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

obtaining the observed information matrix for the poisson log linear model with incomplete data summary we consider inferences about poisson log linear models for which only certain disjoint sums of the data are observable we derive an explicit formula for the observed information matrix associated with the log linear parameters that is intuitively appealing and simple to evaluate suppose we want to fit a log linear model but only certain disjoint sums of the data are observable when the complete data are unobservable one could work directly with the incomplete data likelihood the newton raphson or fisher scoring algorithm could then be used to estimate the parameters as well as the precision of these estimates palmgren ekholm 1987 however often the incomplete data likelihood is complicated relative to the complete data likelihood to avoid working with the more complicated likelihood one could alternatively use the expectation maximization em algorithm dempster laird rubin 1977 to compute the maximum likelihood estimators a positive feature of the em algorithm not shared by the other two approaches is that it is insensitive to starting values unfortunately one does not obtain an estimate of precision as a by product of the em algorithm here we derive an explicit formula for the observed information matrix that can easily be computed an estimate of precision is the inverse of this information matrix evaluated at the maximum likelihood estimates sundberg 1974 derived an expression for the observed information matrix for the incomplete data when the complete data come from the regular exponential family denote the vector of complete data by x and the vector of observable data by y g x if the complete data density has form

the dependency of timbre on fundamental frequency the dependency of the timbre of musical sounds on their fundamental frequency f0 was examined in three experiments in experiment i subjects compared the timbres of stimuli produced by a set of 12 musical instruments with equal f0 duration and loudness there were three sessions each at a different f0 in experiment ii the same stimuli were rearranged in pairs each with the same difference in f0 and subjects had to ignore the constant difference in pitch in experiment iii instruments were paired both with and without an f0 difference within the same session and subjects had to ignore the variable differences in pitch experiment i yielded dissimilarity matrices that were similar at different f0 s suggesting that instruments kept their relative positions within timbre space experiment ii found that subjects were able to ignore the salient pitch difference while rating timbre dissimilarity dissimilarity matrices were symmetrical suggesting further that the absolute displacement of the set of i

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

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

analysis of capture recapture data with a rasch type model allowing for conditional dependence and multidimensionality summary in this article we show that if subjects are assumed to be homogeneous within a finite set of latent classes the basic restrictions of the rasch model conditional independence and unidimensionality can be relaxed in a flexible way by simply adding appropriate columns to a basic design matrix when discrete covariates are available so that subjects may be classified into strata we show how a joint modeling approach can achieve greater parsimony parameter estimates may be obtained by maximizing the conditional likelihood given the total number of captures with a combined use of the em and fisher scoring algorithms we also discuss a technique for obtaining confidence intervals for the size of the population under study based on the profile likelihood

the effects of model selection on confidence intervals for the size of a closed population one encounters in the literature estimates of some rates of genetic and congenital disorders based on log linear methods to model possible interactions among sources often the analyst chooses the simplest model consistent with the data for estimation of the size of a closed population and calculates confidence intervals on the assumption that this simple model is correct however despite an apparent excellent fit of the data to such a model we note here that the resulting confidence intervals may well be misleading in that they can fail to provide an adequate coverage probability we illustrate this with a simulation for a hypothetical population based on data reported in the literature from three sources the simulated nominal 95 per cent confidence intervals contained the modelled population size only 30 per cent of the time only if external considerations justify the assumption of plausible interactions of sources would use of the simpler model s interval be justified

momentum operators with gauge potentials local quantization of magnetic flux and representation of canonical commutation relations commutation properties of two dimensional momentum operators with gauge potentials are investigated a notion of local quantization of magnetic flux is introduced to characterize physically the strong commutativity of the momentum operators in terms of the notion a necessary and sufficient condition is given for the position and the momentum operators to be equivalent to the schrodinger representation of the canonical commutation relations

gauge theory on a non simply connected domain and representations of canonical commutation relations a quantum system of a particle interacting with a non abelian gauge field on the non simply connected domain m r2 an nn 1 is considered where an n 1 n are fixed isolated points in r2 the gauge potential a of the gauge field is a p p anti hermitian matrix valued 1 form on m and may be strongly singular at the points an n 1 n if a is flat then the physical momentum and the position operators pj qj 2j 1 of the particle satisfy the canonical commutation relations ccr with two degrees of freedom on a suitable dense domain of the hilbert space l2 r2 cp a necessary and sufficient condition for this representation to be the schrodinger 2 system is given in terms of the wilson loops of the rectangles not intersecting an n 1 n this also gives a characterization for the representation to be non schrodinger it is proven that for a class of gauge potentials which is not necessarily flat pj is essentially self adjoint moreover an example which gives a class of non schrodinger repres

aharonov bohm quantum systems on a punctured 2 torus this paper deals with aharonov bohm a b quantum systems on a punctured two dimensional torus from the geometric and the operator theoretic point of view first flat connections on the u 1 bundles over the punctured 2 torus are studied which serve as vector potentials for a b effect magnetic fields it is proved that the moduli space of flat connections is identified with the n 1 dimensional torus tn 1 if the punctured torus has n 0 pinholes at which solenoids are assumed to penetrate the 2 torus for a given point of tn 1 an associated flat connection is constructed in terms of the weierstrass zeta function on c together with an inhomogeneous linear function on r2 a b quantum systems are defined in terms of position operators and momentum operators coupled with the a b potentials necessary and sufficient conditions are given for two a b quantum systems to be unitarily equivalent further the a b hamiltonian is defined and analysed from the viewpoint of operator theory the deficiency indices of the a b hamiltonian are determined to be n m n m where m is the number of solenoids whose fluxes are not quantized finally the eigenvalue problem is studied for the a b hamiltonian with all fluxes quantized to obtain eigenvalues together with eigenfunctions which are described in terms of the weierstrass sigma functions

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

an extension of fourier analysis for the n torus in the magnetic field and its application to spectral analysis of the magnetic laplacian we solved the schrodinger equation for a particle in a uniform magnetic field in the n dimensional torus we obtained a complete set of solutions for a broad class of problems the torus tn rn is defined as a quotient of the euclidean space rn by an arbitrary n dimensional lattice the lattice is not necessary either cubic or rectangular the magnetic field is also arbitrary however we restrict ourselves within potential free problems the schrodinger operator is assumed to be the laplace operator defined with the covariant derivative we defined an algebra that characterizes the symmetry of the laplacian and named it the magnetic algebra we proved that the space of functions on which the laplacian acts is an irreducible representation space of the magnetic algebra in this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus we developed a new method for fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the laplacian

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

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

on the pauli operator for the aharonov bohm effect with two solenoids we consider a spin 1 2 charged particle in the plane under the influence of two idealized aharonov bohm fluxes we show that the pauli operator as a differential operator is defined by appropriate boundary conditions at the two vortices further we explicitly construct a basis in the deficiency subspaces of the symmetric operator obtained by restricting the domain to functions with supports separated from the vortices this construction makes it possible to apply the krein s formula to the pauli operator

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

canonical commutation relations the weierstrass zeta function and infinite dimensional hilbert space representations of the quantum group uq sl2 a two dimensional quantum system of a charged particle interacting with a vector potential determined by the weierstrass zeta function is considered the position and the physical momentum operators give a representation of the canonical commutation relations with two degrees of freedom if the charge of the particle is not an integer the case corresponding to the aharonov bohm effect then the representation is inequivalent to the schrodinger representation it is shown that the inequivalent representation induces infinite dimensional hilbert space representations of the quantum group uq sl some properties of these representations of uq sl are investigated

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

likelihood inference on the underlying structure of irt models the assumptions underlying item response theory irt models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model it is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which however are necessary but not sufficient in this paper we describe how the theory for likelihood based inference under equality and inequality constraints may be used to test the underlying assumptions of irt models it turns out that the analysis based directly on the latent structure is simpler and more flexible in particular we indicate how several interesting extensions of the rasch model may be obtained by partial relaxation of the basic constraints an application to a data set provided by educational testing service is used to illustrate the approach

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

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

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

essential self adjointness for semi bounded magnetic schrodinger operators on non compact manifolds abstract we prove essential self adjointness for semi bounded below magnetic schrodinger operators on complete riemannian manifolds with a given positive smooth measure which is fixed independently of the metric some singularities of the scalar potential are allowed this is an extension of the povzner wienholtz simader theorem the proof uses the scheme of wienholtz but requires a refined invariant integration by parts technique as well as the use of a family of cut off functions which are constructed by a non trivial smoothing procedure due to karcher

canonical quantization on a doubly connected space and the aharonov bohm phase abstract we consider the canonical quantization schrodinger representation on a doubly connected space r r 2 x y x2 y2 r2 r 0 we show that when we employ 2 dimensional orthogonal coordinates ox1x2 there are uncountably many different self adjoint extensions puj of pj i xj j 1 2 and none of the pairs pj qj j j 1 2 qj xj satisfies the weyl relation then we construct a new canonical pair of canonical momentum and position operators so that the pair can satisfy the weyl relation by using the streamline coordinates as its application in the weyl relation with respect to the pair of the mv momentum and position operators by the above new canonical pair we find the aharonov bohm phase

a sample coverage approach to multiple system estimation with application to census undercount abstract the concept of sample coverage used in animal abundance estimation is modified to evaluate the undercount of a census lack of independence between the census and its postenumeration survey leads to correlation bias for the standard estimator of population size an additional recapture sample besides the census and postenumeration survey can be used to estimate the correlation bias due to two types of dependences this work expresses the correlation bias for the three sample model as a function of expected sample coverage and measures of dependence between lists a nonparametric population size estimator that incorporates the correlation bias is proposed a simulation study investigates the performance of the proposed procedure data from a 1988 dress rehearsal study for the 1990 census conducted by the u s bureau of the census are used to illustrate the proposed three system estimation procedure and to compare the resulting estimates with those given by darroch fienberg glonek and junker

spatially explicit maximum likelihood methods for capture recapture studies live trapping capture recapture studies of animal populations with fixed trap locations inevitably have a spatial component animals close to traps are more likely to be caught than those far away this is not addressed in conventional closed population estimates of abundance and without the spatial component rigorous estimates of density cannot be obtained we propose new flexible capture recapture models that use the capture locations to estimate animal locations and spatially referenced capture probability the models are likelihood based and hence allow use of akaike s information criterion or other likelihood based methods of model selection density is an explicit parameter and the evaluation of its dependence on spatial or temporal covariates is therefore straightforward additional nonspatial variation in capture probability may be modeled as in conventional capture recapture the method is tested by simulation using a model in which capture probability depends only on location relative to traps point estimators are found to be unbiased and standard error estimators almost unbiased the method is used to estimate the density of red eyed vireos vireo olivaceus from mist netting data from the patuxent research refuge maryland u s a estimates agree well with those from an existing spatially explicit method based on inverse prediction a variety of additional spatially explicit models are fitted these include models with temporal stratification behavioral response and heterogeneous animal home ranges

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

material identification of real impact sounds effects of size variation in steel glass wood and plexiglass plates identification of the material of struck objects of variable size was investigated previous studies on this issue assumed recognition to be based on acoustical measures of damping this assumption was tested comparing the power of a damping measure in explaining identification data with that of several other acoustical descriptors listeners performance was perfect with respect to gross material categories steel glass and wood plexiglass comprising materials of vastly different mechanical properties impaired performance was observed for materials within the same gross category identification being based on the size of the objects alone the damping descriptor accounted for the identification of the gross categories however other descriptors such as signal duration explained the results equally well materials within the same gross category were identified mainly on the basis of signal frequency overall poor support for the relevance of damping to material perception was found an analysis of the acoustical support for perfect material identification was carried out sufficient acoustical information for perfect performance was found thus procedural biases for the origin of the effects of size could be discarded pointing toward their cognitive rather than methodological nature identification performance was explained in terms of the regularities of the everyday acoustical environment

aharonov bohm effect with δ type interaction a quantum particle interacting with a thin solenoid and a magnetic flux is described by a five parameter family of hamilton operators obtained via the method of self adjoint extensions one of the parameters the value of the flux corresponds to the aharonov bohm effect the other four parameters correspond to the strength of a singular potential barrier the spectrum and eigenstates are computed and the scattering problem is solved

a remark concerning canonical commutation relations an elementary quantum mechanical example of canonical commutation relations not equivalent to the schrodinger representation is discussed it demonstrates that the nelson phenomenon occurs in a natural situation

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

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

representation theoretic aspects of two dimensional quantum systems in singular vector potentials canonical commutation relations quantum algebras and reduction to lattice quantum systems some representation theoretic aspects of a two dimensional quantum system of a charged particle in a vector potential a which may be singular on an infinite discrete subset d of r2 are investigated for each vector v in a set v d r2 0 the projection pv of the physical momentum operator p p a to the direction of v is defined by pv v p as an operator acting in l2 r2 where p idx idy x y r2 with dx resp dy being the generalized partial differential operator in the variable x resp y and r is a parameter denoting the charge of the particle it is proven that pv is essentially self adjoint and an explicit formula is derived for the strongly continuous one parameter unitary group eitpv t r generated by the self adjoint operator pv the closure of pv i e the magnetic translation to the direction of the vector v the magnetic translations along curves in r2 d are also considered conjugately to pv and pw w v d a self adjoint multiplication operator qv w is introduced which is a

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

operator theoretical analysis of a representation of a supersymmetry algebra in hilbert space operator theoretical analysis is made on unbounded representations in hilbert spaces of a supersymmetry susy algebra coming from a supersymmetric quantum field theory in two dimensional space time a basic idea for the analysis is to apply the theory of strongly anticommuting self adjoint operators a theorem on integrability of a representation of the susy algebra is established moreover it is shown that strong anticommutativity of self adjoint operators is a natural and suitable concept in analyzing representations of the susy algebra in hilbert space

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

auditory detection of hollowness the airborne sounds produced by freely vibrating hollow and solid bars were synthesized according to the equations of bar motion from theoretical acoustics and were presented to listeners over headphones in a two interval forced choice task listeners were asked to distinguish between the hollow and solid bar sounds as bar length was varied at random from one presentation to the next all other physical properties of the bar were held constant across trials listener decision strategies for detecting hollowness in iron aluminum and wood bars were determined from regression weights describing the relation between the listener s response and the frequency intensity and decay modulus of the individual partials comprising these sounds the obtained weights were compared to those of a hypothetical listener that bases judgments on the acoustic relations intrinsic to hollowness as determined from the equations for motion results indicate that listeners adopt roughly one of two decision strategies either basing judgments on the appropriate acoustic relations or basing judgments predominantly on frequency alone the decision strategy of some listeners also changed from one type to the other with a change in bar material or upon replication of the same condition the results are interpreted in terms of the vulnerability of the intrinsic acoustic relations to small perturbations in acoustic parameters as would be associated with listener internal noise they demonstrate that basic limits of human sensitivity can have a profound effect on the identification of rudimentary source attributes from sound even in conditions where acoustic variation is largely dictated by physical variation in the source

on population size estimators in the poisson mixture model summary estimating population sizes via capture recapture experiments has enormous applications the poisson mixture model can be adopted for those applications with a single list in which individuals appear one or more times we compare several nonparametric estimators including the chao estimator the zelterman estimator two jackknife estimators and the bootstrap estimator the target parameter of the chao estimator is a lower bound of the population size those of the other four estimators are not lower bounds and they may produce lower confidence limits for the population size with poor coverage probabilities a simulation study is reported and two examples are investigated

connecting the latent multinomial link et al 2010 biometrics 66 178 185 define a general framework for analyzing capture recapture data with potential misidentifications in this framework the observed vector of counts y is considered as a linear function of a vector of latent counts x such that y ax with x assumed to follow a multinomial distribution conditional on the model parameters bayesian methods are then applied by sampling from the joint posterior distribution of both x and in particular link et al 2010 propose a metropolis hastings algorithm to sample from the full conditional distribution of x where new proposals are generated by sequentially adding elements from a basis of the null space kernel of a we consider this algorithm and show that using elements from a simple basis for the kernel of a may not produce an irreducible markov chain instead we require a markov basis as defined by diaconis and sturmfels 1998 the annals of statistics 26 363 397 we illustrate the importance of markov bases with three capture recapture examples we prove that a specific lattice basis is a markov basis for a class of models including the original model considered by link et al 2010 and confirm that the specific basis used in their example with two sampling occasions is a markov basis the constructive nature of our proof provides an immediate method to obtain a markov basis for any model in this class

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

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

deficiency indices and singular boundary conditions in quantum mechanics we consider schrodinger operators h in l2 rn n n with countably infinitely many local singularities of the potential which are separated from each other by a positive distance it is proved that due to locality each singularity yields a separate contribution to the deficiency index of h in the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self adjoint boundary conditions

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

modified martingale estimation for recapture experiments with hetrogeneous capture probabilities summary an estimation method of lloyd yip 1991 based on martingales and the assumption of beta distributed capture probabilities is modified to improve its performance for all but highly heterogeneous populations this estimator is compared to the jackknife estimator by simulation under both beta and non beta conditions some expressions for standard error are developed but found to behave poorly for realistic sample sizes bootstrap estimates of standard error appear superior but do not lead to accurate confidence intervals because of the difficulties in bias estimation

quasi symmetric latent class models with application to rater agreement suppose we observe responses on several categorical variables having the same scale we consider latent class models for the joint classification that satisfy quasi symmetry the models apply when subject specific response distributions are such that i for a given subject responses on different variables are independent and ii odds ratios comparing marginal distributions of the variables are identical for each subject these assumptions are often reasonable in modeling multirater agreement when a sample of subjects is rated independently by different observers in this application the model parameters describe two components of agreement strength of association between classifications by pairs of observers and degree of heterogeneity among the observers marginal distributions we illustrate the models by analyzing a data set in which seven pathologists classified 118 subjects in terms of presence or absence of carcinoma yielding seven categorical classifications with the same binary scale a good fitting model has a latent classification that differentiates between subjects on whom there is agreement and subjects on whom there is disagreement

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

a class of latent markov models for capture recapture data allowing for time heterogeneity and behavior effects we propose an extension of the latent class model for the analysis of capture recapture data which allows us to take into account the effect of a capture on the behavior of a subject with respect to future captures the approach is based on the assumption that the variable indexing the latent class of a subject follows a markov chain with transition probabilities depending on the previous capture history several constraints are allowed on these transition probabilities and on the parameters of the conditional distribution of the capture configuration given the latent process we also allow for the presence of discrete explanatory variables which may affect the parameters of the latent process to estimate the resulting models we rely on the conditional maximum likelihood approach and for this aim we outline an em algorithm we also give some simple rules for point and interval estimation of the population size the approach is illustrated by applying it to two data sets concerning small mammal populations

on identifiability in capture recapture models we study the issue of identifiability of mixture models in the context of capture recapture abundance estimation for closed populations such models are used to take account of individual heterogeneity in capture probabilities but their validity was recently questioned by link 2003 biometrics 59 1123 1130 on the basis of their nonidentifiability we give a general criterion for identifiability of the mixing distribution and apply it to establish identifiability within families of mixing distributions that are commonly used in this context including finite and beta mixtures our analysis covers binomial and geometrically distributed outcomes in an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models

magnetic translation groups in an n dimensional torus and their representations a charged particle in a uniform magnetic field in a two dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry we study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions the magnetic translation group mtg is defined as a group of translations that leave the gauge field invariant we show that the mtg in an n dimensional torus is isomorphic to a central extension of a cyclic group z 1 z 2l tm by u 1 with 2l m n we construct and classify irreducible unitary representations of the mtg in a three torus and apply the representation theory to three examples we briefly describe a representation theory for a general n torus the mtg in an n torus can be regarded as a generalization of the so called noncommutative torus

point interactions in two dimensions basic properties approximations and applications to solid state physics on etudie rigoureusement l operateur de schrodinger formellement donne par h y dans l 2 r 2 et on montre comment l approcher en termes d hamiltoniens a courte portee transformes d echelles on considere des questions semblables pour l operateur h j 1 n j y j n n on etudie les proprietes spectrales du modele a un electron d un cristal a 2 dimensions avec des interactions ponctuelles

spectral and temporal cues for perception of material and action categories in impacted sound sources in two experiments similarity ratings and categorization performance with recorded impact sounds representing three material categories wood metal glass being manipulated by three different categories of action drop strike rattle were examined previous research focusing on single impact sounds suggests that temporal cues related to damping are essential for material discrimination but spectral cues are potentially more efficient for discriminating materials manipulated by different actions that include multiple impacts e g dropping rattling perceived similarity between material categories across different actions was correlated with the distribution of long term spectral energy spectral centroid similarity between action categories was described by the temporal distribution of envelope energy temporal centroid or by the density of impacts moreover perceptual similarity correlated with the pattern of confusion in categorization judgments listeners tended to confuse materials with similar spectral centroids and actions with similar temporal centroids and onset densities to confirm the influence of these different features spectral cues were removed by applying the envelopes of the original sounds to a broadband noise carrier without spectral cues listeners retained sensitivity to action categories but not to material categories conversely listeners recognized material but not action categories after envelope scrambling that preserved long term spectral content

an analysis of categorical repeated measurements in the presence of an external factor summary this paper provides a log linear method for the analysis of contingency tables where the population of individuals is divided into distinct subpopulations and where repeated measurements are made on each individual the proposed model for the full joint probabilities is quasi symmetry within each subpopulation the model is derived from one of two within individual models the method by which the hypotheses that flow from the model are tested is an extension of the test of marginal symmetry achieved by testing complete symmetry conditional on quasi symmetry

auditory discrimination of material changes in a struck clamped bar the principles of theoretical acoustics were applied to approximately reconstruct the sound pressure waveform at the ear as would be generated by an idealized struck clamped bar the result is an inharmonic sum of damped sinusoids whose individual acoustic parameters frequency intensity and decay modulus are for a fixed geometry and fixed driving force uniquely determined by the material composition of the bar in the standard 2ifc procedure listeners were asked to discriminate changes in material composition based on their perception of the acoustic waveform listener strategies for discriminating such changes were estimated by perturbing slightly the individual acoustic parameters from trial to trial and computing correlations with the listener s response cf r a lutfi and e oh j acoust soc am 95 2963 a 1994 in general the correlations reveal that listeners fail to make optimal use of the information in the acoustic waveform by tending to give undue weight for a given material change to changes in component frequency in some case the accompanying reduction in performance efficiency amounted to 80

low risk population size estimates in the presence of capture heterogeneity summary population estimation methods are used for estimating the size of a population from samples of individuals in many applications the probability of being observed in the sample varies across individuals resulting in sampling bias we show that in this setting estimators of the population size have high and sometimes infinite risk leading to large uncertainty in the population size as an alternative we propose estimating the population of individuals with observation probability exceeding a small threshold we show that estimators of this quantity have lower risk than estimators of the total population size the proposed approach is shown empirically to result in large reductions in mean squared error in a common model for capture recapture population estimation with heterogeneous capture probabilities

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

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

estimating population size for capture recapture data when capture probabilities vary by time and individual animal there have been no estimators of population size associated with the capture recapture model when the capture probabilities vary by time and individual animal this work proposes a nonparametric estimation technique that is appropriate for such a model using the idea of sample coverage which is defined as the proportion of the total individual capture probabilities of the captured animals a simulation study was carried out to show the performance of the proposed estimation procedure numerical results indicate that it generally works satisfactorily when the coefficient of variation of the individual capture probabilities is relatively large an example is also given for illustration

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

the performance of mixture models in heterogeneous closed population capture recapture summarydorazio and royle 2003 biometrics59 351 364 investigated the behavior of three mixture models for closed population capture recapture analysis in the presence of individual heterogeneity of capture probability their simulations were from the beta binomial distribution with analyses from the beta binomial the logit normal and the finite mixture latent class models in this response simulations from many different distributions give a broader picture of the relative value of the beta binomial and the finite mixture models and provide some preliminary insights into the situations in which these models are useful

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

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