operads and knot spaces let em denote the space of embeddings of the interval i 1 1 in the cube im with endpoints and tangent vectors at those endpoints fixed on opposite faces of the cube equipped with a homotopy through immersions to the unknot see definition 5 1 by proposition 5 17 em is homotopy equivalent to emb i im x i lmm l im in 28 mcclure and smith define a cosimplicial object o associated to an operad with multiplication 0 whose homotopy invariant totalization we denote tot see definition 2 17 and definition 2 5 below let cm denote the rath kontsevich operad introduced in 22 whose entries are compactified configuration spaces and which is weakly equivalent to the little ra disks operad 37 see definition 4 1 and theorem 4 5

a metric for performance evaluation of multi target tracking algorithms performance evaluation of multi target tracking algorithms is of great practical importance in the design parameter optimization and comparison of tracking systems the goal of performance evaluation is to measure the distance between two sets of tracks the ground truth tracks and the set of estimated tracks this paper proposes a mathematically rigorous metric for this purpose the basis of the proposed distance measure is the recently formulated consistent metric for performance evaluation of multi target filters referred to as the ospa metric multi target filters sequentially estimate the number of targets and their position in the state space the ospa metric is therefore defined on the space of finite sets of vectors the distinction between filtering and tracking is that tracking algorithms output tracks and a track represents a labeled temporal sequence of state estimates associated with the same target the metric proposed in this paper is therefore defined on the space of finite sets of tracks and incorporates the labeling error numerical examples demonstrate that the proposed metric behaves in a manner consistent with our expectations

facilitating the gibbs sampler the gibbs stopper and the griddy gibbs sampler abstract the article briefly reviews the history literature and form of the gibbs sampler an importance sampling device is proposed for converting the output of the gibbs sampler to a sample from the exact posterior this gibbs stopper technique is also useful for assessing convergence of the gibbs sampler for moderate sized problems also presented is an approach for implementing the gibbs sampler in nonconjugate situations the basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation questions relating to the number of nodes in the approximation gap size between successive nodes and the treatment of unbounded intervals for a given conditional are discussed the methodology is illustrated using a genetic linkage model a nonlinear regression model and the cox model

convergence of the homology spectral sequence of a cosimplicial space we produce new convergence conditions for the homology spectral sequence of a cosimplicial space by requiring that each codegree of the cosimplicial space has finite type mod p homology specifically we find conditions which ensure strong convergence if and only if the total space has p good components we also find exotic convergence conditions for cosimplicial spaces not covered by the strong convergence conditions these results give new convergence conditions for example for the eilenberg moore spectral sequence and for mapping spaces

a consistent metric for performance evaluation of multi object filters the concept of a miss distance or error between a reference quantity and its estimated controlled value plays a fundamental role in any filtering control problem yet there is no satisfactory notion of a miss distance in the well established field of multi object filtering in this paper we outline the inconsistencies of existing metrics in the context of multi object miss distances for performance evaluation we then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi object performance evaluation metrics

statistical estimation of the parameters of a moving source from array data on propose une methode d estimation des parametres d un modele de retard temporel lineaire la methode compare les transformees de fourier a differentes frequences

on line bayesian estimation of signals in symmetric spl alpha stable noise in this paper we describe on line bayesian filtering methods for time series models with heavy tailed spl alpha stable noise the filtering methodology is based on a scale mixtures of normals smin representation of the spl alpha stable distribution which reexpresses the intractable stable distribution in a conditionally gaussian form we describe how the method can be used for estimation of time varying autoregressive signals buried in symmetric spl alpha stable noise efficiently implemented using an adaptation to an existing rao blackwellized particle filter the methodology is shown to work well with both simulated and real corrupted audio data for which the spl alpha stable noise distribution is found to fit the noise data better than other more standard heavy tailed distributions

the eckmann hilton argument and higher operads abstract the classical eckmann hilton argument shows that two monoid structures on a set such that one is a homomorphism for the other coincide and moreover the resulting monoid is commutative this argument immediately gives a proof of the commutativity of the higher homotopy groups a reformulation of this argument in the language of higher categories is suppose we have a one object one arrow 2 category then its hom set is a commutative monoid a similar argument due to a joyal and r street shows that a one object one arrow tricategory is the same as a braided monoidal category in this paper we begin to investigate how one can extend this argument to arbitrary dimension we provide a simple categorical scheme which allows us to formalise the eckmann hilton type argument in terms of the calculation of left kan extensions in an appropriate 2 category then we apply this scheme to the case of n operads in the author s sense and classical symmetric operads we demonstrate that there exists a functor of symmetrisation sym n from a certain subcategory of n operads to the category of symmetric operads such that the category of one object one arrow one n 1 arrow algebras of a is isomorphic to the category of algebras of sym n a under some mild conditions we present an explicit formula for sym n a which involves taking the colimit over a remarkable categorical symmetric operad we will consider some applications of the methods developed to the theory of n fold loop spaces in the second paper of this series

batalin vilkovisky algebras and two dimensional topological field theories by a batalin vilkovisky algebra we mean a graded commutative algebraa together with an operator a a 1 such that 2 0 and a a is a graded derivation ofa for alla a in this article we show that there is a natural structure of a batalin vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions we make use of a technique from algebraic topology the theory of operads

on the deformation complex of homotopy affine actions abstract an affine action of an associative algebra a on a vector space v is an algebra morphism a v end v where v is a vector space and v end v is the algebra of affine transformations of v the one dimensional version of the swiss cheese operad denoted sc 1 is the operad whose algebras are affine actions of associative algebras this operad is koszul and admits a minimal model denoted by sc 1 algebras over this minimal model are called homotopy affine actions they consist of an a morphism a v end v where a is an a algebra in this paper we prove a relative version of deligne s conjecture in other words we show that the deformation complex of a homotopy affine action has the structure of an algebra over an sc 2 operad that structure is naturally compatible with the e 2 structure on the deformation complex of the a algebra

a goodness of fit approach to testing mean residual times the random residual lifetime is a random variable representing the remaining life of a system of age x 0 the mean residual life at age x is the expected value of the remaining life beyond that age which is well known and extensively studied for both testing and estimation in this article a new approach is presented for testing constant versus decreasing residual life the new test is much simpler to compute asymptotically normal and performs better than previous tests in terms of power and pitman asymptotic efficiencies for several alternatives

multivariable cochain operations and little cubes this paper has two goals the first see theorem 2 15 and remark 2 16 a is to construct a small em chain operad s which acts naturally on the normalized cochains s x of a topological space x this is of interest in view of a theorem of mandell 15 page 44 which states that if 9 is any e chain operad over f the algebraic closure of the field with p elements which acts naturally on s x 0 f then the homotopy category of connected p complete nilpotent spaces of finite type

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

on some fourier methods for inference abstract common statistical procedures such as maximum likelihood and m estimation admit generalized representations in the fourier domain the fourier domain provides fertile ground for approaching a number of difficult problems in inference in particular the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain robustness features as well a numerical illustration involving the symmetric stable laws is given

optimal design and refinement of the linera model with applications to repeated measurements designs the information matrices of one design in a finer and a simpler linear model are compared to each other the orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e g by cheng and wu 1980 examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum moreover nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved if the numbers of units and periods are sufficiently large

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

a test for second order stationarity of a multivariate time series it is well known that the discrete fourier transforms dft of a second order stationary time series between two distinct fourier frequencies are asymptotically uncorrelated in contrast for a large class of second order nonstationary time series including locally stationary time series this property does not hold in this paper these starkly differing properties are used to define a global test for stationarity based on the dft of a vector time series it is shown that the test statistic under the null of stationarity asymptotically has a chi squared distribution whereas under the alternative of local stationarity asymptotically it has a noncentral chi squared distribution further if the time series is gaussian and stationary the test statistic is pivotal however in many econometric applications the assumption of gaussianity can be too strong but under weaker conditions the test statistic involves an unknown variance that is extremely difficult to directly estimate from the data to overcome this issue a scheme to estimate the unknown variance based on the stationary bootstrap is proposed the properties of the stationary bootstrap under both stationarity and nonstationarity are derived these results are used to show consistency of the bootstrap estimator under stationarity and to derive the power of the test under nonstationarity the method is illustrated with some simulations the test is also used to test for stationarity of ftse 100 and dax 30 stock indexes from january 2011 december 2012

deconvolution of multiple time series the problem of estimating simultaneously two convolved vector time series corrupted by additive noise is considered by regarding one of the series as being stochastic and the other as fixed it is shown that the fixed component can be estimated by maximizing a frequency domain approximation to the likelihood the stochastic series is estimated by using an approximation to the conditional mean evaluated at the current maximum likelihood estimators an example involving a multiple deconvolution of seismic source and receiver functions is given

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

analytic implementations of the cardinalized probability hypothesis density filter the probability hypothesis density phd recursion propagates the posterior intensity of the random finite set rfs of targets in time the cardinalized phd cphd recursion is a generalization of the phd recursion which jointly propagates the posterior intensity and the posterior cardinality distribution in general the cphd recursion is computationally intractable this paper proposes a closed form solution to the cphd recursion under linear gaussian assumptions on the target dynamics and birth process based on this solution an effective multitarget tracking algorithm is developed extensions of the proposed closed form recursion to accommodate nonlinear models are also given using linearization and unscented transform techniques the proposed cphd implementations not only sidestep the need to perform data association found in traditional methods but also dramatically improve the accuracy of individual state estimates as well as the variance of the estimated number of targets when compared to the standard phd filter our implementations only have a cubic complexity but simulations suggest favorable performance compared to the standard joint probabilistic data association jpda filter which has a nonpolynomial complexity

the bar complex of an e infinity algebra the standard reduced bar complex b a of a differential graded algebra a inherits a natural commutative algebra structure if a is a commutative algebra we address an extension of this construction in the context of e infinity algebras we prove that the bar complex of any e infinity algebra can be equipped with the structure of an e infinity algebra so that the bar construction defines a functor from e infinity algebras to e infinity algebras we prove the homotopy uniqueness of such natural e infinity structures on the bar construction we apply our construction to cochain complexes of topological spaces which are instances of e infinity algebras we prove that the n th iterated bar complexes of the cochain algebra of a space x is equivalent to the cochain complex of the n fold iterated loop space of x under reasonable connectedness completeness and finiteness assumptions on x

approximating posterior distributions by mixtures kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions resulting in revised approximations that are mixtures of standard parametric forms usually multivariate normal or t distributions adaptive refinement of such mixture approximations involves repeating this process to home in successively on the posterior in fairly low dimensional problems this provides a general and automatic method of approximating posteriors by mixtures so that marginal densities and other summaries may be easily computed

the odd origin of gerstenhaber brackets batalin vilkovisky operators and master equations using five basic principles we treat gerstenhaber lie brackets batalin vilkovisky bv operators and master equations appearing in mathematical and physical contexts in a unified way the different contexts for this are given by the different types of feynman graphs that underlie the particular situation two of the maxims we bring forth are 1 that extending to the non connected graphs gives a commutative multiplication forming a part of the bv structure and 2 that there is a universal odd twist that unifies and explains seemingly ad hoc choices of signs and is responsible for the bv operator being a differential our treatment results in uniform general theorems these allow us to prove new results and recover and connect many constructions that have appeared independently throughout the literature the more general point of view also allows us to disentangle the necessary from the circumstantial

associahedra cyclohedra and a topological solution to the a deligne conjecture abstract we give a topological solution to the a deligne conjecture using associahedra and cyclohedra to this end we construct three cw complexes whose cells are indexed by products of polytopes giving new explicit realizations of the polytopes in terms of different types of trees we are able to show that the cw complexes are cell models for the little discs the cellular chains of one complex in particular which is built out of associahedra and cyclohedra naturally act on the hochschild cochains of an a algebra yielding an explicit topological and minimal solution to the a deligne conjecture along the way we obtain new results about the cyclohedra such as new decompositions into products of cubes and simplices which can be used to realize them via a new iterated blow up construction

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

optimal cross over designs for full interaction models we consider repeated measurement designs when a residual or carry over effect may be present in at most one later period since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects we consider a model with interactions between carry over and direct treatment effects when the aim of the experiment is to study the effects of a treatment used alone we obtain universally optimal approximate designs we also propose some efficient designs with a reduced number of subjects 1 introduction in repeated measurement designs or crossover designs interference is often observed between a direct treatment effect and the treatment applied in the previous period we denote by uv the effect of treatment u when it is preceded by treatment v there are several ways to model such effects the simplest one is to assume that there is no interference in this case uv u the direct treatment effect for a parsimonious interference model we may assume that the direct and the carry over effects are additive in this case uv u v where u is the direct effect of treatment u and v is the carry over effect due to treatment v in practice this model is often unrealistic kempton ferris and david 2001 propose an interference model in which a treatment which has a large direct effect will also have a large carry over effect more precisely they assume that the carry over effect is proportional to the direct effect bailey and kunert 2006 obtain optimal designs under this model

an efficient implementation of reid s multiple hypothesis tracking algorithm and its evaluation for the purpose of visual tracking an efficient implementation of reid s multiple hypothesis tracking mht algorithm is presented in which the k best hypotheses are determined in polynomial time using an algorithm due to murly 1968 the mht algorithm is then applied to several motion sequences the mht capabilities of track initiation termination and continuation are demonstrated together with the latter s capability to provide low level support of temporary occlusion of tracks between 50 and 150 corner features are simultaneously tracked in the image plane over a sequence of up to 51 frames each corner is tracked using a simple linear kalman filter and any data association uncertainty is resolved by the mht kalman filter parameter estimation is discussed and experimental results show that the algorithm is robust to errors in the motion model an investigation of the performance of the algorithm as a function of look ahead tree depth indicates that high accuracy can be obtained for tree depths as shallow as three experimental results suggest that a real time mht solution to the motion correspondence problem is possible for certain classes of scenes

restricted canonical correlations given two random vectors y 1 and y 2 the first canonical correlation between them is defined as sup correlation y 1 y 2 e rp e rq however in many practical situations e g educational testing problems neural networks some natural restrictions on the coefficients and may arise which should be incorporated in this maximization procedure the maximum correlation subject to such constraints is referred to as the restricted canonical correlation this problem is treated here under the nonnegativity restriction on and the analysis is extended to more general form of inequality constraints and also when the restrictions are present only on some of the coefficients restricted versions of some other related measures are also discussed this includes principal component analysis and different modifications of canonical correlations anomalies with higher order correlation are also described some properties of restricted canonical correlation including its bounds are studied

a metric on the space of finite sets of trajectories for evaluation of multi target tracking algorithms in this article we propose a metric on the space of finite sets of trajectories for assessing multi target tracking algorithms in a mathematically sound way the main use of the metric is to compare estimates of trajectories from different algorithms with the ground truth of trajectories the proposed metric includes intuitive costs associated to localization error for properly detected targets missed and false targets and track switches at each time step the metric computation is based on solving a multi dimensional assignment problem we also propose a lower bound for the metric which is also a metric for sets of trajectories and is computable in polynomial time using linear programming we also extend the proposed metrics on sets of trajectories to random finite sets of trajectories

on the relation between garch and stable processes stable and garch processes have been advocated for modeling financial data the aim of this note is to compare the two processes it is shown that the unconditional distribution of variaties from a garch like process which explicity models the clustering of volatility and exhibits the fat tail property as well can be stable given suitable conditions the conditional distributions are stable as well while it is generally realized that processes with variates that have unconditional nonnormal stable densities have a high frequency of outliers it is less well known that they can exhibit the clustering phenomenon too the clustering is obtained through stable subordination with conditional scaling

a test for stationarity for irregularly spaced spatial data summary the analysis of spatial data is based on a set of assumptions which in practice need to be checked a commonly used assumption is that the spatial random field is second order stationary in the paper a test for spatial stationarity for irregularly sampled data is proposed the test is based on a transformation of the data a type of fourier transform where the correlations between the transformed data are close to 0 if the random field is second order stationary however if the random field were second order non stationary this property does not hold using this property a test for second order stationarity is constructed the test statistic is based on measuring the degree of correlation in the transformed data the asymptotic sampling properties of the test statistic are derived under both stationarity and non stationarity of the random field these results motivate a graphical tool which allows a visual representation of the non stationary features the method is illustrated with simulations and a real data example

searching for structure in curve samples abstract the shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema inflection points and so on when analyzing a sample of regression curves it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise a method is proposed for identifying typical features without relying on an a priori specified functional model for the curves the approach is based on the frequencies of occurrence of structural features as for example maxima in the curve sample along the x axis important tools are nonparametric regression and differentiation and kernel density estimation apart from a theoretical foundation the usefulness of the method is documented by application to two interesting biomedical areas growth and develop

monte carlo inference in econometric models with symmetric stable disturbances the paper develops markov chain monte carlo methods to perform exact posterior analysis in models with symmetric stable paretian disturbances it is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a gibbs sampler with metropolis independence chains the new method is shown to perform satisfactorily in constructed examples the method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution

maximum likelihood estimation of stochastic frontier models by the fourier transform the paper is concerned with several kinds of stochastic frontier models whose likelihood function is not available in closed form first with output oriented stochastic frontier models whose one sided errors have a distribution other than the standard ones exponential or half normal the gamma and beta distributions are leading examples second with input oriented stochastic frontier models which are common in theoretical discussions but not in econometric applications third with two tiered stochastic frontier models when the one sided error components follow gamma distributions fourth with latent class models with gamma distributed one sided error terms fifth with models whose two sided error component is distributed as stable paretian and the one sided error is gamma the principal aim is to propose approximations to the density of the composed error based on the inversion of the characteristic function which turns out to be manageable using the fourier transform procedures that are based on the asymptotic normal form of the log likelihood function and have arbitrary degrees of asymptotic efficiency are also proposed implemented and evaluated in connection with output oriented stochastic frontiers the new methods are illustrated using data for us commercial banks electric utilities and a sample from the national youth longitudinal survey

beta mapping and beta regression for changes of ordinal rating measurements on likert scales a comparison of the change scores among multiple treatment groups patient reported outcome and observer evaluative studies in clinical trials and post hoc analyses often use instruments that measure responses on ordinal rating or likert scales we propose a flexible distributional approach by modeling the change scores from the baseline to the end of the study using independent beta distributions the two shape parameters of the fitted beta distributions are estimated by matching moments covariates and the interaction terms are included in multivariate beta regression analyses under generalized linear mixed models these methods are illustrated on the treatment satisfaction data in an overactive bladder drug study with four treatment arms monte carlo simulations were conducted to compare the type 1 errors and statistical powers using a beta likelihood ratio test of the proposed method against its fully nonparametric or parametric alternatives

hochschild homology of structured algebras abstract we give a general method for constructing explicit and natural operations on the hochschild complex of algebras over any prop with a multiplication we think of such algebras as a algebras with extra structure as applications we obtain an integral version of the costello kontsevich soibelman moduli space action on the hochschild complex of open tcfts the tradler zeinalian and kaufmann actions of sullivan diagrams on the hochschild complex of strict frobenius algebras and give applications to string topology in characteristic zero our main tool is a generalization of the hochschild complex

a novel joint multitarget estimator for multi bernoulli models in this paper the joint multitarget jom estimator proposed for the joint target detection and tracking jott filter is reformulated for the gaussian mixture gm implementations of the multitarget multi bernoulli member filters for this purpose a mode finding algorithm is employed to search for the most significant mode of a gm density thus the maximum a posterior map estimates of bernoulli targets are determined in addition the multi bernoulli versions of the two conflicting objective functions for the pareto optimal value of the unknown jom estimation constant are derived simulations compare the performance of the proposed jom estimator with that of the marginal multitarget mam estimator in a multitarget tracking scenario where the probability of target detection is a function of target states the simulation results demonstrate that the proposed jom estimator outperforms the mam estimator under moderately low observable conditions this is because the incomplete cost function of the mam estimator is not adequate to obtain accurate cardinality estimates of targets without considering how well targets are localized nevertheless the proposed jom estimator may suffer from track termination latency more than the mam estimator due to the definition of its cost function

the cobar construction as a hopf algebra we show that the integral cobar construction c x of a 1 reduced simplicial set x has the structure of a homotopy hopf algebra this leads to a rational differential lie algebra x given by a differential d on the free lie algebra l s 1 x the universal enveloping algebra u x is naturally isomorphic to c x let x be a 1 reduced simplicial set and let s 1 x be the desuspension of the reduced chain complex x of x the cobar construction is given by a differential d on the tensor algebra t s 1 x defined over the homology of c x coincides with the homology of the loop space x a formula for d was given by adams ad we show that the cobar construction c x has over the additional natural structure of a homotopy hopf algebra consisting of a coassociative diagonal and a derivation homotopy e explicit formulas for and e are given in 2 9 the result is based on the geometric cobar construction in b using the fundamental theory of anick a we derive from the data c x e a differential lie algebra which is defined by a differential d on the free rational lie algebra l s 1 x the homology of x coincides with the rational homotopy groups of x moreover we describe a cocommutative diagonal together with a derivation homotopy h and a natural iso morphism of differential hopf algebras formulas for h and are obtained by an induction a map f x y between 1 reduced simplicial sets induces the map f l s 1 f l s 1 x l s 1 y between free lie algebras which is compatible with the differential d hence x x yields a canonical functor from 1 reduced simplicial sets to free differential lie algebras this functor induces an isomorphism of rational homotopy categories in fact is up to homotopy naturally equivalent to the functor npg of quillen q which is the composite of four intricate functors we describe in b inductively a sequence of elements 2 3 which determine the differential d and we compute the quadratic part of d a complete formula for d however is highly intricate since it can be considered as a kind of simplicial form of the classical hausdorff formula see 4 9 4 we cannot expect a simple form of the differential d since the homology of x yields the rational homotopy groups of x that is this supplements the result of kan k who gave a combinatorial description of x in terms of the free simplicial group gx hence x requires computations in free groups while the formula for x requires only the computation of the homology of a chain complex of rational vector spaces we point out that x is a chain complex of finite type if x has only finitely many non degenerate simplices hence in this case d yields a finite formula for n x such a formula was not yet achieved in the literature for example using the sullivan method one obtains x only implicitly by computing a minimal model of the de rham algebra a x see bousfield gugenheim bg here a x is defined explicitly in terms of x but is not of finite type if x has only finitely many non degenerate simplices so that a x does not give a finite formula for n x in this case the minimal model m x of a x is of finite type and hence also gives a finite formula for n x there is however no explicit formula for m x in terms of x in the literature and m x is not natural in x on the other hand also the model x of quillen is considerably larger than x above and is only defined as the normalization of a simplicial object see 4 9 4 below

a joint multitarget estimator for the joint target detection and tracking filter abstract this paper proposes a joint multitarget jom estimator for the joint target detection and tracking jott filter an efficient choice to the unknown jom estimation constant i e hypervolume around target state estimate is proposed as a pareto optimal solution to a multi objective nonlinear convex optimization problem the multi objective function is formulated as two convex objective functions in conflict the first objective function is the information theoretic part of the problem and aims for entropy maximization while the second one arises from the constraint in the definition of the jom estimator and aims to improve the accuracy of the jom estimates the pareto optimal solution is obtained using the weighted sum method where objective weights are determined as linear predictions from autoregressive models in contrast to the marginal multitarget mam estimator the target present decision from the jom estimator depends on the spatial information as well as the cardinality information in the finite set statistics fisst density the simulation results demonstrate that the jom estimator achieves better track management performance in terms of track confirmation latency and track maintenance than the mam estimator for different values of detection probability however the proposed jom estimator suffers from track termination latency more than the mam estimator since the localization performance of the jott filter does deteriorate gradually after target termination

high efficiency estimation for the positive stable laws abstract a moment method based on the sample averages of x t and x 2t with suitably chosen t is suggested for estimating the index a and scale parameter c 1 of the positive stable distribution with laplace transform e exp x exp c the corresponding cramer rao lower bounds are computed by using a new and simple fourier technique which is based on an idea of jarrett it is found that the asymptotic efficiencies of the proposed estimators exceed 97 for all values of between zero and 994 a comparison is made with the optimal asymptotic efficiencies attainable by using a different moment method based on e t 1 x and e 2 t 2 x

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

a new test for mean residual life times summary the mean residual life at age t is the expected value of the remaining life beyond that age a new u statistic is derived for testing constant versus decreasing mean residual life the new test is easier to compute and performs better for several alternatives than previous tests

a class of transformed mean residual life models with censored survival data this article features online supplementary material the mean residual life function is an attractive alternative to the survival function or the hazard function of a survival time in practice it provides the remaining life expectancy of a subject surviving up to time t in this study we propose a class of transformed mean residual life models for fitting survival data under right censoring to estimate the model parameters we make use of the inverse probability of censoring weighting approach and develop a system of estimating equations efficiency and robustness of the estimators are also studied both asymptotic and finite sample properties of the proposed estimators are established and the approach is applied to two real life datasets collected from clinical trials

the recursive form of error bounds for rfs state and observation with p_d this paper presents recursive performance bounds for dynamic estimation and tracking problems in both single and multiple target cases within the framework of finite set statistics because the targets can appear and disappear when the detection probability of a sensor is less than unity pd 1 we must determine the existence or nonexistence of the state as well as its value following the possible detection miss sequences within the framework of a random vector possible observation sets sequences are first defined based on these sequences the performance bounds can be represented by a multivariate function of some time based auxiliary elements recursive relations for all the auxiliary elements are derived rigorously for the multitarget case this recursive estimated bound can be applied without data association applications are analyzed through simulations to verify our theoretical results and show that our bounds are tighter than all other bounds for the case where detection probability pd 1

cosimplicial objects and little n cubes i in this paper we show that if a cosimplicial space has a certain kind of combinatorial structure then its total space has an action of an operad weakly equivalent to the little n cubes operad our results are also valid for cosimplicial spectra

a classification of taylor towers of functors of spaces and spectra abstract we describe new structure on the goodwillie derivatives of a functor and we show how the full taylor tower of the functor can be recovered from this structure this new structure takes the form of a coalgebra over a certain comonad which we construct and whose precise nature depends on the source and target categories of the functor in question the taylor tower can be recovered from standard cosimplicial cobar constructions on the coalgebra formed by the derivatives we get from this an equivalence between the homotopy category of polynomial functors and that of bounded coalgebras over this comonad for functors with values in the category of spectra we give a rather explicit description of the associated comonads and their coalgebras in particular for functors from based spaces to spectra we interpret this new structure as that of a divided power right module over the operad formed by the derivatives of the identity on based spaces

beyond map estimation with the track oriented multiple hypothesis tracker the track oriented multiple hypothesis tracker tomht is a popular algorithm for tracking multiple targets in a cluttered environment in tracking parlance it is known as a multi scan maximum a posteriori map estimator multi scan because it enumerates possible data associations jointly over several scans and map because it seeks the most likely data association conditioned on the observations this paper extends the tomht building on its internal representation to support probabilistic queries other than map estimation specifically by summing over the tomht s pruned space of data association hypotheses one can compute marginal probabilities of individual tracks since this summation is generally intractable any practical implementation must replace it with an approximation we introduce a factor graph representation of the tomht s data association posterior and use variational message passing to approximate track marginals in an empirical evaluation we show that marginal estimates computed through message passing compare favorably to those computed through explicit summation over the k best hypotheses especially as the number of possible hypotheses increases we also show that track marginals enable parameter estimation in the tomht via a natural extension of the expectation maximization algorithm used in single target tracking in our experiments online em updates using approximate marginals significantly increased tracker robustness to poor initial parameter specification

conditions for optimality in experimental designs abstract the purpose of this paper is to establish some results on optimal criteria in experimental designs some relationships between optimality criteria are shown in particular we extend results on the p criteria we prove the yeh biometrika 73 1986 701 conjecture that gives a necessary and sufficient condition for a design to be universally optimal we also give a similar result based on the eigenvalues of the information matrix

optimized self localization for slam in dynamic scenes using probability hypothesis density filters in many applications sensors that map the positions of objects in unknown environments are installed on dynamic platforms as measurements are relative to the observer s sensors scene mapping requires accurate knowledge of the observer state however in practice observer reports are subject to positioning errors simultaneous localization and mapping addresses the joint estimation problem of observer localization and scene mapping state of the art approaches typically use visual or optical sensors and therefore rely on static beacons in the environment to anchor the observer estimate however many applications involving sensors that are not conventionally used for simultaneous localization and mapping slam are affected by highly dynamic scenes such that the static world assumption is invalid this paper proposes a novel approach for dynamic scenes called generalized motion gem slam based on probability hypothesis density filters the proposed approach probabilistically anchors the observer state by fusing observer information inferred from the scene with reports of the observer motion this paper derives the general theoretical framework for gem slam and shows that it generalizes existing probability hypothesis density phd based slam algorithms simulations for a model specific realization using range bearing sensors and multiple moving objects highlight that gem slam achieves significant improvements over three benchmark algorithms

some statistical methods for random process data from seismology and neurophysiology examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology the problems addressed include frequency estimation for decaying cosinusoids signal estimation association measurement causal connection assessment estimation of speed and direction and structural modeling the techniques employed include complex demodulation nonlinear regression probit analysis deconvolution maximum likelihood singular value decomposition fourier analysis and averaging

a maximum likelihood approach to frequency wavenumber analysis this paper is concerned with the likelihood ratio detection and maximum likelihood estimation of plane waves traversing a small array on irregularly placed sensors a new detection statistic is proposed this statistic is related to the high resolution procedure of capon however it has a known null distribution in the case that no signal is present given that a wave is present the asymptotic distribution of the maximum likelihood estimate of the wave parameters is derived the problems of detection and estimation are distinguished they are approached via the fundamental statistical procedures of likelihood ratio testing and maximum likelihood estimation the solutions of both problems are found to be based upon the same quantity the maximum likelihood statistic the development leads to a clarification of the interrelationships and comparative properties of the conventional the least squares the high resolution and the new procedure the approach is via fourier inference

chern simons perturbation theory ii we study the perturbation theory for three dimensional chern simons quantum field theory on a general compact three manifold without boundary we show that after a simple change of variables the action obtained by brs gauge fixing in the lorentz gauge has a superspace formulation the basic properties of the propagator and the feynman rules are written in a precise manner in the language of differential forms using the explicit description of the propagator singularities we prove that the theory is finite finally the anomalous metric dependence of the 2 loop partition function on the riemannian metric which was introduced to define the gauge fixing can be cancelled by a local counterterm as in the 1 loop case in fact the counterterm is equal to the chern simons action of the metric connection normalized precisely as one would expect based on the framing dependence of witten s exact solution invited talk at the xxth conference on differential geometric methods in physics new york june 1991

bayes regression with autoregressive errors a gibbs sampling approach abstract this paper develops a practical framework for the bayesian analysis of gaussian and student t regression models with autocorrelated errors as is customary in classical estimation procedures the posteriors are conditioned on the initial observations recourse is taken to the method of gibbs sampling an iterative markovian sampling method and it is shown that the proposed approach can readily deal with high order autoregressive processes without requiring an importance sampling function or other tuning constants several examples including one with ar 4 errors are used to illustrate the ideas

conditions for universal optimality of block designs summary kiefer 1975 introduced the criterion of universal optimality and provided a sufficient condition for a design being universally optimal the condition requires maximum trace and complete symmetry from the information matrix of a design in many instances this condition cannot be achieved in this paper kiefer s condition is generalized and applications are found in the justification of universal optimality over the class of binary block designs

modules and morita theorem for operads associative rings a b are called morita equivalent when the categories of left modules over them are equivalent we call two classical linear operads p q morita equivalent if the categories of algebras over them are equivalent we transport a part of morita theory to the operadic context by studying modules over operads as an application of this philosophy we consider an operadic version of the sheaf of linear differential operators on a super manifold m and give a comparison theorem between algebras over this sheaf on m and m red

bayesian sequential track formation this paper presents a theoretical framework for track building in multiple target scenarios from the bayesian point of view it is assumed that the number of targets is fixed and known we propose two optimal methods for building tracks sequentially the first one uses the labelling of the current multitarget state estimate that minimizes the mean square labeled optimal subpattern assignment error this method requires knowledge of the posterior density of the vector valued state the second assigns the labeling that maximizes the probability that the current multi target state estimate is optimally linked with the available tracks at the previous time step in this case we only require knowledge of the random finite set posterior density without labels

on firing rate estimation for dependent interspike intervals if interspike intervals are dependent the instantaneous firing rate does not catch important features of spike trains in this case the conditional instantaneous rate plays the role of the instantaneous firing rate for the case of samples of independent interspike intervals if the conditional distribution of the interspikes intervals isis is unknown it becomes difficult to evaluate the conditional firing rate we propose a nonparametric estimator for the conditional instantaneous firing rate for markov stationary and ergodic isis an algorithm to check the reliability of the proposed estimator is introduced and its consistency properties are proved the method is applied to data obtained from a stochastic two compartment model and to in vitro experimental data

testing for self excitation in jumps this paper extends the notion of self excitation in jumps to a rich class of continuous time semimartingale models proposes statistical tests to detect its presence in a discretely observed sample path at high frequency and derives the tests asymptotic properties our statistical setting is semiparametric except for necessary parametric assumptions on the jump size measure the other components of the semimartingale model are left essentially unrestricted we analyze the finite sample performance of our tests in monte carlo simulations

bayesian inference for stable distributions abstract very little work on stable distribution parameter estimation and inference appears in the literature due to the nonexistence of the probability density function this has led in particular to a dearth of bayesian work in this area but bayesian computation via markov chain monte carlo allows us to sample from the distribution of the parameters of the stable distributions by exploiting a particular mathematical representation involving the stable density

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

the gaussian mixture probability hypothesis density filter a new recursive algorithm is proposed for jointly estimating the time varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty detection uncertainty noise and false alarms the approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density phd recursion to propagate the posterior intensity which is a first order statistic of the random finite set of targets in time at present there is no closed form solution to the phd recursion this paper shows that under linear gaussian assumptions on the target dynamics and birth process the posterior intensity at any time step is a gaussian mixture more importantly closed form recursions for propagating the means covariances and weights of the constituent gaussian components of the posterior intensity are derived the proposed algorithm combines these recursions with a strategy for managing the number of gaussian components to increase efficiency this algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented kalman filters

nonasymptotic gaussian approximation for inference with stable noise the results of a series of theoretical studies are reported examining the convergence rate for different approximate representations of alpha stable distributions although they play a key role in modelling random processes with jumps and discontinuities the use of alpha stable distributions in inference often leads to analytically intractable problems the lepage series which is a probabilistic representation employed in this work is used to transform an intractable infinite dimensional inference problem into a finite dimensional conditionally gaussian parametric problem a major component of our approach is the approximation of the tail of this series by a gaussian random variable standard statistical techniques such as expectation maximization em markov chain monte carlo and particle filtering can then be readily applied in addition to the asymptotic normality of the tail of this series we establish explicit nonasymptotic bounds on the approximation error their proofs follow classical fourier analytic arguments using esseen s smoothing lemma specifically we consider the distance between the distributions of i the tail of the series and an appropriate gaussian ii the full series and the truncated series and iii the full series and the truncated series with an added gaussian term in all three cases sharp bounds are established and the theoretical results are compared with the actual distances computed numerically in specific examples of symmetric alpha stable distributions this analysis facilitates the selection of appropriate truncations in practice and offers theoretical guarantees for the accuracy of resulting estimates one of the main conclusions obtained is that for the purposes of inference the use of a truncated series together with an approximately gaussian error term has superior statistical properties and is likely a preferable choice in practice

on the self linking of knots this note describes a subcomplex f of the de rham complex of parametrized knot space which is combinatorial over a number of universal anomaly integrals the self linking integrals of guadaguini martellini and mintchev perturbative aspects of chern simons field theory phys lett b 227 111 1989 and bar natan perturbative aspects of the chern simons topological quantum field theory ph d thesis princeton university 1991 also on the vassiliev knot invariants to appear in topology are seen to represent the first nontrivial element in h0 f occurring at level 4 and are anomaly free however already at the next level an anomalous term is possible

optimal repeated measurement designs for a model with partial interactions we consider crossover designs for a model with partial interactions in this model the carryover effect depends on whether the treatment is preceded by itself or not when the aim of the experiment is to study the total effects corresponding to a single treatment we obtain approximate optimal symmetric designs within the competing class of circular designs by generalizing the method introduced by kushner 1997 and kunert martin 2000 this generalization places the method proposed by bailey druilhet 2004 into kushner s context the optimal designs obtained are not binary as in kunert martin 2000 we also propose efficient designs generated by only one sequence

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea