experimental study of ilu preconditioners for indefinite matrices incomplete lu factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices however their failure rate is still too high for them to be useful as black box library software for general matrices besides fatal breakdowns due to zero pivots the major causes of failure are inaccuracy and instability of the triangular solves when there are small pivots both these problems can occur but these problems can also occur without small pivots through examples from actual problems this paper shows how these problems evince themselves how these problems can be detected and how these problems can sometimes be circumvented through pivoting reordering scaling perturbing diagonal elements and preserving symmetric structure the goal of this paper is to gain a better practical understanding of ilu preconditioners and help improve their reliability

on comparison of mixture models for closed population capture recapture studies summary a mixture model is a natural choice to deal with individual heterogeneity in capture recapture studies pledger 2000 biometrics 56 434 442 2005 biometrics 61 868 876 advertised the use of the two point mixture model dorazio and royle 2003 biometrics 59 351 364 2005 biometrics 61 874 876 suggested that the beta binomial model has advantages the controversy is related to the nonidentifiability of the population size link 2003 biometrics 59 1123 1130 and certain boundary problems the total bias is decomposed into an intrinsic bias an approximation bias and an estimation bias we propose to assess the approximation bias the estimation bias and the variance with the intrinsic bias excluded when comparing different estimators the boundary problems in both models and their impacts are investigated real epidemiological and ecological examples are analyzed

estimating the species accumulation curve using mixtures as a significant tool in ecological studies the species accumulation curve or the collector s curve is the graph of the expected number of detected species as a function of sampling effort the problem of estimating the species accumulation curve based on an empirical data set arising from quadrat sampling is studied in a nonparametric binomial mixture model it will be shown that estimating the species accumulation curve not only is independent of the unknown number of species but also includes estimating the number of species as a limiting case for the purpose of interpolation moment based estimators associated with asymptotic confidence intervals are developed from several points of view a likelihood based procedure is developed for the purpose of extrapolation associated with bootstrap confidence intervals the proposed methods are illustrated by ecological data sets

comparing species assemblages via species accumulation curves comparing species assemblages given incidence based data is of importance in ecological studies often done by a visual inspection of estimated species accumulation curves or by an ad hoc use of 95 pointwise confidence bands of these curves it is shown that comparing species assemblages is a challenging problem a chi 2 test is proposed an adjustment using an eigenvalue decomposition is proposed to overcome computational difficulties the bootstrap method is also suggested to approximate the distribution of the proposed test statistic the eigenvalue adjusted eva chi 2 test and the eva bootstrap test are assessed by a simulation study both the eva chi 2 and the eva bootstrap tests are applied to a study that involves two woody seedling species assemblages

robust solutions of linear programming problems contaminated with uncertain data optimal solutions of linear programming problems may become severely infeasible if the nominal data is slightly perturbed we demonstrate this phenomenon by studying 90 lps from the well known netlib collection we then apply the robust optimization methodology ben tal and nemirovski 1 3 el ghaoui et al 5 6 to produce robust solutions of the above lps which are in a sense immuned against uncertainty surprisingly for the netlib problems these robust solutions nearly lose nothing in optimality

estimating the number of classes in a finite population abstract we use an extension of the generalized jackknife approach of gray and schucany to obtain new nonparametric estimators for the number of classes in a finite population of known size we also show that generalized jackknife estimators are closely related to certain horvitz thompson estimators to an estimator of shlosser and to estimators based on sample coverage in particular the generalized jackknife approach leads to a modification of shlosser s estimator that does not suffer from the erratic behavior of the original estimator the performance of both new and previous estimators is investigated by means of an asymptotic variance analysis and a monte carlo simulation study

petersen estimator chapman adjustment list effects and heterogeneity we use a nonparametric mixture model for the purpose of estimating the size of a population from multiple lists in which both the individual effects and list effects are allowed to vary we propose a lower bound of the population size that admits an analytic expression the lower bound can be estimated without the necessity of model fitting the asymptotical normality of the estimator is established both the estimator itself and that for the estimable bound of its variance are adjusted these adjusted versions are shown to be unbiased in the limit simulation experiments are performed to assess the proposed approach and real applications are studied

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

estimating the population size for capture recapture data with unequal catchability a point estimator and its associated confidence interval for the size of a closed population are proposed under models that incorporate heterogeneity of capture probability real data sets provided in edwards and eberhardt 1967 journal of wildlife management 31 87 96 and carothers 1973 journal of animal ecology 42 125 146 are used to illustrate this method and to compare it with other estimates the performance of the proposed procedure is also investigated by means of monte carlo experiments the method is especially useful when most of the captured individuals are caught once or twice in the sample for which case the jackknife estimator usually does not work well numerical results also show that the proposed confidence interval performs satisfactorily in maintaining the nominal levels

the evolution of the minimum degree ordering algorithm over the past fifteen years the implementation of the minimum degree algorithm has received much study and many important enhancements have been made to it this paper describes these various enhancements their historical development and some experiments showing how very effective they are in improving the execution time of the algorithm a shortcoming is also presented that exists in all of the widely used implementations of the algorithm namely that the quality of the ordering provided by the implementations is surprisingly sensitive to the initial ordering for example changing the input ordering can lead to an increase or decrease of as much as a factor of three in the cost of the subsequent numerical factorization this sensitivity is caused by the lack of an effective tie breaking strategy and the authors experiments illustrate the importance of developing such a strategy

nonparametric mle under two closed capture recapture models with heterogeneity we conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture recapture models our models specify mixture models as did previous researchers models which have a common generating distribution say f for the capture probabilities using lindsay and roeder s 1992 journal of the american statistical association 87 785 794 mixture model results and the em algorithm a nonparametric maximum likelihood estimator mle of f for any specified population size n is obtained then the nonparametric mle of the n f pair and thus for n is determined perhaps most importantly since our mle pair maximizes the likelihood under the entire nonparametric probability model it provides an excellent foundation for estimating properties of estimators conducting a goodness of fit test and performing a likelihood ratio test these are illustrated in the paper

inverse optimization for the recovery of constraint parameters abstract most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set we propose two approaches to impute unspecified left hand side constraint coefficients in addition to a cost vector for a given linear optimization problem the first approach identifies parameters minimizing the duality gap while the second minimally perturbs prior estimates of the unspecified parameters to satisfy strong duality if it is possible to satisfy the optimality conditions exactly we apply these two approaches to the general linear optimization problem we also use them to impute unspecified parameters of the uncertainty set for robust linear optimization problems under interval and cardinality constrained uncertainty each inverse optimization model we propose is nonconvex but we show that a globally optimal solution can be obtained either in closed form or by solving a linear number of linear or convex optimization problems

nonparametric lower bounds for species richness and shared species richness under sampling without replacement summary a number of species richness estimators have been developed under the model that individuals or sampling units are sampled with replacement however if sampling is done without replacement so that no sampled unit can be repeatedly observed then the traditional estimators for sampling with replacement tend to overestimate richness for relatively high sampling fractions ratio of sample size to the total number of sampling units and do not converge to the true species richness when the sampling fraction approaches one based on abundance data or replicated incidence data we propose a nonparametric lower bound for species richness in a single community and also a lower bound for the number of species shared by multiple communities our proposed lower bounds are derived under very general sampling models they are universally valid for all types of species abundance distributions and species detection probabilities for abundance data individuals detectabilities are allowed to be heterogeneous among species for replicated incidence data the selected sampling units e g quadrats need not be fully censused and species can be spatially aggregated all bounds converge correctly to the true parameters when the sampling fraction approaches one real data sets are used for illustration we also test the proposed bounds by using subsamples generated from large real surveys or censuses and their performance is compared with that of some previous estimators

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

an estimator of number of species from quadrat sampling summary we consider the problem of estimating the number of distinct species s in a study area from the recorded presence or absence of species in each of a sample of quadrats a generalized jackknife estimator of s is derived along with an estimate of its variance it is compared with the jackknife estimator for s proposed by heltshe and forrester 1983 biometrics39 1 12 and the empirical bayes estimator of mingoti and meeden 1992 biometrics48 863 875 we show that the empirical bayes estimator has the form of a generalized jackknife estimator under a specific model for species distribution we compare the new estimators of s to the empirical bayes estimator via simulation we characterize circumstances under which each is superior

applications and extensions of chao s moment estimator for the size of a closed population summary this article revisits chao s 1989 biometrics 45 427 438 lower bound estimator for the size of a closed population in a mark recapture experiment where the capture probabilities vary between animals model mh first an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities mth is proposed the biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for mth small sample bias reduction techniques for chao s lower bound estimator are also derived the application of the loglinear model underlying chao s estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated a test for the null hypothesis that chao s loglinear model provides unbiased abundance estimators is provided the strategy of systematically using chao s loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a monte carlo experiment its impact on the estimation of the population sizes and of the survival rates is evaluated in a monte carlo experiment

data driven estimation in equilibrium using inverse optimization equilibrium modeling is common in a variety of fields such as game theory and transportation science the inputs for these models however are often difficult to estimate while their outputs i e the equilibria they are meant to describe are often directly observable by combining ideas from inverse optimization with the theory of variational inequalities we develop an efficient data driven technique for estimating the parameters of these models from observed equilibria we use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data a distinguishing feature of our approach is that it supports both parametric and nonparametric estimation by leveraging ideas from statistical learning kernel methods and regularization operators in computational experiments involving nash and wardrop equilibria in a nonparametric setting we find that a we effectively estimate the unknown demand or congestion function respectively and b our proposed regularization technique substantially improves the out of sample performance of our estimators

extending the lincoln petersen estimator for multiple identifications in one source the lincoln petersen estimator is one of the most popular estimators used in capture recapture studies it was developed for a sampling situation in which two sources independently identify members of a target population for each of the two sources it is determined if a unit of the target population is identified or not this leads to a 2 2 table with frequencies f11 f10 f01 f00 indicating the number of units identified by both sources by the first but not the second source by the second but not the first source and not identified by any of the two sources respectively however f00 is unobserved so that the 2 2 table is incomplete and the lincoln petersen estimator provides an estimate for f00 in this paper we consider a generalization of this situation for which one source provides not only a binary identification outcome but also a count outcome of how many times a unit has been identified using a truncated poisson count model truncating multiple identifications larger than two we propose a maximum likelihood estimator of the poisson parameter and ultimately of the population size this estimator shows benefits in comparison with lincoln petersen s in terms of bias and efficiency it is possible to test the homogeneity assumption that is not testable in the lincoln petersen framework the approach is applied to surveillance data on syphilis from izmir turkey

a markov chain based multi elimination preconditioner for elliptic pde problems abstract preconditioning is a simple but very powerful technique for accelerating the convergence of an iterative method for solving large sparse linear systems traditionally to design a good preconditioner implemented on a personal computer or a cluster of computer systems with cpus the preconditioner should meet the following three conditions a the preconditioner is a good approximation of the inverse of the original linear coefficient matrix in some sense b setting up the components needed for the preconditioning operator is easy and c the cost for the application of the preconditioner with a given vector is low however as new computer systems are rapidly invented such designing strategies need to be reinvestigated motivated by the random walk technique which is a computationally intensive task we proposed a different preconditioner based on a multi elimination algorithm where the inversion operator is approximated explicitly by a partial product of the neumann series of the iterative matrix for the original system the computation of such an approximation takes advantages of the strengths of the gpu system we report some numerical results implemented by cuda petsc in our implementation we adopt the hybrid gpu cpu approach that preconditioning setup and application are performed on gpu while krylov subspace iteration which requires a certain degree of communications is done on cpu this method minimizes data communication between gpu cpu which is a bottleneck for many existing algorithms

data driven inverse optimization with imperfect information in data driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal thus the observer seeks the agent s objective function that best explains a historical sequence of signals and corresponding optimal actions we formalize this inverse optimization problem as a distributionally robust program minimizing the worst case risk that the estimated decision i e the decision implied by a particular candidate objective differs from the agent s actual response to a random signal we show that our framework offers attractive out of sample performance guarantees for different prediction errors and that the emerging inverse optimization problems can be reformulated as or approximated by tractable convex programs when the prediction error is measured in the space of objective values a main strength of the proposed approach is that it naturally generalizes to situations where the observer has imperfect information e g when the agent s true objective function is not contained in the space of candidate objectives when the agent suffers from bounded rationality or implementation errors or when the observed signal response pairs are corrupted by measurement noise

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

a sparse approximate inverse preconditioner for nonsymmetric linear systems this paper is concerned with a new approach to preconditioning for large sparse linear systems a procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods some theoretical properties of the preconditioner are discussed and numerical experiments on test matrices from the harwell boeing collection and from tim davis s collection are presented our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners furthermore the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners

simple capture recapture models permitting unequal catchability and variable sampling effort we consider two capture recapture models that imply that the logit of the probability of capture is an additive function of an animal catchability parameter and a parameter reflecting the sampling effort the models are special cases of the rasch model and satisfy the property of quasi symmetry one model is log linear and the other is a latent class model for the log linear model point and interval estimates of the population size are easily obtained using standard software such as glim

estimating the total number of distinct species using presence and absence data summary consider the problem of estimating the total number of distinct species in some specified region under investigation suppose the region is divided into n disjoint subregions or quadrats of equal area a sample of size n quadrats is chosen n 1 the other is to place at random n quadrats of equal area and fixed shape in the region of investigation in both cases the n quadrats in the sample are assumed to be disjoint and are totally observed so in fact when quadrat sampling is used a random sample of space is taken instead of a random sample of individuals it has been observed that species are often present with some natural clumping which creates dependence between quadrats and within quadrats heltshe and forrester 1983 and smith and van belle 1984 introduced some estimators for s when quadrat sampling is used see also burnham and overton 1979 the estimators they proposed are nonparametric and were developed by using jackknife and bootstrap arguments for a particular example palmer 1990 compared several estimators and showed that the first order jackknife estimator is preferred within this group in this paper we introduce some empirical bayes estimators for s when quadrat sampling is used by imposing a grid on the region the probabilistic model used to derive these estimators is basically a version of the efron and thisted 1976 model adapted to the case of quadrat

estimating species richness using the jackknife procedure an exact expression is given for the jackknife estimate of the number of species in a community and for the variance of this number when quadrat sampling procedures are used the jackknife estimate is a function of the number of species that occur in one and only one quadrat the variance of the number of species can be constructed as can approximate two sided confidence intervals the behavior of the jackknife estimate as affected by quadrat size sample size and sampling area is investigated by simulation

estimating the number of species a review how many kinds are there suppose that a population is partitioned into c classes in many situations interest focuses not on estimation of the relative sizes of the classes but on estimation of c itself for example biologists and ecologists may be interested in estimating the number of species in a population of plants or animals numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue and linguists may be interested in estimating the size of an author s vocabulary in this article we review the problem of statistical estimation of c many approaches have been proposed some purely data analytic and others based in sampling theory in the latter case numerous variations have been considered the population may be finite or infinite if finite samples may be taken with replacement multinomial sampling or without replacement hypergeometric sampling or by bernoulli sampling if infinite sampling may be multinomial or bernoulli or the sample may be th

stochastic preconditioning for diagonally dominant matrices this paper presents a new stochastic preconditioning approach for large sparse matrices for the class of matrices that are rowwise and columnwise irreducibly diagonally dominant we prove that an incomplete rm ldl t factorization in a symmetric case or an incomplete ldu factorization in an asymmetric case can be obtained from random walks and used as a preconditioner it is argued that our factor matrices have better quality i e better accuracy size trade offs than preconditioners produced by existing incomplete factorization methods therefore a resulting preconditioned krylov subspace iterative solver requires less computation than traditional methods to solve a set of linear equations with the same error tolerance the advantage increases for larger and denser matrices these claims are verified by numerical tests and we provide techniques that can potentially extend the theory to non diagonally dominant matrices

interval estimation for mark recapture studies of closed populations textbooks continue to recommend the use of an asymptotic normal distribution to provide an interval estimate for the unknown size n of a closed population studied by a mark recapture experiment or multiple record system a likelihood interval approach is proposed and its implementation demonstrated for a range of models for such studies including all main effect and interaction models for incomplete contingency tables

estimating diversity using quadrat sampling pielou 1966 journal of theoretical biology 13 131 144 first proposed the estimation of species diversity and its sampling error by using a pooled quadrat procedure heyer and berven 1973 ecology 54 642 645 modified this procedure by selecting the median of a group of sample permutations zahl 1977 ecology 58 907 913 introduced the jackknife estimation of species diversity under certain conditions pielou s pooled quadrat estimator is shown to be equivalent to zahl s jackknife estimator

an improved nonparametric lower bound of species richness via a modified good turing frequency formula summary it is difficult to accurately estimate species richness if there are many almost undetectable species in a hyperdiverse community practically an accurate lower bound for species richness is preferable to an inaccurate point estimator the traditional nonparametric lower bound developed by chao 1984 scandinavian journal of statistics 11 265 270 for individual based abundance data uses only the information on the rarest species the numbers of singletons and doubletons to estimate the number of undetected species in samples applying a modified good turing frequency formula we derive an approximate formula for the first order bias of this traditional lower bound the approximate bias is estimated by using additional information namely the numbers of tripletons and quadrupletons this approximate bias can be corrected and an improved lower bound is thus obtained the proposed lower bound is nonparametric in the sense that it is universally valid for any species abundance distribution a similar type of improved lower bound can be derived for incidence data we test our proposed lower bounds on simulated data sets generated from various species abundance models simulation results show that the proposed lower bounds always reduce bias over the traditional lower bounds and improve accuracy as measured by mean squared error when the heterogeneity of species abundances is relatively high we also apply the proposed new lower bounds to real data for illustration and for comparisons with previously developed estimators

a generalization of chao s estimator for covariate information this note generalizes chao s estimator of population size for closed capture recapture studies if covariates are available chao s estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size if observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of chao s estimator the key element in this development is the understanding and placement of chao s estimator in a truncated poisson likelihood it is shown that a truncated poisson likelihood with log link with all counts truncated besides ones and twos is equivalent to a binomial likelihood with logit link this enables the development of a generalized chao estimator as the estimated expected value of the frequency of zero counts under a truncated all counts truncated except ones and twos poisson regression model if the regression model accounts for the heterogeneity entirely the generalized chao estimator is asymptotically unbiased a simulation study illustrates the potential in gain of bias reduction comparisons of the generalized chao estimator with the homogeneous zero truncated poisson regression approach are supplied as well the method is applied to a surveillance study on the completeness of farm submissions in great britain

capture recapture estimation with samples of size one using frequency data summary one way in which a capture recapture experiment can be designed is to count each capture occasion as a separate sample and tally the number of individuals caught once twice and so on this paper discusses the estimators currently used for this type of experiment and suggests some new ones each of the estimators is categorized by its derivation following this their properties are discussed particularly their bias and variance with the aim of choosing one or two of the estimators which are the best to use especially in handling a heterogeneous population it is found that the bias adjusted estimator of chao 1989 is the best to use when the number of captures is relatively small and that the estimator of darroch ratcliff 1980 should be used otherwise