bad normed spaces convexity properties separated sets abstract some years ago a parameter denoted by a 1 x was defined in real banach spaces in the same setting several years before a notion called q convexity had been defined studying these two notions seems to be rather awkward and up until now this has not been done in deep here we indicate some properties and connections between these two parameters and some other related ones in infinite dimensional banach spaces we also consider another notion a natural extension of q convexity and we discuss the case when a 1 x attains its maximum value the spaces where this happens can be considered as bad since they cannot have several properties which are usually considered as nice like uniform non squareness or p convexity

the use of mixed logit models to reflect heterogeneity in capture recapture studies summary we examine issues in estimating population size n with capture recapture models when there is variable catchability among subjects we focus on a logistic normal mixed model for which the logit of the probability of capture is an additive function of a random subject and a fixed sampling occasion parameter when the probability of capture is small or the degree of heterogeneity is large the log likelihood surface is relatively flat and it is difficult to obtain much information about n we also discuss a latent class model and a log linear model that account for heterogeneity and show that the log linear model has greater scope models assuming homogeneity provide much narrower intervals for n but are usually highly overly optimistic the actual coverage probability being much lower than the nominal level

a unified treatment of integer parameter models abstract it is shown that there is an analog to the score function the derivative of the log likelihood with respect to the parameter here called the difference score which plays an important theoretical role in integer parameter models a unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score lds it is established that many of the exact results available for exponential family models also hold for lds models in particular we find an information lower bound show the uniqueness of the maximum likelihood estimator establish monotone likelihood ratio and establish optimality properties in two sided tests it is also shown that if one has a multiparameter likelihood in which there is a conditional likelihood depending on n alone then these exact results apply there as well it is also established when and why the usual likelihood methodology will apply to a class of nonstandard models in which the natural approxima

forming post strata via bayesian treed capture recapture models summary for the problem of dual system estimation we propose a bayesian treed capture recapture model to account for heterogeneity of capture probabilities where individual auxiliary information is available the model uses a binary tree to partition the covariate space into homogeneous regions within each of which the capture response can be described adequately by a simple model that assumes equal catchability the attractive features of the proposed model include reduction of correlation bias robustness and practical flexibility as well as simplicity and interpretability in addition it provides a systematic and effective way of forming post strata for the sekar deming estimator of population size we compare the performance of estimators based on this model to those of alternative estimators in three scenarios

statistical inference for poisson and multinomial models for capture recapture experiments summary the classical multinomial model used for estimating the size of a closed population is compared to the highly flexible poisson models introduced by cormack 1981 the multinomial model and generalizations of it which allow for dependence between samples may be obtained from that of cormack by conditioning on the population size the maximum likelihood estimators for n the population size and 0 the vector of parameters describing the capture process are the same in both models completely general formulae for the asymptotic variances of the maximum likelihood estimates of n for both models are given the substantial differences between the variances under the two models are discussed hypotheses concerning 0 may be tested using the log likelihood ratio the procedures which result from both models are asymptotically equivalent under the null hypothesis but differ in power under the alternative

efficient bootstrap simulation on donne deux idees pour renforcer une simulation la premiere est d equilibrer les echantillons simules la seconde est de faire un usage explicite des approximations qui ne demandent pas de simulation

a martingale estimating equation for a capture recapture experiment in discrete time we use martingale theory and a method of moments technique to derive a class of estimators for the size of a closed population in a capture recapture experiment in discrete time where the capture probabilities on the successive capture occasions are allowed to be different the same capture probability is assumed to apply to all animals in the population on the same occasion explicit expressions are given for these estimators and their associated standard errors which involve only simple computation an optimal estimator for the population size is found asymptotic results are readily obtained by an application of a martingale central limit theorem two examples are given to compare the results

the foundations of finite sample estimation in stochastic processes generally in the literature on stochastic processes estimation is investigated in terms of asymptotic properties in this paper we establish some finite sample optimal estimation let y1 y2 be a discrete stochastic process since we will be discussing results for samples of finite size n we restrict the process to r in the following the term parameter is used in the same broad sense as by godambe thompson 1984 let y be a class of probability distributions f on r and 0 0 f f e jz be a real parameter let hi be a real function of y 1 yi and 0 be such that

estimating the size of a closed population from a single mark recapture regime by using a diffusion probability of marked individuals a population estimate model was developed to account for the unequal recapture probability of marked animals when their diffusion into the released population has yet to reach the equilibrium we assumed a spatial bias for marked individuals within the finite area of the animals territory and used a correction parameter to account for the bias mark recapture data previously collected for field colonies of the formosan subterranean termite coptotermes formosanus shiraki were applied to the new model and the results were compared with the peterson and weighted mean models

a unified parametric regression model for recapture studies with random removals in continuous time nous combinons la vraisemblance conditionnelle dans des processus de comptage avec l estimateur de horvitz thompson pour obtenir un estimateur de la taille de la population plus efficient que les estimateurs existants des suppressions aleatoires peuvent etre introduites dans le processus de recapture on presente des etudes de simulation pour determiner la performance des estimateurs proposes on donne des exemples sur une repartition d oiseaux et une petite etude de recapture de mammiferes

full likelihood inference for abundance from continuous time capture recapture data capture recapture experiments are widely used cost effective sampling techniques for estimating population sizes or abundances in biology ecology demography epidemiology and reliability studies for continuous time capture recapture data existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation the corresponding wald type confidence intervals for the abundance may have severe undercoverage and their lower limits can be below the number of individuals captured we propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood under both parametric and semiparametric intensity models we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically 2 with 1 degree of freedom simulations indicate that compared with conditional likelihood based methods the maximum full likelihood estimator has a smaller mean square error and the likelihood ratio confidence intervals often have remarkable gains in coverage probability we illustrate the advantages of the proposed approach by analysing illegal immigrant data for the netherlands and prinia flaviventris data from hong kong

inference for exponential order statistic models based on an integrated likelihood function abstract methods of statistical inference are developed for the exponential order statistic eos model where only a subset of order statistics from a collection of n iid exponential random detection times is observable when the rate parameter for detections is unknown the maximum likelihood estimator mle of the unknown integer parameter n can be infinite with substantial probability inference for n is developed using a pseudolikelihood function obtained by integrating out the rate parameter the estimator that maximizes this function called the integrated likelihood estimator ile is shown to be finite and to have better sampling properties than the mle parameter based asymptotics are developed for the case where n is large application of the methodology is illustrated using two datasets

a state space formalism for anisotropic elasticity part ii cylindrical anisotropy abstract a state space formalism for thermoelastic analysis of a cylindrically anisotropic elastic body is developed by proper grouping of the stress and taking r ij instead of ij as the stress variables the three dimensional equations of elasticity in the cylindrical coordinates are concisely formulated into a state equation and an output equation using matrix notations the general solution for the generalized plane problems is derived in a simple manner effects of extension torsion bending temperature change and body force are accounted for systematically the eigen relation arising from the solution process and the degenerate cases of repeated eigenvalues are examined to demonstrate the power of the formalism exact solutions to extension torsion bending and thermo mechanical loading of a general cylindrically anisotropic circular tube or bar are obtained the surface tractions and temperature field may vary in but not in z displacement as well as traction boundary conditions are considered it appears that many problems of anisotropic elasticity are best viewed and treated in the state space framework

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

capture recapture estimation using finite mixtures of arbitrary dimension reversible jump markov chain monte carlo rjmcmc methods are used to fit bayesian capture recapture models incorporating heterogeneity in individuals and samples heterogeneity in capture probabilities comes from finite mixtures and or fixed sample effects allowing for interactions estimation by rjmcmc allows automatic model selection and or model averaging priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models in contrast to likelihood based methods to demonstrate the approach we analyze the standard snowshoe hare and cottontail rabbit data sets from ecology a reliability testing data set

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

association marginal modeling of multivariate categorical responses a maximum likelihood approach abstract generalized log linear models can be used to describe the association structure and or the marginal distributions of multivariate categorical responses we simultaneously model the association structure and marginal distributions using association marginal am models which are specially formulated generalized log linear models that combine two models an association a model which describes the association among all the responses and a marginal m model which describes the marginal distributions of the responses because the model s composite link function is not required to be invertible a large class of models can be entertained and model specification is typically straightforward we propose a mixed freedom constraint parameterization that exploits the special structure of an am model using this parameterization maximum likelihood fitting is straightforward and typically feasible for large sparse tables when a parsimonious association model is used the size of the fitting proble

robust design and the use of auxiliary variables in estimating population size for an open population nous considerons le probleme de l estimation de la taille d une population ouverte ou les donnees sont collectees sur une deuxieme periode a l interieur d une periode primaire selon un plan robuste propose par pollock 1982 une vraisemblance conditionnelle est utilisee pour estimer les parametres associes a un modele lineaire generalise pour lequel la probabilite de capture est supposee suivre une loi logistique qui depend de covariables individuelles un estimateur de type horvitz thompson est utilise pour estimer la taille de la population pour chaque periode primaire et les probabilites du survie entre les periodes primaires les proprietes asymptotiques de l estimateur propose explorees par simulation ont de bonnes proprietes un jeu de donnee attache a une etude de capture recapture de petits mammiferes conduite selon un plan robuste a dummy bottom au sein du browns park national wildlife refuge est analyse

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

multilist population estimation with incomplete and partial stratification multilist capture recapture methods are commonly used to estimate the size of elusive populations in many situations lists are stratified by distinguishing features such as age or sex stratification has often been used to reduce biases caused by heterogeneity in the probability of list membership among members of the population however it is increasingly common to find lists that are structurally not active in all strata we develop a general method to deal with cases when not all lists are active in all strata using an expectation maximization em algorithm we use a flexible log linear modeling framework that allows for list dependencies and differential probabilities of ascertainment in each list finally we apply our method of estimating population size to two examples

the fixed point property via dual space properties abstract a banach space has the weak fixed point property if its dual space has a weak sequentially compact unit ball and the dual space satisfies the weak uniform kadec klee property and it has the fixed point property if there exists e 0 such that for every infinite subset a of the unit sphere of the dual space a a fails to be 2 e separated in particular e convex banach spaces a class of spaces that includes the uniformly nonsquare spaces have the fixed point property

state vector approach to analysis of multilayered magneto electro elastic plates abstract the state vector equations for three dimensional orthotropic and linearly magneto electro elastic media are derived from the governing equations by eliminating x y xy b x b y d x and d y an efficient method is presented for analysis of multilayered magneto electro elastic plates the methodology is based on the mixed formulation in which basic unknowns are formed by collecting not only displacements electrical potential and magnetic potential but also some of stresses electrical displacements and magnetic induction as special case simply supported and multilayered rectangular plate is analyzed under the surface loading numerical results are presented graphically the procedure of numerical calculation shows that the formulation presented here is simple and direct

inference for poisson and multinomial models for capture recapture experiments summary capture recapture models have been formulated both as poisson and as multinomial distributions maximum likelihood estimates of parameters under the two models are compared for parameters which do not involve the population size the asymptotic covariances are shown to be the same for certain classes of capture recapture experiments both poisson and multinomial models can be used in the poisson models cormack 1979 the numbers of observed individuals with different total capture histories w are regarded as independent poisson variates with means npf o n being some measure of the unknown size of the population and p 0 being specified functions of parameters 0 representing the demography of the population and the behavioural interaction of individuals with the sampling process in the multinomial models darroch 1958 n individuals are regarded as being multinomially distributed into a number of capture histories the observable ones with probabilities ph and the unobservable category with probability l p where p xp s 1 sandland cormack 1984 explored the relationships between the poisson and multinomial models and showed that the asymptotic variance of the maximum likelihood estimate of n under the poisson model is related to that obtained fienberg 1972 under the multinomial model by

estimating heterogeneity in the probabilities of enumeration for dual system estimation abstract we show how conditional logistic regression can be used to estimate the probability of being enumerated in a census and apply the model to the 1990 post enumeration survey pes in the united states the estimates can be used in the estimation of population size and the estimation of correlation bias for example unlike the classical stratification approach the logistic approach permits the use of continuous explanatory variables model choice can be based on the standard techniques of the generalized linear models we discuss some special problems caused by the fact that the pes sample area is open to migration between the captures we also consider the effect of data errors in estimation we characterize hard to enumerate populations and give some tentative estimates of correlation bias

connection between static electromagnetoelasticity and anisotropic elasticity and its applications connection between electromagnetoelasticity and anisotropic elasticity is explored in the state space setting in the absence of electric charges and currents the basic equations of static electromagnetoelasticity are formulated into a state equation and an output equation which bear a remarkable resemblance to the corresponding equations of elasticity accordingly the solutions for various steady state problems of electromagnetoelasticity can be determined in parallel to their elastic counterparts for illustration the generalized plane problems are treated within the context exact solutions for the electromagnetoelastic fields in a half space subjected to line loads and in an infinite plate with an elliptic notch under extension are determined in a simple way

parameter based asymptotics in certain cases statistical methods based on standard maximum likelihood asymptotics become valid as the true parameter value approaches a boundary of the parameter space examples are given which motivate a general parameter based asymptotic theory and a result is obtained which covers such situations of particular interest are applications to stochastic process models

estimation of the size of an open population from capture recapture data using weighted martingale methods summary a weighted martingale method akin to a moving average is proposed to allow the use of modified closed population methods in the estimation of the size of a smoothly changing open population when there are frequent capture occasions we concentrate here on modifications to martingale estimating functions for model mt but a wide range of closed population estimators may be modified in this fashion the method is motivated by and applied to weekly capture recapture data from the mai po bird sanctuary in hong kong simulations show that the weighted martingale estimator compared well with the jolly seber estimator when the conditions for the latter to be valid are met and it performed far better when individuals were allowed to leave and reenter the population expressions are derived for the asymptotic bias and variance of the estimator in an appendix

an inference procedure for a capture and recapture experiment with time dependent capture probabilities summary estimates for the size of a closed population are given for multiple recapture studies in discrete time the estimates are derived by a method of moments for martingales an estimate and associated standard error of the population size are derived for a homogeneous population when the capture probabilities are permitted to be time dependent in the discrete case corresponding results are obtained for the continuous case as well explicit expressions are given for these estimates and their standard errors only simple computation is involved

the analysis of group truncated binary data with random effects injury severity in motor vehicle accidents the analysis of group truncated binary data has been previously considered by o neill and barry 1995b biometrics 51 533 541 where the analysis assumed that responses within each group were independent in this paper we consider the analysis of such data when there is group level heterogeneity a generalized linear mixed model is hypothesized to model the response and maximum likelihood estimates are derived for the truncated case a score test is derived to test for heterogeneity finally the method is applied to a set of traffic accident data

a general theory for modeling capture recapture data from a closed population a general theory for estimating the size of a closed population from multiple recapture data is presented this theory is easily extended to open population models for multiple recapture data estimation is based on a log linear model developed for modeling dependent capture recapture data when capture probabilities vary temporally with behavioral response and are heterogeneous among animals models for complete capture history data are developed along with the first log linear models for removal data the maximum likelihood estimator of the model parameters along with the estimated covariance matrix are presented

a multiple record systems estimation method that takes observed and unobserved heterogeneity into account summary we present a model to estimate the size of an unknown population from a number of lists that applies when the assumptions of a homogeneity of capture probabilities of individuals and b marginal independence of lists are violated this situation typically occurs in epidemiological studies where the heterogeneity of individuals is severe and researchers cannot control the independence between sources of ascertainment we discuss the situation when categorical covariates are available and the interest is not only in the total undercount but also in the undercount within each stratum resulting from the cross classification of the covariates we also present several techniques for determining confidence intervals of the undercount within each stratum using the profile log likelihood thereby extending the work of cormack 1992 biometrics48 567 576

a state space formalism for piezothermoelasticity a state space formalism for electrothermoelastic analysis of a linear piezoelectric body is developed a novel feature of the formalism is that by proper grouping of the field variables and using matrix notations the three dimensional equations of piezothermoelasticity are concisely formulated into a state equation and an output equation which bear a striking resemblance to their elastic counterparts the formalism is remarkably simple with which one deals with only three vector quantities with the 13 independent electromechanical variables as their components and six submatrices that represent all the material constants for a piezoelectric material of the most general kind in this work emphasis is placed on the state space formulation and solution to the generalized plane problem exact solutions for a piezoelectric half space under a line of electromechanical loading and an infinite piezoelectric plate with an elliptical notch subjected to inplane loads are determined with relative ease in many cases piezoelectric solutions can be obtained directly from the corresponding elastic solutions by a simple replacement of the corresponding matrices on the basis of the formalism

simple fitting algorithms for incomplete categorical data a popular approach to estimation based on incomplete data is the em algorithm for categorical data this paper presents a simple expression of the observed data log likelihood and its derivatives in terms of the complete data for a broad class of models and missing data patterns we show that using the observed data likelihood directly is easy and has some advantages one can gain considerable computational speed over the em algorithm and a straightforward variance estimator is obtained for the parameter estimates the general formulation treats a wide range of missing data problems in a uniform way two examples are worked out in full

the minimum capture proportion for reliable estimation in capture recapture models summary we derive estimates of the minimum capture proportion required to obtain a reliable estimate of the population size for several continuous and discrete time capture recapture models the models con sidered are mo mt mb m i mu and mtb m the notation of otis et al 1978 wildlife monograph 62 1 135 numerical results with simulation studies are given and two real examples for the model mh are also considered potential applications of these results are suggested

age period cohort models using smoothing splines a generalized additive model approach age period cohort apc models are used to analyze temporal trends in disease or mortality rates dealing with linear dependency among associated effects of age period and cohort however the nature of sparseness in such data has severely limited the use of apc models to deal with these practical limitations and issues we advocate cubic smoothing splines we show that the methods of estimable functions proposed in the framework of generalized linear models can still be considered to solve the non identifiability problem when the model fitting is within the framework of generalized additive models with cubic smoothing splines through simulation studies we evaluate the performance of the cubic smoothing splines in terms of the mean squared errors of estimable functions our results support the use of cubic smoothing splines for apc modeling with sparse but unaggregated data from a lexis diagram copyright 2013 john wiley sons ltd

a class of regression models for multivariate categorical responses summary when data composed of several categorical responses together with categorical or continuous predictors are observed it is often useful to relate the response probabilities to the predictors via a generalised linear model with a composite link function this paper discusses a class of link functions that lie between the two extremes of the multivariate logistic transform of mccullagh nelder 1989 and the log linear decomposition of contingency table analysis the models derived from these link functions are shown to inherit various desirable properties of both the multivariate logistic regression models and the log linear regression models a computational scheme for implementing these models is derived and they are demonstrated to be computationally more tractable than the multivariate logistic regression models their application is illustrated in a numerical example

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

some practical aspects of a conditional likelihood approach to capture experiments the use of conditional likelihood methods in the analysis of capture data allows the modeling of capture probabilities in terms of observable characteristics of the captured individuals and the trapping occasions the resulting models may then be used to estimate the size of the population here the use of conditional likelihood procedures to construct models for capture probabilities is discussed and illustrated by an example

on the bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty we consider the estimation of the size of a closed population often of interest for wild animal populations using a capture recapture study the estimate of the total population size can be very sensitive to the choice of model used to fit to the data we consider a bayesian approach in which we consider all eight plausible models initially described by otis et al 1978 wildlife monographs 62 1 135 within a single framework including models containing an individual heterogeneity component we show how we are able to obtain a model averaged estimate of the total population incorporating both parameter and model uncertainty to illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known before considering a real example relating to a population of dolphins off northeast scotland

a note on the fourier series model for analysing line transect data the fourier series model offers a powerful procedure for the estimation of animal population density from line transect data the estimate is reliable over a wide range of detection functions in contrast analytic confidence intervals yield at best 90 confidence for nominal 95 intervals three solutions one using monte carlo techniques another making direct use of replicate lines and the third based on the jackknife method are discussed and compared

an objective approach to prior mass functions for discrete parameter spaces we present a novel approach to constructing objective prior distributions for discrete parameter spaces these types of parameter spaces are particularly problematic as it appears that common objective procedures to design prior distributions are problem specific we propose an objective criterion based on loss functions instead of trying to define objective probabilities directly we systematically apply this criterion to a series of discrete scenarios previously considered in the literature and compare the priors the proposed approach applies to any discrete parameter space making it appealing as it does not involve different concepts according to the model supplementary materials for this article are available online

mark recapture models with parameters constant in time the jolly seber method which allows for both death and immigration is easy to apply but often requires a larger number of parameters to be estimated tha would otherwise be necessary if i survival rate phi or ii probability of capture p or iii both phi and p can be assumed constant over the experimental period models with a reduced number of parameters are desirable in the present paper maximum likelihood ml solutions for these three situations are derived from the general ml equations of jolly 1979 in sampling biological populations r m cormack g p patil and d s robson eds 277 282 a test is proposed for heterogeneity arising from a breakdown of assumptions in the general jolly seber model tests for constancy of phi and p are provided an example is given in which these models are fitted to data from a local butterfly population

analysis of a multiple recapture census by computing conditional probabilities in a multiple recapture census of a closed population using fixed sample sizes the total number of different animals captured during the census is a sufficient statistic for the population sized conditional on the population size the exact probability distribution of this sufficient statistic may be calculated and an algorithm for doing this is given standard techniques are applied to describe methods for using the conditional probabilities to form median and interval estimates of the population size the methods are illustrated with examples

monte carlo confidence intervals des intervalles de confiance non parametriques obtenus par la methode de monte carlo sont utiles quand les intervalles obtenus par les methodes analytiques sont indisponibles ou ne correspondent pas au niveau nominal on fournit des formules permettant de generer un intervalle de niveau donne et de quantifier la variation due a la methode de monte carlo

model selection an integral part of inference we argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data we consider different philosophies for achieving this goal and suggest strategies for data analysis we illustrate our methods through three examples the first is a poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates the second is a line transect data set for which different models yield substantially different estimates of abundance the third is a simulated example in which truth is known

capture recapture when time and behavioral response affect capture probabilities summary we consider a capture recapture model in which capture probabilities vary with time and with behavioral response two inference procedures are developed under the assumption that recapture probabilities bear a constant relationship to initial capture probabilities these two procedures are the maximum likelihood method both unconditional and conditional types are discussed and an approach based on optimal estimating functions the population size estimators derived from the two procedures are shown to be asymptotically equivalent when population size is large enough the performance and relative merits of various population size estimators for finite cases are discussed the bootstrap method is suggested for constructing a variance estimator and confidence interval an example of the deer mouse analyzed in otis et al 1978 wildlife monographs62 93 is given for illustration

estimation of survival in marked populations with possibly dependent sighting probabilities summary a simply parameterized class of models for the estimation of survival probability in a marked population is introduced which allows tests of dependence between sighting probabilities and constancy of survival or sighting probabilities estimation and hypothesis testing based on the likelihood function are discussed by simulation the asymptotic properties of the test for dependence are shown to hold for quite modest sample sizes the degree of bias in estimation of survival probabilities when dependence between sightings is not taken into account is shown to increase as the probability of a nonsighting following a nonsighting increases a comprehensive analysis of the data from a mark recapture experiment dealing with survival of abalone is given

estimating the number of faults in a system abstract we consider a reliability system with an unknown number of faults which is observed for a fixed length of time failures are assumed to follow an exponential distribution with an unknown mean and we concentrate on estimation of the number of faults v the likelihood function considered as a function of v has its maximum at one of the boundary points the observed number of faults or infinity with substantial probability likelihood interval estimates and improved point estimates are discussed the harmonic mean of the endpoints of the likelihood interval turns out to be a reasonable point estimate we comment on some extensions of this problem suggested in the software reliability literature

the use of auxiliary variables in capture recapture and removal experiments the dependence of animal capture probabilities on auxiliary variables is an important practical problem which has not been considered in the development of estimation procedures for capturerecapture and removal experiments in this paper the linear logistic binary regression model is used to relate the probability of capture to continuous auxiliary variables the auxiliary variables could be environmental quantities such as air or water temperature or characteristics of individual animals such as body length or weight maximum likelihood estimators of the population parameters are considered for a variety of models which all assume a closed population testing between models is also considered the models can also be used when one auxiliary variable is a measure of the effort expended in obtaining the sample

log linear models for capture recapture summary log linear models are developed for capture recapture experiments and their advantages and disadvantages discussed ways in which they can be extended sometimes with only partial success to open populations subpopulations trap dependence and long chains of recapture periods are presented the use of residual patterns and analysis of subsets of data to identify behavioural patterns and acceptable models is emphasised and illustrated with two examples 1 capture recapture the biological problem with which we are concerned is that of estimating the parameters of a free living population of unknown size from a sequence of s samples in each of which any individual either is or is not observed the models in this paper require that each animal be marked naturally or artificially in such a way that we can observe the numbers of animals which have any particular pattern of being or not being observed through the sequence of samples there are t 2s 1 different observable patterns which we shall refer to as capture histories although there is no requirement for physical capture and denote each pattern by a sequence of l s and 2 s representing respectively seen or not seen in a particular sample a general pattern of capture history will be denoted a with ra the number of individuals observed to have this pattern thus for example with s 3 samples and a 121 r 2 is the number of animals seen in the first and third samples but not in the second the pattern with all 2 s is by definition unobservable in general the population will be subject to demographic change by birth or immigration and by death or emigration the simplest assumption for the response of an animal to the observer one which underlies the classical petersen schnabel or jolly seber estimators is that every animal alive in the population at a sampling time has the same probability of being observed this probability may vary from one sample to another or be constant over all or a number of samples if this assumption fails it may do so for either or both of two reasons the first is that of trap dependence the probability of an individual being observed in a sample depending on its past history of capture the second is that of heterogeneity between individuals who because of differences in their behaviour or in where they live inherently have different probabilities of being observed in any sample the basic idea of heterogeneity refers to properties of individuals which remain constant over time but individual animals may also have time varying behaviour the aspect most commonly considered being temporary departure of an individual from the population various excellent texts describe theoretical and practical aspects of capture recapture notably the comprehensive one by seber 1982 the introduction by begon 1979 the

likelihood and observed geometries a partir du point de vue de la conditionnalite on etablit un parallele observe a la theorie de chentsov efron amari etc en utilisant l information observee et un tenseur d asymetrie observee

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

inference on population size in binomial detectability models many models for biological populations including simple mark recapture models and distance sampling models involve a binomially distributed number n of observations x 1 x n on members of a population of size n two popular estimators of n where is a vector parameter are the maximum likelihood estimator and the conditional maximum likelihood estimator c c based on the conditional distribution of x 1 x n given n we derive the large n asymptotic distributions of and c c and give formulae for the biases of log and log c we show that the difference c is remarkably of order 1 and we give a simple formula for the leading part of this difference simulations indicate that in many cases this formula is very accurate and that confidence intervals based on the asymptotic distribution have excellent coverage an extension to product binomial models is given

obtaining confidence limits on parameters of the jolly seber model for capture recapture data on propose quelques transformations de la methode pour les estimateurs des tailles de la population et des probabilites de survie

estimation of population size based on additive hazards models for continuous time recapture experiments summary we use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous time capture recapture experiment and then construct a horvitz thompson type estimator for the unknown population size the resulting estimator is consistent and asymptotically normal with an easily estimated variance simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed 5 ignoring covariates would underestimate the population size and the coverage probability is poor a wildlife example is provided

convexity conditions and normal structure of banach spaces we prove that f convexity the property dual to p convexity of kottman implies uniform normal structure moreover in the presence of the worth property normal structure follows from a weaker convexity condition than f convexity the latter result improves the known fact that every uniformly nonsquare space with the worth property has normal structure

efficiency of martingale methods in recapture studies summary the asymptotic variances of various estimators of the population size from a recapture study are calculated the estimation methods compared are maximum likelihood and a class of natural martingale estimators with both time variation and behavioural response it is found that i the martingale methods appropriate for time variation or behavioural response are fully efficient ii there is no loss of efficiency at all in allowing for time variation iii there is large loss of efficiency in allowing for behavioural response iv there is a natural martingale method that allows for both time variation and behavioural response

stabilizing binomial n estimators abstract the maximum likelihood estimator of the binomial parameter n can be highly unstable resulting in huge fluctuations in the estimate when the data are only slightly perturbed a method of assessing this sensitivity based on perturbing the log likelihood function is proposed and examined

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

statistical inference procedure for a hypergeometric model for capture recapture experiments abstract we use martingale theory and a method of moments technique to derive a class of estimators for a multihypergeometric model for a capture recapture experiment certain choices of weight function lead to some standard estimators explicit expression for the estimators and their associated standard errors of the parameter population size is obtained optimal estimator among the class of estimators is derived which gives the tightest confidence interval for the population size three examples are given a simulation study is given to assess the performance of the proposed estimators with other existing ones

mixture regression models for closed population capture recapture data in capture recapture studies the use of individual covariates has been recommended to get stable population estimates however some residual heterogeneity might still exist and ignoring such heterogeneity could lead to underestimating the population size n in this work we explore two new models with capture probabilities depending on both covariates and unobserved random effects to estimate the size of a population inference techniques including horvitz thompson estimate and confidence intervals for the population size are derived the selection of a particular model is carried out using the akaike information criterion aic first we extend the random effect model of darroch et al 1993 journal of american statistical association 88 1137 1148 to handle unit level covariates and discuss its limitations the second approach is a generalization of the traditional zero truncated binomial model that includes a random effect to account for an unobserved heterogeneity this approach provides useful tools for inference about n since key quantities such as moments likelihood functions and estimates of n and their standard errors have closed form expressions several models for the unobserved heterogeneity are available and the marginal capture probability is expressed using the logit and the complementary log log link functions the sensitivity of the inference to the specification of a model is also investigated through simulations a numerical example is presented we compare the performance of the proposed estimator with that obtained under model mh of huggins 1989 biometrika 76 130 140

p convexity of orlicz bochner function spaces endowed with the orlicz norm abstract in this paper criteria for p convexity of orlicz bochner function spaces equipped with orlicz norm are given although criteria for p convexity of orlicz function spaces equipped with the orlicz norm were known we can easily deduce them from our main results

recapture models under equality constraints for the conditional capture probabilities alessio farcomeni uniroma1 it summary we introduce a general class of capture recapture models in which capture probabilities depend on the previous capture history we discuss constrained versions of the saturated model based on equality constraints despite the seeming complexity inference can be performed through a simple estimating equation the approach is illustrated on a data set about the population of great copper butterflies in willamette valley of o regon it has long been recognized that in capture recapture exper iments the previous capture history may influence capture probabilities and failure to acknowl edge this fact may lead to biased estimates of the unknown population size one of the first model s used denoted by mb included behavioural response to capture by using different probabi lities before and after first capture otis et al 1978 pollock 1991 other examples are given by the markov chain models of yang chao 2005 and the persistence models detailed in ramsey usner 2003 and ramsey severns 2010 in this paper we propose a general class of models which are based on conditional capture probabilities we restrict the satura ted model through equality constraints arguing that the resulting class of models is rich enough to s ummarize a plethora of real data situations the restricted class can be also defined through partitions of the capture histories where capture probabilities conditional on different hist ories belonging to the same partition are equal surprisingly enough the approach based on maximizing the conditional likelihood leads to a straightforward inference based on a simple estimating equation an interesting feature of the proposed model class is that the previous capture histor y can be allowed to influence the capture probability in very flexible ways different models can be fitted and compared through information criteria or likelihood ratio tests

quantifying the effects of unequal catchabilities on jolly seber estimators via sample coverage using the concept of sample coverage we derive an approximation of the bias in the jolly seber population size estimators due to heterogeneity of capture probabilities the resulting bias is expressed as a function of sample coverage average capture probability and the coefficient of variation of individual capture probabilities the effect of unequal catchabilities on the jolly seber survival rate estimators is also briefly discussed we propose new population size estimators which incorporate the heterogeneity of capture probabilities a simulation study investigates the performance of the approximation formulas of biases and the proposed estimation procedure a real data set of male black kneed capsids discussed in jolly biometrika 52 225 247 1965 seber the estimation of animal abundance 1982 and burnham in estimation of analysis of insect populations pp 416 435 1989 illustrates the method

errors in inspection integer parameter maximum likelihood in a finite population abstract in a probability model for possible errors in the inspection of a finite lot containing defective items it is shown how maximum likelihood estimation is affected by whether the sampling is carried out with or without replacement these changes are examined by developing a method for simultaneous maximization over an integer and a scalar parameter a new method for the bounding of the integer solution is introduced the results show that the parameter estimates in the inspection model are generally stable under wide changes in the sampling framework conditions for instability of the solution are identified some apparently new relations for discrete distributions are derived in the process of the investigation

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

a state space formalism for anisotropic elasticity part i rectilinear anisotropy a state space formalism for anisotropic elasticity including the thermal effect is developed a salient feature of the formalism is that it bridges the compliance based and stiffness based formalisms in a natural way the displacement and stress components and the thermoelastic constants of a general anisotropic elastic material appear explicitly in the formulation yet it is simple and clear this is achieved by using the matrix notation to express the basic equations and grouping the stress in such a way that it enables us to cast neatly the three dimensional equations of anisotropic elasticity into a compact state equation and an output equation the homogeneous solution to the state equation for the generalized plane problem leads naturally to the eigen relation and the sextic equation of stroh extension twisting bending temperature change and body forces are accounted for through the particular solution based on the formalism the general solution for generalized plane strain and generalized torsion of an anisotropic elastic body are determined in an elegant manner

tests point estimations and confidence sets for a capture recapture model abstract a capture recapture model that depends on the catch ability of the individuals in a closed population is considered a test is derived to decide if the capture efficiencies are the same for two capture attempts the test given assumes no a priori information about the population and can be used even if one is dealing with relatively small populations statistical inferences are drawn about the size of the population in particular a family of point estimators for the population size n is investigated and compared with the maximum likelihood estimator further confidence intervals for the capture efficiency e are combined with joint confidence regions for n and e to obtain confidence intervals for n it is found that this procedure yields confidence intervals for n whose actual confidence levels are not strongly dependent on the nuisance parameter e for n 200 the procedure given for finding confidence intervals for n is found to be more satisfactory than the standard approach of simply

quantifying precision of mark recapture estimates using the bootstrap and related methods summary bootstrap techniques yield variance estimates under any model for which parameter estimates can be calculated and are useful in cases where analytic variances are not available in closed form or are available only if more restrictive assumptions are made here the application of bootstrap techniques to mark recapture models is discussed the approach also allows generation of robust confidence intervals which extend beyond the permissible parameter range only if the mark recapture model itself allows out of range parameter estimates if an animal population is assumed to be closed i e no death birth or migration two further methods of obtaining confidence limits for population size are suggested the first is based on a robbins monro search for each limit and the second applies the concept of a randomisation or permutation test in the absence of nuisance parameters both methods are exact apart from monte carlo variation and the limitations imposed by a discrete distribution for the second if all possible permutations are enumerated monte carlo variation is eliminated

nonparametric density estimation from biased data with unknown biasing function we present a kernel estimator for the density of a variable when sampling probabilities depend on that variable both the density and sampling bias weight functions are unknown and are estimated nonparametrically to achieve this the method requires that two independent samples be taken from a fixed finite population an estimator of population size follows simply from our density estimator asymptotic bias and standard errors for these estimators are provided and the methodology is illustrated both on simulation data and on a dual list dataset of aboriginal people in the vancouver richmond area of canada

objective priors for discrete parameter spaces this article considers the development of objective prior distributions for discrete parameter spaces formal approaches to such development such as the reference prior approach often result in a constant prior for a discrete parameter which is questionable for problems that exhibit certain types of structure to take advantage of structure this article proposes embedding the original problem in a continuous problem that preserves the structure and then using standard reference prior theory to determine the appropriate objective prior four different possibilities for this embedding are explored and applied to a population size model the hypergeometric distribution the multivariate hypergeometric distribution the binomial beta distribution and the binomial distribution the recommended objective priors for the first third and fourth problems are new

a penalized nonparametric maximum likelihood approach to species richness estimation we propose a class of penalized nonparametric maximum likelihood estimators npmles for the species richness problem we use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem the estimators are constructed using a conditional likelihood that is simpler than the full likelihood we show that the full likelihood npmle solution given by norris and pollock can be found with great accuracy by using an appropriate penalty term on the conditional likelihood so it is an element of our class of estimators a simple and fast algorithm for the penalized npmle is developed it can be used to greatly speed up computation of the unconditional npmle it can also be used to find profile mixture likelihoods based on our goal of attaining high stability while retaining sensitivity we propose an adaptive quadratic penalty function a systematic simulation study using a wide range of scenarios establishes the success of this method relative to its competi

inference on the number of species through geometric lower bounds estimating the number of species in a population from a sample of individuals is investigated in a nonparametric poisson mixture model a sequence of lower bounds to the odds that a species is unseen in the sample are proposed from a geometric perspective a lower bound and its representing mixing distribution can be computed by linear programming with guaranteed convergence these lower bounds can be estimated by the maximum likelihood method and used to construct lower confidence limits for the number of species by the bootstrap method computing the nonparametric maximum likelihood estimator is discussed simulation is used to assess the performance of estimated lower bounds and compare them with several existing estimators a genomic application is investigated

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

bayesian methods for estimation of the size of a closed population summary a bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed the approach allows for a variety of dependence structures between the lists can make use of covariates and explicitly accounts for model uncertainty interval estimates from this approach are compared to frequentist and previously published bayesian approaches several examples are considered