bayesian inference for small sample capture recapture data we consider data on the survival of a population of cephalorhynchus hectori hector s dolphins in a marine area of new zealand to estimate survival probabilities of animal populations a multiple capture recapture sampling scheme can be used in this paper we propose a practical methodology to derive approximations to posterior distributions based on laplace methods we show how to calculate bayes estimates and credible intervals in this setting

asymptotically simple solutions of the vacuum einstein equations in even dimensions we show that a set of conformally invariant equations derived from the fefferman graham tensor can be used to construct global solutions of vacuum einstein equations in all even dimensions this gives in particular a new simple proof of friedrich s result on the future hyperboloidal stability of minkowski space time and extends its validity to even dimensions

a note on n estimators for the binomial distribution abstract consider k success counts from a binomial distribution with unknown n and success probability p we examine the problem of estimating n by integrating the likelihood for n and p over a beta density for p we obtain the beta binomial distribution resulting in stable and reasonably efficient estimators of n which compare favorably with and are often better than the estimates introduced by olkin et al 1981

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

bayesian inspection model with the negative binomial prior in the presence of inspection errors one of the basic assumptions in bayesian inspection models is that we have some prior knowledge about the number of defects in a certain product or software system the prior knowledge can be often described as a probability distribution e g poisson distribution in the paper we propose three conditions that should be put forth as desirable properties for a prior probability distribution of the number of defects in the product we review various prior probability distributions and test if they meet those conditions the negative binomial distribution is found to be the only one that satisfies all the desirable conditions with the negative binomial prior we analyze the effects of various parameters on the bayesian estimate of the number of undetected errors still remaining in the product

bayesian analyses for a multiple capture recapture model summary in multiple capture recapture surveys the probability of capture can vary between sampling occasions the model accounting for this variation is known as at bayes empirical bayes and bayes empirical bayes solutions are given to the problems of interval estimation decision making and point estimation of the population size n when the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate estimates obtained from empirical bayes and bayes empirical bayes methods compare closely to bayesian methods using a reference prior distribution for the capture probabilities however when the number of sampling occasions is large and the number of recaptured units observed on each sampling occasion is small inferences obtained using different reference priors can differ considerably

inference for the binomial n parameter a hierarchical bayes approach summary a hierarchical bayes approach to the problem of estimating n in the binomial distribution is presented this provides a simple and flexible way of specifying prior information and also allows a convenient representation of vague prior knowledge it yields solutions to the problems of interval estimation prediction and decision making as well as that of point estimation the bayes estimator compares favourably with the best previously proposed point estimators in the literature unknown parameters n and 0 most of the literature about statistical analysis of this model has focused on point estimation of n while interval estimation prediction and decision making have been little considered see 2 i adopt a hierarchical bayes approach this provides a simple way of specifying prior information and also allows a convenient representation of vague prior knowledge using limiting improper prior forms it leads to solutions of the problems of interval estimation prediction and decision making as well as that of point estimation a difficulty with bayesian analysis of this problem has been the absence of a sufficiently flexible and tractable family of prior distributions mainly due to the fact that n is an integer the present approach gets around this by first assuming that n has a poisson distribution the resulting hyperparameters are then continuous valued and one may use existing results about conjugate and vague priors in better understood settings

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

bayesian capture recapture methods for error detection and estimation of population size heterogeneity and dependence summary this paper considers estimation of the unknown size n of a population based on multiple capture recapture samples we extend the bayesian multiple recapture model to accommodate possible heterogeneity and dependence among the samples and possible heterogeneity within the samples in the dependent model we show that posterior inference for n is independent of almost all the nuisance parameters we develop a flexible bayesian model for heterogeneity within samples and demonstrate how gibbs sampling can be used to calculate the bayesian estimator for n and other quantities of interest the performance of the proposed estimators is evaluated by simulation under both correct and incorrect model specifications and we illustrate our methods in two examples about software review and estimation of a cottontail rabbit population

bayesian estimation of animal abundance for line transect sampling this paper develops a bayesian model for estimating the density of a closed animal population from data obtained by the line transect method the detection function is assumed to be half normal and the data are neither grouped nor truncated a bayes estimator is constructed with respect to a gamma prior density and two loss functions relative squared error and absolute squared error the bayes estimator is compared with the maximum likelihood estimator as well as the fourier series estimator using two data sets

capture recapture estimation via gibbs sampling capture recapture models are widely used in the estimation of population sizes based on data augmentation considerations we show how gibbs sampling can be applied to calculate bayes estimates in this setting as a result formulations which were previously avoided because of analytical and numerical intractability can now be easily considered for practical application we illustrate this potential by using gibbs sampling to calculate bayes estimates for a hierarchical capture recapture model in a real example

relative invariants ideal classes and quasi canonical modules of modular rings of invariants abstract we describe quasi canonical modules for modular invariant rings r of finite group actions on factorial gorenstein domains from this we derive a general quasi gorenstein criterion in terms of certain 1 cocycles this generalizes a recent result of a braun for linear group actions on polynomial rings which itself generalizes a classical result of watanabe for non modular invariant rings we use an explicit classification of all reflexive rank one r modules which is given in terms of the class group of r or in terms of r semi invariants this result is implicitly contained in a paper of nakajima 1982 15

on the calabi flow in this paper we study the calabi flow on a polarized kahler manifold and some related problems we first give a precise statement on the short time existence of the calabi flow for any c 3 a m initial kahler potential as an application we prove a stability result any metric near a constant scalar curvature kahler csck metric will flow to a nearby csck metric exponentially fast secondly we prove that a compactness theorem in the space of the kahler metrics given uniform ricci bound and potential bound as an application we prove the calabi flow can be extended once ricci curvature stays uniformly bounded lastly we prove a removing singularity result about a weak constant scalar curvature metric in a punctured disc

inference and prediction for a general order statistic model with unknown population size abstract suppose that the first n order statistics from a random sample of n positive random variables are observed where n is unknown this the general order statistic model has been applied to the study of market penetration capture recapture burn in in repairable systems software reliability growth the estimation of the number of individuals exposed to radiation and the estimation of the number of unseen species inference is to be made about the unknown parameters especially n and future observations are to be predicted a bayes empirical bayes approach to inference is presented this permits the comparison of competing perhaps nonnested models for the distribution of the random variables in a natural way it also provides easily implemented inference and prediction procedures that avoid the difficulties of non bayesian methods one such difficulty is that the maximum likelihood estimator of n may be infinite results are given for the case in which vague prior information about the model

the calabi flow on kahler surfaces with bounded sobolev constant i we consider the formation of singularities along the calabi flow by assuming the uniformly bounded sobolev constants on kahler surfaces we prove that if curvature tensor is not uniformly bounded then one can form a singular model called deepest bubble such deepest bubble has to be a scalar flat ale kahler metric in certain kahler classes on toric fano surfaces the sobolev constants are a priori bounded along the calabi flow with small calabi energy we can also show in certain cases no deepest bubble can form along the flow it follows that the curvature tensor is uniformly bounded and the flow exists for all time and converges to an extremal metric subsequently to illustrate our results more clearly we focus on an example on mathbb cp 2 blown up three points at generic position our result also implies existence of constant scalar curvature metrics on mathbb cp 2 blown up three points at generic position in the kahler classes where the exceptional divisors have the same area

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

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

a bayesian analysis of multiple recapture sampling for a closed population summary this paper considers from a bayesian viewpoint inferences about the size of a closed animal population from data obtained by a multiple recapture sampling scheme the method developed enables prior information about the population size and the catch probabilities to be utilized to produce considerable improvements in certain cases on ordinary maximum likelihood methods several ways of expressing such prior information are explored and a practical example of the uses of these ways is given the main result of the paper is an approximation to the posterior distribution of sample size that exhibits the contributions made by the likelihood and the prior ideas the multiple recapture sampling scheme involves taking samples from a population of animals at each stage counting the number of marked animals in the sample marking the previously unmarked animals and returning the sample to the population the literature is reviewed by cormack 1968 and the papers most relevant to our problem are those of chapman 1952 and darroch 1958 in these papers maximum likelihood estimates for the population parameters and variances for these estimates are given our approach differs from previous ones by introducing prior information about the population size and about the propensities of the animals to be captured called catch probabilities by some previous authors the incorporation of these propensities is a feature not shared by many previous approaches darroch 1958 found their introduction into his model does not change the maximum likelihood estimates of the population size our approach will show that strong prior knowledge about the catch probabilities can greatly affect inference about the population size and it is in this respect that the greatest difference from previous approaches lies although it is recognized that models of an open population incorporating death and immigration such as those of jolly 1965 and seber 1965 are more practically realistic we feel that our method which deals only with a closed population is worth investigating as a step towards providing a bayesian treatment of the open population problem

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

exact and asymptotic inference for the size of a population on montre que la vraisemblance a un maximum local unique et que l algorithme iteratif propose converge vers celui ci

a new bayesian method for nonparametric capture recapture models in presence of heterogeneity summary the intrinsic heterogeneity of individuals is a potential source of bias in estimation procedures for capture recapture models to account for this heterogeneity in the model a hierarchical structure has been proposed whereby the probabilities that each animal is caught on a single occasion are modelled as independent draws from a common unknown distribution f however there is general agreement that modelling f by a simple parametric curve may lead to unsatisfactory results here we propose an alternative bayesian approach that relies on a different parameterisation which imposes no assumption on the shape of f but drives the problem back to a finite dimensional setting our approach avoids some identifiability issues related to such a recapture model while allowing for a formal bayesian default analysis results of analyses of computer simulations and of real data show that the method performs well