new families of binary sequences with optimal three level autocorrelation in this correspondence we give several new families of binary sequences of period n with optimal three level autocorrelation where n spl equiv 2 mod 4 these sequences are either balanced or almost balanced our construction is based on cyclotomy

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

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

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

representation of compositional relations in fuzzy reasoning abstract this paper deals with the representation of the compositional relations in fuzzy reasoning we show that the compositional relations of fuzzy reasoning under min zadeh operation can be represented by the largest solution of some fuzzy relational inequalities or relational equations

confidence intervals for densities in line transect sampling we consider the problem of estimating the density d of a population of objects or animals with ungrouped data from line transect sampling we present a method of deriving an approximate confidence interval for d this confidence interval requires the estimation of a certain standard deviation by the bootstrap method it also requires the estimation with negligible bias of the value f o of a density functions we present a method of bias reduction in the case wheref o is estimated by the fourier series method monte carlo simulations indicate that the coverage rates are smaller than their nominal values but the bias reduction offers an improvement especially when f is peaked at 0 or when it is long tailed

new constructions of binary sequences with optimal autocorrelation value magnitude in this paper we give three new constructions of binary sequences of period an with optimal autocorrelation value or optimal autocorrelation magnitude using n 4 interleaved sequences yu and gong recently found any binary sequence of period an with optimal autocorrelation value constructed from an almost difference set by arasu et al is an n 4 interleaved sequence for which all four columns in its n 4 array are shift equivalent up to the complement we found that it is not necessary that four columns are shift equivalent instead it could be a pair of related sequences together with their shifts as the column sequences the first construction is to use a generalized gmw sequence of period n 2k 1 and its modified version the second construction is to use a twin prime sequence of length n p p 2 and its modified version and the third construction a pair of legendre sequences of period n p p odd prime with their respective first terms complementary the 2 level autocorrelation property is not needed for the legendre sequence the comparison with the known constructions are given for the new sequences with optimal autocorrelation value their corresponding new almost difference sets are also derived

binary and quadriphase sequences with optimal autocorrelation properties a survey time discrete signals with good autocorrelation properties are used in various applications in communications engineering from an implementation point of view usually sequences with a small phase alphabet and a maximal energy efficiency i e a uniform envelope are most favorable for this reason known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence in many cases the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted these almost binary and almost quadriphase sequences are considered as well the optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd periodic autocorrelation function respectively for sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case the best known parameters obtained by computer search are compared with the constructed results

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

local bandwidth selection for kernel estimation of population densities with line transect sampling summary seber 1986 biometrics42 267 292 suggested an approach to biological population density estimation using kernel estimates of the probability density of detection distances in line transect sampling chen 1996a applied statistics45 135 150 and others have employed cross validation to choose a global bandwidth for the kernel estimator or have suggested adaptive kernel estimation chen 1996b biometrics52 1283 1294 because estimation of the density is required at only a single point we investigate a local bandwidth selection procedure that is a modification of the method of schucany 1995 journal of the american statistical association90 535 540 for nonparametric regression we report on simulation results comparing the proposed method and a local normal scale rule with cross validation and adaptive estimation the local bandwidths and normal scale rule produce estimates with mean squares that are half the size of the others in most cases consistency results are also provided

perpendicular distance models for line transect sampling summary perpendicular distance line transect models are examined to assess whether any single model can provide a general procedure for analysing line transect data of the two parameter models considered the hazard rate model appears promising whereas the exponential power series and exponential quadratic models do not of the nonparametric models the fourier series is the best developed and is favoured by many researchers as a general model however for a given data set the fourier series estimate may be highly dependent on the number of terms selected and so the model is not a clear improvement over the hazard rate model a similar variable term model using hermite polynomials is considered and is shown to be less dependent on the number of terms selected there has been some debate about whether the derivative of the density function of perpendicular distances evaluated at 0 should be 0 so that the function has a shoulder the problem is examined in detail and it is argued that reliable estimation is not possible from line transect data unless a shoulder exists many data sets appear to exhibit no shoulder possible reasons are examined

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

some properties of infinite fuzzy relational equations on complete brouwerian lattices this paper deals with fuzzy relational equations email protected x b where both a a j j j and b are known b has an irredundant continuous join decomposition x x j j j t is unknown represents sup inf composition j is an infinite index set on complete brouwerian lattices at first a necessary and sufficient condition for existence of the attainable solutions the unattainable solutions respectively and some properties of the attainable solutions the unattainable solutions respectively are formulated then the solution set of the fuzzy relational equations is described

unattainable solutions of a fuzzy relation equation in a fuzzy relation equation the properties of the solution set have been investigated especially when the basic spaces are all finite sets however when the basic spaces are infinite a few properties are known in this paper we use the concepts of attainability and unattainability of a solution to clarify some properties of the solution set and show the condition for existence of a partially attainable solution and an unattainable one

new design of quaternary low correlation zone sequence sets and quaternary hadamard matrices in this correspondence we present new construction methods for quaternary low correlation zone lcz sequence sets from a binary sequence with good autocorrelation we show that the sets obtained by our methods are optimal or nearly optimal with respect to the tang fan matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period family size and zone size we also give a construction method for a quaternary lcz sequence set from a binary lcz sequence set finally we give a new construction method for quaternary hadamard matrices by the inverse of the gray map

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

new design of low correlation zone sequence sets in this paper we present several construction methods for low correlation zone lcz sequence sets first we propose a design scheme for binary lcz sequence sets with parameters 2n 1 2 m l 2 in this scheme we can freely set the lcz length l and the resulting lcz sequence sets have the size m which is almost optimal with respect to tang fan and matsufuji bound second given a q ary lcz sequence set with parameters n m l epsi and even q we construct another q ary lcz sequence set with parameters 2n 2m l 2epsi or 2n 2m l 1 2epsi especially the new set with parameters 2n 2m l 2 can be optimal in terms of the set size if a q ary optimal lcz sequence set with parameters n m l 1 is used

latticized linear programming and fuzzy relation inequalities abstract a logical linear programming problem the latticized linear programming is proposed based on fuzzy lattice and fuzzy relation inequalities the proposed problem is essentially an optimization problem which should be useful under certain logical if then situations to illustrate the proposed approach numerical examples are solved

on the variable circular plot method of estimating animal density the development by ornithologists of the variable circular plot method of estimating bird densities from observer to bird distances has led to estimation problems similar to those of line transect sampling however to apply line transect methods without modification requires that the distance data be transformed to areas by squaring the implications of this transformation on the assumed shapes for the detection curve have not been investigated in the literature this paper illustrates that application of line transect models to area data may lead to poor model performance and erroneous conclusions developments based on distance data are discussed briefly and binomial models are derived for the special case in which birds are categorised simply according to whether they are within or beyond a specified distance

reachable solution set of a fuzzy relation equation abstract the largest element of the solution set of a fuzzy relation equation has been found by e sanchez inform and control 30 1976 38 48 but the smallest element does not exist it is difficult to expose the solution of the fuzzy relation equation in the case of the determinate relation equations complete consequences have been found by wang peizhuang and yuan meng relation equation and relation inequalities selected papers on fuzzy subsets beijing normal university march 1980 in the case of the fuzzy relation equations wang and yuan have given a class of special solutions which probably possesses some minimality characterizations in this paper the reachable solution set of the fuzzy relation equation is given for the fuzzy relation equation on the finite sets a neat and efficient method for solving it is given

sets of solution set invariant coefficient matrices of simple fuzzy relation equations abstract a set of coefficient matrices which are invariant to a solution set of a simple fuzzy relation equation is considered the equipollency of the cardinal numbers of solution sets of simple fuzzy relation equations for two constant vectors is also shown

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

an arma type probability density estimator on etudie les proprietes d un estimateur de densite de probabilite ayant la forme rationnelle d un spectre arma sous diverses conditions sur les coefficients de fourier de la densite on montre que l estimateur arma a une erreur quadratique moyenne integree asymptotiquement plus petite que le meilleur estimateur de serie de fourier effile

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

two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities this paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities fri with the max einstein composition operator if its feasible domain is non empty then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions also an efficient algorithm is proposed to solve the model based on the structure of fri path the concept of partial solution and the branch and bound approach the algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions some sufficient conditions are given that under them some of the optimal components of the model are directly determined some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions then the reduced domain is decomposed if possible into several sub domains with smaller dimensions that finding the components of the optimal solution in each sub domain is very easy in order to obtain an optimal solution of the original problem we propose another more efficient algorithm which combines the first algorithm these procedures and the decomposition method furthermore sufficient conditions are suggested that under them the problem has a unique optimal solution also a comparison between the recently proposed algorithm and the known ones will be made

modeling association among demographic parameters in analysis of open population capture recapture data we present a hierarchical extension of the cormack jolly seber cjs model for open population capture recapture data in addition to recaptures of marked animals we model first captures of animals and losses on capture the parameter set includes capture probabilities survival rates and birth rates the survival rates and birth rates are treated as a random sample from a bivariate distribution thus the model explicitly incorporates correlation in these demographic rates a key feature of the model is that the likelihood function which includes a cjs model factor is expressed entirely in terms of identifiable parameters losses on capture can be factored out of the model since the computational complexity of classical likelihood methods is prohibitive we use markov chain monte carlo in a bayesian analysis we describe an efficient candidate generation scheme for metropolis hastings sampling of cjs models and extensions the procedure is illustrated using mark recapture data for the moth gonodontis bidentata

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

bayesian estimation of movement and survival probabilities from capture recapture data summary the arnason schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture recapture data the missing data structure of this capture recapture model is exhibited and summarised via a directed graph representation taking advantage of this structure we implement a gibbs sampling algorithm from which bayesian estimates and credible intervals for survival and movement probabilities are derived convergence of the algorithm is proved using a duality principle we illustrate our approach through a real example

some properties of sup min fuzzy relational equations on infinite domains abstract this paper deals with a sup min fuzzy relational equation on infinite domains some properties of its solution set will be obtained in particular a necessary and sufficient condition describing the attainable solution resp the unattainable solution is formulated in the end the solution set will be given under some conditions

the line transect method a nonparametric estimator based on shape restrictions summary a new estimator for population density based on line transect surveys is presented its sampling behaviour is investigated through simulation studies advantages of the proposed estimator include its simple intuitive base its stable behaviour over a wide variety of detection curves the ease with which it can be computed and the availability of reliable confidence limits the simulation results point to a general improvement in efficiency over existing estimators

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 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

a new construction of zero difference balanced functions and its applications in this paper a new construction of zero difference balanced functions defined on is given where is an odd positive integer based on the generic constructions proposed by ding optimal constant composition codes and perfect difference systems of sets with new parameters can be generated from the zero difference balanced functions constructed in this paper

binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation generated by the polynomial z sup d z 1 sup d we present a construction for binary pseudorandom sequences of period 2 sup m 1 with ideal autocorrelation property using the polynomial z sup d z 1 sup d we show that the sequence obtained from the polynomial becomes an m sequence for certain values of d we also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is 3k spl plusmn 1 where k is a positive integer these new sequences are represented using a trace function and the results are tabulated

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

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

a new family of almost difference sets and some necessary conditions almost difference sets have important applications in cryptography and coding theory in this paper new families of almost difference sets are constructed some necessary conditions for the existence of v k spl lambda t almost difference sets in z sub v are derived

bayesian analysis of the sequential inspection plan via the gibbs sampler a complex product such as a software system is often inspected more than once in a sequential manner to further improve its quality and reliability in such a case a particularly important task is to accurately estimate the number of errors still remaining in the product after a series of multiple inspections in the paper we first develop a maximum likelihood method of estimating both the number of undiscovered errors in the product and the detection probability we then compare its performance with that of an existing estimation method that has several limitations we also propose a bayesian method with noninformative priors which performs very well in a monte carlo simulation study as the prior knowledge is elicited and incorporated in the analysis the prediction accuracy of the bayesian method improves even further thus it would be worthwhile to use various estimation methods and compare their estimates in a specific inspection environment

some new classes of zero difference balanced functions zero difference balanced zdb functions were introduced recently by ding for the construction of optimal constant composition codes and optimal and perfect difference systems of sets they are closely related to partitioned difference families in this paper we present generic constructions of zdb functions from functions with difference balanced property in particular two classes of zdb functions with new and flexible parameters are reported employing these new zdb functions we obtain at the same time optimal 1 constant composition codes 2 constant weight codes and 3 perfect difference systems of sets all with new and flexible parameters

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

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

detectability functions in observing spatial point processes whenever populations modelled as spatial point patterns are sampled the observational methods used influence the form of the associated delectability functions in this paper we show how the properties of estimators of population quantities depend on the delectability functions in combination with the stochastic structure of the point process giving rise to the spatial patterns criteria for optimal delectability functions indicative of the most efficient observational methods are derived for the inference objectives of i estimating expected density and ii predicting or estimating realized density within a study region detectability functions related to observational methods such as plots of various shapes line transects radial transects and aerial surveys are compared numerically for a point process with aggregation tendencies for a given effective area observed constant delectability over the study region is optimal for predicting realized density while some curious doughnut shaped functions are more efficient for estimating the expected density parameter

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

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

radial distance models for the line transect method line transect estimation of wildlife populations can be based on either right angle distances or radial distances estimation based on radial distances requires more restrictive assumptions about the mechanism by which observations are generated we examine this mechanism and show that the mean sighting angle may frequently be larger than predicted by hayne s fixed distance model or by eberhardt s variable distance model the modified and generalized hayne s models are also investigated an alternative approach based on hazard rate analysis is suggested but we conclude that a nonparametric right angle distance model will generally result in more reliable estimation than any radial distance model

optimal partitioned cyclic difference packings for frequency hopping and code synchronization optimal partitioned cyclic difference packings pcdps are shown to give rise to optimal frequency hopping sequences and optimal comma free codes new constructions for pcdps based on almost difference sets and cyclic difference matrices are given these produce new infinite families of optimal pcdps and hence optimal frequency hopping sequences and optimal comma free codes the existence problem for optimal pcdps in bbz3m with m base blocks of size three is also solved for all m 8 16 mod 24

optimal frequency hopping sequences a combinatorial approach frequency hopping multiple access fhma spread spectrum communication systems employing multiple frequency shift keying mfsk as data modulation technique are investigated from a combinatorial approach a correspondence between optimal frequency hopping fh sequences and partition type difference packings is first established by virtue of this correspondence fhma systems with a single optimal fh sequence each are constructed from various combinatorial structures such as affine geometries cyclic designs and difference families combinatorial recursive constructions are also presented many new infinite series of optimal fh sequences are thus obtained these new fh sequences are also useful in ultra wideband uwb communication systems

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 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

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 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

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

cyclotomic constructions of zero difference balanced functions with applications based on a recent work of ding wang and xiong we present some cyclotomic constructions of zero difference balanced zdb functions which interpret the previous construction proposed by cai zeng helleseth tang and yang the resulted zdb functions can be used to generate optimal constant composition codes and perfect difference systems of sets with new parameters

binary sequences with optimal autocorrelation sequences have important applications in ranging systems spread spectrum communication systems multi terminal system identification code division multiple access communication systems global positioning systems software testing circuit testing computer simulation and stream ciphers sequences and error correcting codes are also closely related in this paper we give a well rounded treatment of binary sequences with optimal autocorrelation we survey known ones and construct new ones

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

high rate self synchronizing codes self synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error tolerant self synchronizing codes may be realized as cosets of linear codes ideally difference systems of sets should sacrifice as few bits as possible for a given code length alphabet size and error tolerance capability however it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low in fact the majority of known optimal difference systems of sets are for exceptionally noisy channels requiring a substantial amount of bits for synchronization to address this problem we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent our constructions utilize optimal difference systems of sets as ingredients and when applied carefully generate asymptotically optimal ones with higher information rates we also give direct constructions for optimal difference systems of sets with high information rates and error tolerance that generate binary and ternary self synchronizing codes

hazard models for line transect surveys with independent observers summary the likelihood function for data from independent observer line transect surveys is derived and a hazard model is proposed for the situation where animals are available for detection only at discrete time points under the assumption that the time points of availability follow a poisson point process we obtain an analytical expression for the detection function we discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions discrete and continuous hazard models are compared and the robustness of the discrete model is investigated finally the methodology is applied to data from a survey for minke whales in the northeastern atlantic

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12