamic ranking via crowdsourcing rank aggregation based on pairwise comparisons over a set of items has a wide range of applications although considerable research has been devoted to the development of rank aggregation algorithms one basic question is how to efficiently collect a large amount of high quality pairwise comparisons for the ranking purpose because of the advent of many crowdsourcing services a crowd of workers are often hired to conduct pairwise comparisons with a small monetary reward for each pair they compare since different workers have different levels of reliability and different pairs have different levels of ambiguity it is desirable to wisely allocate the limited budget for comparisons among the pairs of items and workers so that the global ranking can be accurately inferred from the comparison results to this end we model the active sampling problem in crowdsourced ranking as a bayesian markov decision process which dynamically selects item pairs and workers to improve the ranking accuracy under a budget constraint we further develop a computationally efficient sampling policy based on knowledge gradient as well as a moment matching technique for posterior approximation experimental evaluations on both synthetic and real data show that the proposed policy achieves high ranking accuracy with a lower labeling cost

feynman kac formula for heat equation driven by fractional white noise we establish a version of the feynman kac formula for the multidimensional stochastic heat equation with a multiplicative fractional brownian sheet we use the techniques of malliavin calculus to prove that the process defined by the feynman kac formula is a weak solution of the stochastic heat equation from the feynman kac formula we establish the smoothness of the density of the solution and the holder regularity in the space and time variables we also derive a feynman kac formula for the stochastic heat equation in the skorokhod sense and we obtain the wiener chaos expansion of the solution

consistency of sequential bayesian sampling policies we consider bayesian information collection in which a measurement policy collects information to support a future decision this framework includes ranking and selection continuous global optimization and many other problems in sequential experimental design we give a sufficient condition under which measurement policies sample each measurement type infinitely often ensuring consistency i e that a globally optimal future decision is found in the limit this condition is useful for verifying consistency of adaptive sequential sampling policies that do not do forced random exploration making consistency difficult to verify by other means we demonstrate the use of this sufficient condition by showing consistency of two previously proposed ranking and selection policies optimal computing budget allocation ocba for linear loss and the knowledge gradient policy with independent normal priors consistency of the knowledge gradient policy was shown previously while the consistency result for ocba is new

fractional feynman kac equation for weak ergodicity breaking the continuous time random walk ctrw is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps a power law distribution of the waiting times 1 leads to subdiffusion x 2 t for 0 1 in closed systems the long stagnation periods cause time averages to divert from the corresponding ensemble averages which is a manifestation of weak ergodicity breaking the time average of a general observable u t 1 t 0 t u x d is a functional of the path and is described by the well known feynman kac equation if the motion is brownian here we derive forward and backward fractional feynman kac equations for functionals of ctrw in a binding potential we use our equations to study two specific time averages the fraction of time spent by a particle in half box and the time average of the particle s position in a harmonic field in both cases we obtain the probability density function of the time averages for t and the first two moments our results show that both the occupation fraction and the time averaged position are random variables even for long times except for 1 when they are identical to their ensemble averages using our fractional feynman kac equation we also study the dynamics leading to weak ergodicity breaking namely the convergence of the fluctuations to their asymptotic values

subdiffusion chemotaxis and anomalous aggregation we propose a nonlinear random walk model which is suitable for the analysis of both chemotaxis and anomalous subdiffusive transport we derive the master equations for the population density for the case when the transition rate for a random walk depends on residence time chemotactic substance and population density we introduce the anomalous chemotactic sensitivity and find an anomalous aggregation phenomenon so we suggest a different explanation of the well known effect of chemotactic collapse

information collection for linear programs with uncertain objective coefficients consider a linear program lp with uncertain objective coefficients for which we have a bayesian prior we can collect information to improve our understanding of these coefficients but this may be expensive giving us a separate problem of optimizing the collection of information to improve the quality of the solution relative to the true cost coefficients we formulate this information collection problem for lps for the first time and derive a knowledge gradient policy which finds the marginal value of each measurement by solving a sequence of lps we prove that this policy is asymptotically optimal and demonstrate its performance on a network flow problem

feynman kac formula for the heat equation driven by fractional noise with hurst parameter h 1 2 in this paper a feynman kac formula is established for stochastic partial differential equation driven by gaussian noise which is with respect to time a fractional brownian motion with hurst parameter h 1 2 to establish such a formula we introduce and study a nonlinear stochastic integral from the given gaussian noise to show the feynman kac integral exists one still needs to show the exponential integrability of nonlinear stochastic integral then the approach of approximation with techniques from malliavin calculus is used to show that the feynman kac integral is the weak solution to the stochastic partial differential equation

operating characteristic and average sample number of binary and multi hypothesis sequential probability ratio test the operating characteristic oc and average sample number asn of the sequential probability ratio test sprt and multi hypothesis sprt msprt are studied we consider the case where the observation sequence is independent but not necessarily identically distributed also the thresholds for the test can be time varying based on the governing equations for oc and asn of the sprt developed in our previous work a solution for the general case is proposed the governing equations for oc and asn of the msprt are also obtained numerical solutions for msprt are developed basically the solutions rely on approximating the original test by truncation that is truncating the test at some finite time k we show that under some mild conditions the approximation error diminishes as k increases at the cost of increased computation numerical examples are provided to demonstrate our solutions by comparing with monte carlo simulations simon s lower bound and dragalin s method if available for asn

fractional chemotaxis diffusion equations we introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding the mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations different models are proposed depending on the timing of the chemotactic forcing generalizations of the models to include linear reaction dynamics are also derived finally a monte carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations the model equations developed here could be used to replace keller segel type equations in biological systems with transport hindered by traps macromolecular crowding or other obstacles

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

a lower bound for the correct subset selection probability and its application to discrete event system simulations ordinal optimization concentrates on finding a subset of good designs by approximately evaluating a parallel set of designs and reduces the required simulation time dramatically for discrete event simulation and optimization the estimation of the confidence probability cp that the selected designs contain at least one good design is crucial to ordinal optimization however it is very difficult to estimate this probability in des simulation especially for complicated des with large number of designs this paper proposes two simple lower bounds for quantifying the confidence probability numerical testing is presented

optimality of cusum rule approximations in change point detection problems application to nonlinear state space systems the well known cumulative sum cusum sequential rule for abrupt model change detection in stochastic dynamic systems relies on the knowledge of the probability density functions of the system output variables conditional on their past values and on the system functioning mode at each time step this paper shows how to build an asymptotically optimal detection rule under the common average run length arl constraint when these densities are not available but can be consistently estimated this is the case for nonlinear state space systems observed through output variables for such systems a new class of particle filters based on convolution kernels allows to get consistent estimates of the conditional densities leading to an optimal cusum like filter detection rule fdr

economic analysis of simulation selection problems ranking and selection procedures are standard methods for selecting the best of a finite number of simulated design alternatives based on a desired level of statistical evidence for correct selection but the link between statistical significance and financial significance is indirect and there has been little or no research into it this paper presents a new approach to the simulation selection problem one that maximizes the expected net present value of decisions made when using stochastic simulation we provide a framework for answering these managerial questions when does a proposed system design whose performance is unknown merit the time and money needed to develop a simulation to infer its performance for how long should the simulation analysis continue before a design is approved or rejected we frame the simulation selection problem as a stoppable version of a bayesian bandit problem that treats the ability to simulate as a real option prior to project implementation for a single proposed system we solve a free boundary problem for a heat equation that approximates the solution to a dynamic program that finds optimal simulation project stopping times and that answers the managerial questions for multiple proposed systems we extend previous bayesian selection procedures to account for discounting and simulation tool development costs

fractional feynman kac equation with space dependent anomalous exponent to describe the distribution of functionals for inhomogeneous subdiffusion in space and time dependent force field we derive forward and backward time fractional feynman kac equations with space dependent anomalous exponent based on the space jump random walk model in our examples we get the statistic of occupation fraction and first passage time for anomalous infiltration of free particles in disordered systems by applying the backward version

exact solution of a generalized kramers fokker planck equation retaining retardation effects in order to describe non gaussian kinetics in weakly damped systems the concept of continuous time random walks is extended to particles with finite inertia one thus obtains a generalized kramers fokker planck equation which retains retardation effects i e nonlocal couplings in time and space it is shown that despite this complexity exact solutions of this equation can be given in terms of superpositions of gaussian distributions with varying variances in particular the long time behavior of the respective low order moments is calculated

fractional diffusion in inhomogeneous media starting from the continuous time random walk ctrw scheme with the space dependent waiting time probability density function pdf we obtain the time fractional diffusion equation with varying in space fractional order of time derivative as an example we study the evolution of a composite system consisting of two separate regions with different subdiffusion exponents and demonstrate the effects of non trivial drift and subdiffusion whose laws are changed in the course of time

functional feynman kac equations for limit lognormal multifractals a novel technique of functional feynman kac equations is developed for the probability distribution of the limit lognormal multifractal process introduced by mandelbrot in statistical models and turbulence m rosenblatt and c van atta eds springer new york 1972 and constructed explicitly by bacry delour and muzy phys rev e 64 026103 2001 the distribution of the process is known to be determined by the complicated stochastic dependence structure of its increments sdsi it is shown that the sdsi has two separate layers of complexity that can be captured in a precise way by a pair of functional feynman kac equations for the laplace transform exact solutions are obtained as power series expansions in the intermittency parameter using a novel intermittency differentiation rule the expansion of the moments gives a new representation of the selberg integral

sequential detection of targets in multichannel systems it is supposed that there is a multichannel sensor system which performs sequential detection of a target sequential detection is done by implementing a generalized wald s sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows one to fix the false alarm rate and the rate of missed detections at specified levels we present the asymptotic performance of this sequential detection procedure and show that it is asymptotically optimal in the sense of minimizing the expected sample size when the probabilities of erroneous decisions are small we do not assume that the observations are independent and identically distributed i i d the first order asymptotic optimality result holds for general statistical models that are not confined to the restrictive i i d assumption however for i i d and quasi i i d cases where the log likelihood ratios can be represented in the form of sums of random walks and slowly changing sequences we obtain much stronger results specifically using the nonlinear renewal theory we are able to obtain both tight expressions for the error probabilities and higher order approximations for the average sample size up to a vanishing term the performance of the multichannel sequential detection algorithm is illustrated by an example of detection of a deterministic signal in correlated colored gaussian noise in this example we provide both the results of theoretical analysis and the results of a monte carlo experiment these results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best nonsequential algorithm

selecting a selection procedure selection procedures are used in a variety of applications to select the best of a finite set of alternatives best is defined with respect to the largest mean but the mean is inferred with statistical sampling as in simulation optimization there are a wide variety of procedures which begs the question of which selection procedure to select the main contribution of this paper is to identify through extensive experimentation the most effective selection procedures when samples are independent and normally distributed we also a summarize the main structural approaches to deriving selection procedures b formalize new sampling allocations and stopping rules c identify strengths and weaknesses of the procedures d identify some theoretical links between them and e present an innovative empirical test bed with the most extensive numerical comparison of selection procedures to date the most efficient and easiest to control procedures allocate samples with a bayesian model for uncertainty about the means and use new adaptive stopping rules proposed here

multihypothesis sequential probability ratio tests i asymptotic optimality the problem of sequential testing of multiple hypotheses is considered and two candidate sequential test procedures are studied both tests are multihypothesis versions of the binary sequential probability ratio test sprt and are referred to as msprts the first test is motivated by bayesian optimality arguments while the second corresponds to a generalized likelihood ratio test it is shown that both msprts are asymptotically optimal relative not only to the expected sample size but also to any positive moment of the stopping time distribution when the error probabilities or more generally risks associated with incorrect decisions are small the results are first derived for the discrete time case of independent and identically distributed i i d observations and simple hypotheses they are then extended to general possibly continuous time statistical models that may include correlated and nonhomogeneous observation processes it also demonstrated that the results can be extended to hypothesis testing problems with nuisance parameters where the composite hypotheses due to nuisance parameters can be reduced to simple ones by using the principle of invariance these results provide a complete generalization of the results given by veeravalli and baum see ibid vol 41 p 1994 97 1995 where it was shown that the quasi bayesian msprt is asymptotically efficient with respect to the expected sample size for i i d observations

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

information collection on a graph we derive a knowledge gradient policy for an optimal learning problem on a graph in which we use sequential measurements to refine bayesian estimates of individual edge values in order to learn about the best path this problem differs from traditional ranking and selection in that the implementation decision the path we choose is distinct from the measurement decision the edge we measure our decision rule is easy to compute and performs competitively against other learning policies including a monte carlo adaptation of the knowledge gradient policy for ranking and selection

the correlated knowledge gradient for simulation optimization of continuous parameters using gaussian process regression we extend the concept of the correlated knowledge gradient policy for the ranking and selection of a finite set of alternatives to the case of continuous decision variables we propose an approximate knowledge gradient for problems with continuous decision variables in the context of a gaussian process regression model in a bayesian setting along with an algorithm to maximize the approximate knowledge gradient in the problem class considered we use the knowledge gradient for continuous parameters to sequentially choose where to sample an expensive noisy function in order to find the maximum quickly we show that the knowledge gradient for continuous decisions is a generalization of the efficient global optimization algorithm proposed in d r jones m schonlau and w j welch j global optim 13 1998 pp 455 492

on distributions of functionals of anomalous diffusion paths functionals of brownian motion have diverse applications in physics mathematics and other fields the probability density function pdf of brownian functionals satisfies the feynman kac formula which is a schrodinger equation in imaginary time in recent years there is a growing interest in particular functionals of non brownian motion or anomalous diffusion but no equation existed for their pdf here we derive a fractional generalization of the feynman kac equation for functionals of anomalous paths based on sub diffusive continuous time random walk we also derive a backward equation and a generalization to levy flights solutions are presented for a wide number of applications including the occupation time in half space and in an interval the first passage time the maximal displacement and the hitting probability we briefly discuss other fractional schrodinger equations that recently appeared in the literature

a quantile based approach to system selection abstract we propose a quantile based ranking and selection r s procedure for comparing a finite set of stochastic systems via simulation our r s procedure uses a quantile set of the simulated probability distribution of a performance characteristic of interest that best represents the most appropriate selection criterion as the basis for comparison since this quantile set may represent either the downside risk upside risk or central tendency of the performance characteristic the proposed approach is more flexible than the traditional mean based approach to r s we first present a procedure that selects the best system from among k systems and then we modified that procedure for the case where k 1 systems are compared against a standard system we present a set of experiments to highlight the flexibility of the proposed procedures

outlier resistant algorithms for detecting a change in a stochastic process outlier resistant algorithms that detect a change from a given nominal stationary process to another such process are given the nominal processes are assumed to be mutually independent and to satisfy some general regularity conditions the outlier sequences are assumed to be independently and identically distributed and independent of the nominal processes the proposed algorithms are sequential and consist of uniformly bounded steps the asymptotic performance of the algorithms is analyzed both in the absence and the presence of outliers breakdown points and influence functions are defined and analyzed the algorithms are studied in more detail for gaussian autoregressive nominal processes

on the convergence rates of expected improvement methods we consider a ranking and selection problem with independent normal observations and we analyze the asymptotic sampling rates of expected improvement ei methods in this setting such methods often perform well in practice but a tractable analysis of their convergence rates is difficult because of the nonlinearity and nonconvexity of the ei calculations we present new results indicating that for known sampling noise variants of ei produce asymptotic simulation allocations that are essentially identical to those chosen by the optimal computing budget allocation ocba methodology which is known to yield near optimal asymptotic performance in ranking and selection this is the first general equivalence result between ei and ocba and it provides insight into the good practical performance of ei we also derive the limiting allocation for ei under unknown sampling variance

residence time statistics for normal and fractional diffusion in a force field we investigate statistics of occupation times for an over damped brownian particle in an external force field using a backward fokker planck equation introduced by majumdar and comtet for an arbitrary potential field the distribution of occupation times is expressed in terms of solutions of the corresponding first passage time problem this general relationship between occupation times and first passage times is valid for normal markovian diffusion and for non markovian sub diffusion the latter modeled using the fractional fokker planck equation for binding potential fields we find in the long time limit ergodic behavior for normal diffusion while for the fractional framework weak ergodicity breaking is found in agreement with previous results of bel and barkai on the continuous time random walk on a lattice for non binding cases rich physical behaviors are obtained and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite our work establishes a link between fractional calculus and ergodicity breaking