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

the delivery man problem and cumulative matroids given a complete directed graph g v a the delivery man problem dmp consists of determining a hamiltonian circuit minimizing the sum of distances along the circuit from a given vertex v1 to every vertex of v including v1 itself there exists a number of applications of the dmp in the fields of distribution and machine scheduling the dmp is np hard the objective of this paper is to develop new theoretical results and an exact algorithm for the problem a new integer linear programming formulation is provided and results on the matroidal structure of a class of combinatorial problems are developed these are used to derive lower bounds for the dmp these bounds are embedded into an enumerative algorithm the largest problems solved to optimality with the proposed algorithm involve 60 vertices this compares favorably with previously published methods

a single pass algorithm for spectrum estimation with fast convergence we propose a single pass algorithm for estimating spectral densities of stationary processes our algorithm is computationally fast in the sense that when a new observation arrives it can provide a real time update within o 1 computation the proposed algorithm is probabilistically fast in that for stationary processes whose auto covariances decay geometrically the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor we also establish asymptotic normality for the recursive estimate a simulation study is carried out and it confirms the superiority over the classical batched mean estimates

endemic bubbles generated by delayed behavioral response global stability and bifurcation switches in an sis model during infectious disease outbreaks people may reduce their contact numbers or take other precautions to prevent transmission the change in their behavior can be directly or indirectly triggered by the density of infected individuals in the population in this paper we investigate an sis susceptible infected susceptible model where the transmission rate is a decreasing function of the prevalence of the disease determined by a reduction function h with the assumption that such a change in the transmission rate occurs with some time delay we prove that if the basic reproduction number r 0 is less than one then the disease free equilibrium is globally asymptotically stable while for r 0 1 a unique endemic equilibrium exists and the disease uniformly persists regardless of the delay or the specific form of h however characterized by the shape of the response function h various dynamics are possible if r 0 1 roughly speaking if h is decreasing slowly weak response then the end

global dynamics in a commodity market model a b s t r a c t we study the global behavior of the price dynamics in a commodity market governed by a balance between demand and supply while the dependence of demand on price is considered instantaneous the supply term contains a delay leading to a delay differential equation a discrete model is naturally defined as a limit case of this equation we provide a thorough study of the discrete case and use these results to get new sufficient conditions for the global convergence of the solutions to the positive equilibrium in the continuous case for when the equilibrium is unstable we provide some bounds for the amplitude of the oscillations that are quite sharp when the delay is large

an attraction repulsion point process model for respiratory syncytial virus infections summary how is the progression of a virus influenced by properties intrinsic to individual cells we address this question by studying the susceptibility of cells infected with two strains of the human respiratory syncytial virus rsv a and rsv b in an in vitro experiment spatial patterns of infected cells give us insight into how local conditions influence susceptibility to the virus we observe a complicated attraction and repulsion behavior a tendency for infected cells to lump together or remain apart we develop a new spatial point process model to describe this behavior inference on spatial point processes is difficult because the likelihood functions of these models contain intractable normalizing constants we adapt an mcmc algorithm called double metropolis hastings to overcome this computational challenge our methods are computationally efficient even for large point patterns consisting of over 10 000 points we illustrate the application of our model and inferential approach to simulated data examples and fit our model to various rsv experiments because our model parameters are easy to interpret we are able to draw meaningful scientific conclusions from the fitted models

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

sufficient burn in for gibbs samplers for a hierarchical random effects model we consider gibbs and block gibbs samplers for a bayesian hierarchical version of the one way random effects model drift and minorization conditions are established for the underlying markov chains the drift and minorization are used in conjunction with results from j s rosenthal j amer statist assoc 90 1995 558 566 and g o roberts and r l tweedie stochastic process appl 80 1999 211 229 to construct analytical upper bounds on the distance to stationarity these lead to upper bounds on the amount of burn in that is required to get the chain within a prespecified total variation distance of the stationary distribution the results are illustrated with a numerical example 1 introduction we consider a bayesian hierarchical version of the standard normal theory one way random effects model the posterior density for this model is intractable in the sense that the integrals required for making inferences cannot be computed in closed form hobert and geyer 1998 analyzed a gibbs sampler and a block gibbs sampler for this problem and showed that the markov chains underlying these algorithms converge to the stationary i e posterior distribution at a geometric rate however hobert and geyer stopped short of constructing analytical upper bounds on the total variation distance to stationarity in this article we construct such upper bounds and this leads to a method for determining a sufficient burn in our results are useful from a practical standpoint because they obviate troublesome ad hoc convergence diagnostics cowles and carlin 1996 and

approximation schemes for minimum latency problems the minimum latency problem also known as the traveling repairman problem is a variant of the traveling salesman problem in which the starting node of the tour is given and the goal is to minimize the sum of the arrival times at the other nodes we present a quasi polynomial time approximation scheme qptas for this problem when the instance is a weighted tree when the nodes lie in mathbb r d for some fixed d and for planar graphs we also present a polynomial time constant factor approximation algorithm for the general metric case the currently best polynomial time approximation algorithm for general metrics due to goemans and kleinberg computes a 3 59 approximation

the method of simulated scores for the estimation of ldv models the method of simulated scores mss is presented for estimating limited dependent variables models ldv with flexible correlation structure in the unobservables we propose simulators that are continuous in the unknown parameter vectors and hence standard optimization methods can be used to compute the mss estimators that employ these simulators the first continuous method relies on a recursive conditioning of the multivariate normal density through a cholesky triangularization of its variance covariance matrix the second method combines results about the conditionals of the multivariate normal distribution with gibbs resampling techniques we establish consistency and asymptotic normality of the mss estimators and derive suitable rates at which the number of simulations must rise if biased simulators are used

on the geometric convergence of the gibbs sampler summary the rate of convergence of the gibbs sampler is discussed the gibbs sampler is a monte carlo simulation method with extensive application to computational issues in the bayesian paradigm conditions for the geometric rate of convergence of the algorithm for discrete and continuous parameter spaces are derived and an illustrative exponential family example is given this paper investigates conditions under which the gibbs sampler gelfand and smith 1990 tanner and wong 1987 geman and geman 1984 converges at a geometric rate the main results appear in sections 2 and 3 where geometric convergence results are established with respect to total variation and supremum norms under fairly natural conditions on the underlying distribution for ease of exposition we shall concentrate on the two most commonly encountered situations where the state space is finite or continuous all our results will establish uniform convergence a strong form of geometric convergence under appropriate regularity conditions uniform convergence is a useful property in its own right but also happens to be a sufficient condition for certain ergodic central limit theorems such results are important for estimation in markov chain simulation but will not be considered in detail here our approach is to apply the theory of markov chains to the specific gibbs sampler case in the finite state space case uniform ergodicity is automatic however the situation is more complicated for continuous state spaces where even well behaved underlying distributions can give rise to markov chains which converge slowly or have unbounded kernels we give two results in this context corollary 2 and corollary 3 which establish uniform convergence under different sets of conditions on the underlying density finally we apply these results to an example of a bayesian hierarchical model where regularity conditions for geometric convergence are naturally satisfied here the hierarchical structure of the model is crucial in permitting application of corollary 3

a unified solution framework for multi attribute vehicle routing problems vehicle routing attributes are extra characteristics and decisions that complement the academic problem formulations and aim to properly account for real life application needs hundreds of methods have been introduced in recent years for specific attributes but the development of a single general purpose algorithm which is both efficient and applicable to a wide family of variants remains a considerable challenge yet such a development is critical for understanding the proper impact of attributes on resolution approaches and to answer the needs of actual applications this paper contributes towards addressing these challenges with a component based design for heuristics targeting multi attribute vehicle routing problems and an efficient general purpose solver the proposed unified hybrid genetic search metaheuristic relies on problem independent unified local search genetic operators and advanced diversity management methods problem specifics are confined to a limited part of the method and are addressed by means of assignment sequencing and route evaluation components which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities extensive computational experiments on 29 prominent vehicle routing variants 42 benchmark instance sets and overall 1099 instances demonstrate the remarkable performance of the method which matches or outperforms the current state of the art problem tailored algorithms thus generality does not necessarily go against efficiency for these problem classes

bayesian analysis of contingent claim model error abstract this paper formally incorporates parameter uncertainty and model error into the implementation of contingent claim models we make hypotheses for the distribution of errors to allow the use of likelihood based estimators consistent with parameter uncertainty and model error we then write a bayesian estimator which does not rely on large sample properties but allows exact inference on the relevant functions of the parameters option value hedge ratios and forecasts this is crucial because the common practice of frequently updating the model parameters leads to small samples even for simple error structures and the black scholes model the bayesian estimator does not have an analytical solution markov chain monte carlo estimators help solve this problem we show how they extend to some generalizations of the error structure we apply these estimators to the black scholes given recent work using non parametric function to price options we nest the b s in a polynomial expansion of its inputs despite improved in sample fit the expansions do not yield any out of sample improvement over the b s also the out of sample errors though larger than in sample are of the same magnitude this contrasts with the performance of the popular implied tree methods which produce outstanding in sample but disastrous out of sample fit as dumas fleming and whaley 1997 show this means that the estimation method is as crucial as the model itself

optimal mean squared error batch sizes when an estimator of the variance of the sample mean is parameterized by batch size one approach for selecting batch size is to pursue the minimal mean squared error mse we show that the convergence rate of the variance of the sample mean and the bias of estimators of the variance of the sample mean asymptotically depend on the data process only through its marginal variance and the sum of the autocorrelations weighted by their absolute lags combining these results with variance results of goldsman and meketon we obtain explicit asymptotic approximations for mse optimal batch size optimal mse and robustness for four quadratic form estimators of the variance of the sample mean our empirical results indicate that the asymptotic approximations are reasonably accurate for sample sizes seen in practice although we do not discuss batch size estimation procedures the empirical results suggest that the explicit asymptotic batch size approximation which depends only on a summary measure which we re

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

convergence rates and asymptotic standard errors for markov chain monte carlo algorithms for bayesian probit regression consider a probit regression problem in which y 1 y n are independent bernoulli random variables such that pr y i 1 x i t where x i is a p dimensional vector of known covariates that are associated with y i is a p dimensional vector of unknown regression coefficients and denotes the standard normal distribution function we study markov chain monte carlo algorithms for exploring the intractable posterior density that results when the probit regression likelihood is combined with a flat prior on we prove that albert and chib s data augmentation algorithm and liu and wu s px da algorithm both converge at a geometric rate which ensures the existence of central limit theorems for ergodic averages under a second moment condition although these two algorithms are essentially equivalent in terms of computational complexity results of hobert and marchev imply that the px da algorithm is theoretically more efficient in the sense that the asymptotic variance in the central limit theorem under the px da algorithm is no larger than that under albert and chib s algorithm we also construct minorization conditions that allow us to exploit regenerative simulation techniques for the consistent estimation of asymptotic variances as an illustration we apply our results to van dyk and meng s lupus data this example demonstrates that huge gains in efficiency are possible by using the px da algorithm instead of albert and chib s algorithm

a coupling regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms abstract here i propose a convergence diagnostic for markov chain monte carlo mcmc algorithms based on couplings of a markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value the diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains and provides a lower bound on the effective sample size of a mcmc run it also provides a simple procedure for obtaining what is with high probability an independent sample from the stationary distribution

on the applicability of regenerative simulation in markov chain monte carlo we consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in markov chain monte carlo chan geyer 1994 established a central limit theorem for ergodic averages by assuming that the underlying markov chain is geometrically ergodic and that a simple moment condition is satisfied while it is relatively straightforward to check chan geyer s conditions their theorem does not lead to a consistent and easily computed estimate of the variance of the asymptotic normal distribution conversely mykland et al 1995 discuss the use of regeneration to establish an alternative central limit theorem with the advantage that a simple consistent estimator of the asymptotic variance is readily available however their result assumes a pair of unwieldy moment conditions whose verification is difficult in practice in this paper we show that the conditions of chan geyer s theorem are sufficient to establish the central limit theorem of mykland et al this result in conjunction with other recent developments should pave the way for more widespread use of the regenerative method in markov chain monte carlo our results are illustrated in the context of the slice sampler

fixed width output analysis for markov chain monte carlo markov chain monte carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages a fundamental question is when sampling should stop that is at what point the ergodic averages are good estimates of the desired quantities we consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user specified value hence calculating a monte carlo standard error is a critical step in assessing the simulation output we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution we give sufficient conditions for the strong consistency of both methods and investigate their finite sample properties in various examples

a simple and effective metaheuristic for the minimum latency problem abstract the minimum latency problem mlp is a variant of the traveling salesman problem which aims to minimize the sum of arrival times at vertices the problem arises in a number of practical applications such as logistics for relief supply scheduling and data retrieval in computer networks this paper introduces a simple metaheuristic for the mlp based on a greedy randomized approach for solution construction and iterated variable neighborhood descent with random neighborhood ordering for solution improvement extensive computational experiments on nine sets of benchmark instances involving up to 1000 customers demonstrate the good performance of the method which yields solutions of higher quality in less computational time when compared to the current best approaches from the literature optimal solutions known for problems with up to 50 customers are also systematically obtained in a fraction of seconds

automatic optimal batch size selection for recursive estimators of time average covariance matrix abstractthe time average covariance matrix tacm k z k where k is the auto covariance function is an important quantity for the inference of the mean of an rd valued stationary process d 1 this article proposes two recursive estimators for with optimal asymptotic mean square error amse under different strengths of serial dependence the optimal estimator involves a batch size selection which requires knowledge of a smoothness parameter k z k k for some this article also develops recursive estimators for combining these two estimators we obtain a fully automatic procedure for optimal online estimation for consistency and convergence rates of the proposed estimators are derived applications to confidence region construction and markov chain monte carlo convergence diagnosis are discussed supplementary materials for this article are available online

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

a few remarks on fixed width output analysis for markov chain monte carlo by jones et al our aim is to relax assumptions and simplify proofs in results given by jones haran caffo and neath in the recent paper fixed width output analysis for markov chain monte carlo

convergence analysis of the gibbs sampler for bayesian general linear mixed models with improper priors bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density however if a conditionally conjugate prior density is adopted then there is a simple gibbs sampler that can be employed to explore the posterior density a popular default among the conditionally conjugate priors is an improper prior that takes a product form with a flat prior on the regression parameter and so called power priors on each of the variance components in this paper a convergence rate analysis of the corresponding gibbs sampler is undertaken the main result is a simple easily checked sufficient condition for geometric ergodicity of the gibbs markov chain this result is close to the best possible result in the sense that the sufficient condition is only slightly stronger than what is required to ensure posterior propriety the theory developed in this paper is extremely important from a practical standpoint because it guarantees the existence of central limit theorems that allow for the computation of valid asymptotic standard errors for the estimates computed using the gibbs sampler

domain decomposition method for the global dynamics of delay differential equations with unimodal feedback x t zkmx t c f x tkt with unimodal feedback is studied the existence of the global attractor is shown and bounds of the attractor are given we find attractive invariant intervals and give sufficient conditions that guarantee that all solutions enter the domain where f 0 is negative with respect to a positive equilibrium so the results for delayed monotone feedback can be applied to describe the asymptotic behaviour of solutions in particular the existence of heteroclinic orbits from the trivial equilibrium to a periodic orbit oscillating around the positive equilibrium is established numerical examples using nicholson s blowflies equation and the mackey glass equation are provided to illustrate the main results

convergence of slice sampler markov chains we analyse theoretical properties of the slice sampler we find that the algorithm has extremely robust geometric ergodicity properties for the case of just one auxiliary variable we demonstrate that the algorithm is stochastically monotone and we deduce analytic bounds on the total variation distance from stationarity of the method by using foster lyapunov drift condition methodology

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

geometric ergodicity of gibbs samplers for bayesian general linear mixed models with proper priors when a bayesian version of the general linear mixed model is created by adopting a conditionally conjugate prior distribution a simple block gibbs sampler can be employed to explore the resulting intractable posterior density in this article it is shown that under mild conditions that nearly always hold in practice the block gibbs markov chain is geometrically ergodic

estimates and standard errors for ratios of normalizing constants from multiple markov chains via regeneration in the classical biased sampling problem we have k densities 1 k each known up to a normalizing constant i e for l 1 k l l ml where l is a known function and ml is an unknown constant for each l we have an iid sample from l and the problem is to estimate the ratios ml ms for all l and all s this problem arises frequently in several situations in both frequentist and bayesian inference an estimate of the ratios was developed and studied by vardi and his co workers over two decades ago and there has been much subsequent work on this problem from many different perspectives in spite of this there are no rigorous results in the literature on how to estimate the standard error of the estimate we present a class of estimates of the ratios of normalizing constants that are appropriate for the case where the samples from the l s are not necessarily iid sequences but are markov chains we also develop an approach based on regenerative simulation for obtaining standard errors for the estimates of ratios of normalizing constants these standard error estimates are valid for both the iid case and the markov chain case

specification tests based on mcmc output abstract two test statistics are proposed to determine model specification after a model is estimated by an mcmc method the first test is the mcmc version of ios a test and its asymptotic null distribution is normal the second test is motivated from the power enhancement technique of fan et al 2015 it combines a component j 1 that tests a null point hypothesis in an expanded model and a power enhancement component j 0 obtained from the first test it is shown that j 0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified also shown is that j 1 is asymptotically 2 distributed suggesting that the second test is asymptotically pivotal when the null model is correctly specified the main feature of the first test is that no alternative model is needed the second test has several properties first its size distortion is small and hence bootstrap methods can be avoided second it is easy to compute from mcmc output and hence is applicable to a wide range of models including latent variable models for which frequentist methods are difficult to use third when the test statistic rejects the null model and j 1 takes a large value the test suggests the source of misspecification the finite sample performance is investigated using simulated data the method is illustrated in a linear regression model a linear state space model and a stochastic volatility model using real data

a bayesian approach for incorporating variable rates of heterogeneity in linkage analysis a widely used approach for dealing with locus heterogeneity in linkage analysis is based on mixture likelihood in which a single mixing heterogeneity parameter represents the probability that each family is of linked type however in general different types of families exhibit different heterogeneity levels to incorporate this variability we propose a new approach wherein each family has its own heterogeneity parameter representing the probability that it is of linked type these parameters are nuisance parameters whereas the main parameter of interest is the location of the disease gene if there is any we model the problem in the bayesian framework and implement it using the markov chain monte carlo mcmc methodology in particular we use the reversible jump mcmc sampler to move between the two models linkage and no linkage we first estimate the posterior probability of linkage on a chromosome and the corresponding bayes factor if linkage is inferred then the location of the disease gene

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

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

adaptive markov chain monte carlo through regeneration abstract markov chain monte carlo mcmc is used for evaluating expectations of functions of interest under a target distribution this is done by calculating averages over the sample path of a markov chain having as its stationary distribution for computational efficiency the markov chain should be rapidly mixing this sometimes can be achieved only by careful design of the transition kernel of the chain on the basis of a detailed preliminary exploratory analysis of an alternative approach might be to allow the transition kernel to adapt whenever new features of are encountered during the mcmc run however if such adaptation occurs infinitely often then the stationary distribution of the chain may be disturbed we describe a framework based on the concept of markov chain regeneration which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages

variance bounding and geometric ergodicity of markov chain monte carlo kernels for approximate bayesian computation approximate bayesian computation has emerged as a standard computational tool when dealing with intractable likelihood functions in bayesian inference we show that many common markov chain monte carlo kernels used to facilitate inference in this setting can fail to be variance bounding and hence geometrically ergodic which can have consequences for the reliability of estimates in practice this phenomenon is typically independent of the choice of tolerance in the approximation we prove that a recently introduced markov kernel can inherit the properties of variance bounding and geometric ergodicity from its intractable metropolis hastings counterpart under reasonably weak conditions we show that the computational cost of this alternative kernel is bounded whenever the prior is proper and present indicative results for an example where spectral gaps and asymptotic variances can be computed as well as an example involving inference for a partially and discretely observed time homogeneous pure jump markov process we also supply two general theorems one providing a simple sufficient condition for lack of variance bounding for reversible kernels and the other providing a positive result concerning inheritance of variance bounding and geometric ergodicity for mixtures of reversible kernels

a branch and cut and price algorithm for the cumulative capacitated vehicle routing problem abstract in this paper we consider the cumulative capacitated vehicle routing problem ccvrp which is a variation of the well known capacitated vehicle routing problem cvrp in this problem the traditional objective of minimizing total distance or time traveled by the vehicles is replaced by minimizing the sum of arrival times at the customers we propose a branch and cut and price algorithm for obtaining optimal solutions to the problem to the best of our knowledge this is the first published exact algorithm for the ccvrp we present computational results based on a set of standard cvrp benchmarks and investigate the effect of modifying the number of vehicles available

bayesian hierarchical multivariate formulation with factor analysis for nested ordinal data this article devises a bayesian multivariate formulation for analysis of ordinal data that records teacher classroom performance along multiple dimensions to assess aspects characterizing good instruction study designs for scoring teachers seek to measure instructional performance over multiple classroom measurement event sessions at varied occasions using disjoint intervals within each session and employment of multiple ratings on intervals scored by different raters a design which instantiates a nesting structure with each level contributing a source of variation in recorded scores we generally possess little a priori knowledge of the existence or form of a sparse generating structure for the multivariate dimensions at any level in the nesting that would permit collapsing over dimensions as is done under univariate modeling our approach composes a bayesian data augmentation scheme that introduces a latent continuous multivariate response linked to the observed ordinal scores with the latent response mean constructed as an additive multivariate decomposition of nested level means that permits the extraction of de noised continuous teacher level scores and the associated correlation matrix a semi parametric extension facilitates inference for teacher level dependence among the dimensions of classroom performance under multi modality induced by sub groupings of rater perspectives we next replace an inverse wishart prior specified for the teacher covariance matrix over dimensions of instruction with a factor analytic structure to allow the simultaneous assessment of an underlying sparse generating structure our formulation for bayesian factor analysis employs parameter expansion with an accompanying post processing sign re labeling step of factor loadings that together reduce posterior correlations among sampled parameters to improve parameter mixing in our markov chain monte carlo mcmc scheme we evaluate the performance of our formulation on simulated data and make an application for the assessment of the teacher covariance structure with a dataset derived from a study of middle and high school algebra teachers

sis model on homogeneous networks with threshold type delayed contact reduction we study the dynamics of a delayed sis epidemic model on homogeneous networks where it is assumed that individuals modify their contact patterns upon realizing the risk of infection this decision is made with some time delay and it is threshold type when the density of infected nodes reaches a critical value the number of links is reduced by a given factor such assumptions lead to a delay differential equation with discontinuous right hand side we show that if the basic reproduction number r 0 1 then the disease will be eradicated while it persists for r 0 1 in the latter case there is a globally asymptotically stable endemic equilibrium except for a crucial interval of reproduction numbers where the system shows oscillations we construct explicitly the unique slowly oscillatory periodic solution which has strong attractivity properties and show the existence of rapidly oscillatory periodic solutions with any frequency the amplitude of the oscillations is determined by the time delay our results indicate that with such information delays the link density of a network has an important effect on the qualitative dynamics of infectious diseases

a classification of formulations for the time dependent traveling salesman problem abstract the time dependent traveling salesman problem tdtsp is a generalization of the classical traveling salesman problem where the cost of any given arc is dependent of its position in the tour the tdtsp can model several real world applications e g one machine sequencing in this paper we present a classification of formulations for the tdtsp this framework includes both new and old formulations the new formulation presented in this paper is derived from a quadratic assignment model for the tdtsp in a first step lawler s transformation procedure is used to derive an equivalent linearized version of the quadratic model in a second step a stronger formulation is obtained by tightening some constraints of the previous formulation it is shown that in terms of linear relaxations the latter formulation is either equivalent or better than other formulations already known from the literature finally we compare these formulations with other well known formulations for the classical traveling salesman problem

batch means and spectral variance estimators in markov chain monte carlo calculating a monte carlo standard error mcse is an important step in the statistical analysis of the simulation output obtained from a markov chain monte carlo experiment an mcse is usually based on an estimate of the variance of the asymptotic normal distribution we consider spectral and batch means methods for estimating this variance in particular we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases in addition for the batch means and overlapping batch means methods we establish conditions ensuring consistency in the mean square sense which in turn allows us to calculate the optimal batch size up to a constant of proportionality finally we examine the empirical finite sample properties of spectral variance and batch means estimators and provide recommendations for practitioners

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

strong consistency and other properties of the spectral variance estimator consistent estimation of the variance parameter of a stochastic process allows construction under certain conditions of a confidence interval for the mean of the process if the variance estimator is strongly consistent fixed width confidence interval construction is valid for large samples it has long been known that the spectral variance estimator of steady state simulation output analysis is consistent in the mean square sense here we provide strong consistency of this estimator thereby justifying fixed width confidence interval construction for the spectral method a characterization of spectral density function estimators is also introduced this characterization provides insight into the relation between spectral methods and overlapping batch means type variance estimators finally some of the mathematical conditions provide qualitative insight into the relation between the process correlation and certain parameters of spectral methods

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

improving the fully sequential sampling scheme of anscombe chow robbins a new sequential sampling scheme is proposed in which after an initial batch sample sampling is continued in batches of data dependent sizes at most k such batches and then one at a time with a data dependent stopping rule this new scheme requires about the same sample size as the fully sequential anscombe chow robbins acr sampling scheme but substantially fewer sampling operations the problem of constructing fixed width confidence intervals for the mean of a normal population with unknown variance is used as an illustration

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

regeneration in markov chain samplers abstract markov chain sampling has recently received considerable attention in particular in the context of bayesian computation and maximum likelihood estimation this article discusses the use of markov chain splitting originally developed for the theoretical analysis of general state space markov chains to introduce regeneration into markov chain samplers this allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance the approach is applied to several samplers including certain metropolis samplers that can be used on their own or in hybrid samplers and is illustrated in several examples

geometric ergodicity of van dyk and meng s algorithm for the multivariate student s t model let denote the posterior distribution that results when a random sample of size n from a d dimensional location scale student s t distribution with degrees of freedom is combined with the standard noninformative prior van dyk and meng developed an efficient markov chain monte carlo mcmc algorithm for sampling from and provided considerable empirical evidence to suggest that their algorithm converges to stationarity much faster than the standard data augmentation algorithm in addition to its practical importance this algorithm is interesting from a theoretical standpoint because it is based upon a markov chain that is not positive recurrent in this article we formally analyze the relevant sub markov chain underlying van dyk and meng s algorithm in particular we establish drift and minorization conditions that show that for many d n triples the sub markov chain is geometrically ergodic this is the first general rigorous analysis of an mcmc algorithm based upon a nonpositive recurr

bayesian inference based on stationary fokker planck sampling a novel formalism for bayesian learning in the context of complex inference models is proposed the method is based on the use of the stationary fokker planck sfp approach to sample from the posterior density stationary fokker planck sampling generalizes the gibbs sampler algorithm for arbitrary and unknown conditional densities by the sfp procedure approximate analytical expressions for the conditionals and marginals of the posterior can be constructed at each stage of sfp the approximate conditionals are used to define a gibbs sampling process which is convergent to the full joint posterior by the analytical marginals efficient learning methods in the context of artificial neural networks are outlined offline and incremental bayesian inference and maximum likelihood estimation from the posterior are performed in classification and regression examples a comparison of sfp with other monte carlo strategies in the general problem of sampling from arbitrary densities is also presented it is shown that sfp is able to jump large low probability regions without the need of a careful tuning of any step size parameter in fact the sfp method requires only a small set of meaningful parameters that can be selected following clear problem independent guidelines the computation cost of sfp measured in terms of loss function evaluations grows linearly with the given model s dimension

mathematical formulations and exact algorithm for the multitrip cumulative capacitated single vehicle routing problem abstract this paper addresses the multitrip cumulative capacitated single vehicle routing problem mt ccsvrp in this problem inspired by disaster logistics a single vehicle can perform successive trips to serve a set of affected sites and minimize an emergency criterion the sum of arrival times two mixed integer linear programs a flow based model and a set partitioning model are proposed for small instances with 20 sites an exact algorithm for larger cases transforms the mt ccsvrp into a resource constrained shortest path problem where each node corresponds to one trip and the sites to visit become resources the resulting problem can be solved via an adaptation of bellman ford algorithm to a directed acyclic graph with resource constraints and a cumulative objective function seven dominance rules two upper bounds and five lower bounds speed up the procedure computational results on instances derived from classical benchmark problems for the capacitated vrp indicate that the exact algorithm outperforms a commercial mip solver on small instances and can solve cases with 40 sites to optimality

the demand weighted vehicle routing problem abstract in this paper we present an exact method for the demand weighted vehicle routing problem this problem arises when the objective is to minimize the distance traveled by the vehicles weighted by the number of passengers on the routes the resulting model is a non convex mixed integer quadratic program and we show how to reformulate this problem as a linear integer program with auxiliary variables the reformulation provides very tight lower bounds on the optimal solution value and little enumeration is required however the reformulated model is very large and therefore it is solved with a branch price and cut algorithm using coin or software we provide computational results with actual data from a large urban university

monte carlo exact conditional tests for log linear and logistic models summary the form of the exact conditional distribution of a sufficient statistic for the interest parameters given a sufficient statistic for the nuisance parameters is derived for a generalized linear model with canonical link general results for log linear and logistic models are given a gibbs sampling approach for generating from the conditional distribution is proposed which enables monte carlo exact conditional tests to be performed examples include tests for goodness of fit of the all two way interaction model for a 28 table and of a simple logistic model tests against non saturated alternatives are also considered

dimension reduction and alleviation of confounding for spatial generalized linear mixed models summary non gaussian spatial data are very common in many disciplines for instance count data are common in disease mapping and binary data are common in ecology when fitting spatial regressions for such data one needs to account for dependence to ensure reliable inference for the regression coefficients the spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data but this model suffers from two major shortcomings variance inflation due to spatial confounding and high dimensional spatial random effects that make fully bayesian inference for such models computationally challenging we propose a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects we illustrate the application of our approach to simulated binary count and gaussian spatial data sets and to a large infant mortality data set

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality

an improved approximation ratio for the minimum latency problem networks and matroids given a tour visiting n points in a metric space the latency of one of these points p is the distance traveled in the tour before reaching p the minimum latency problem mlp asks for a tour passing through n given points for which the total latency of the n points is minimum in effect we are seeking the tour with minimum average arrival time this problem has been studied in the operations research literature where it has also been termed the delivery man problem and the traveling repairman problem the approximability of the mlp was first considered by sahni and gonzalez in 1976 however unlike the classical traveling salesman problem tsp it is not easy to give any constant factor approximation algorithm for the mlp recently blum et al a blum p chalasani d coppersimith w pulleyblank p raghavan m sudan proceedings of the 26th acm symposium on the theory of computing 1994 pp 163 171 gave the first such algorithm obtaining an approximation ratio of 144 in this work we develop an algorithm which improves this ratio to 21 55 moreover combining our algorithm with a recent result of garg n garg proceedings of the 37th ieee symposium on foundations of computer science 1996 pp 302 309 provides an approximation ratio of 10 78 the development of our algorithm involves a number of techniques that seem to be of interest from the perspective of the tsp and its variants more generally

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea