estimating a state space model from point process observations a widely used signal processing paradigm is the state space model the state space model is defined by two equations an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit latent stimulus we develop an algorithm to estimate a state space model observed through point process measurements we represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus given the latent process neural spiking activity is characterized as a general point process defined by its conditional intensity function we develop an approximate expectation maximization em algorithm to estimate the unobservable state space process its parameters and the parameters of the point process the em algorithm combines a point process recursive nonlinear filter algorithm the fixed interval smoothing algorithm and the state space covariance algorithm to compute the complete data log likelihood efficiently we use a kolmogorov smirnov test based on the time rescaling theorem to evaluate agreement between the model and point process data we illustrate the model with two simulated data examples an ensemble of poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local bernoulli process

performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

dynamic stochastic models for time dependent ordered paired comparison systems abstract when paired comparisons are made sequentially over time as for example in chess competitions it is natural to assume that the underlying abilities do change with time previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities the parameters that determine the functions have to be specified a priori and are based on rational reasoning we suggest an alternative scheme for keeping track with the underlying abilities our approach is based on two components a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time the response model is a very general paired comparison model allowing for ties and ordered responses the transition model incorporates random walk models and local linear trend models taken together these two components form a non gaussian state space model based on recent results rec

orthogonal weight perturbation algorithms in partially adaptive arrays single port adaptive algorithms have been proposed to circumvent the need to implement a separate receiver for each adaptive element in an adpative antenna in this paper transient and steady state performance of a bounded single port perturbation algorithm is obtained and compared with that of the least mean square lms algorithm results are developed both with and without a hardlimiter on one input to the correlator techniques for adaptively changing both the algorithm step size and perturbation amplitude are given simulation results are presented and compared with theoretical results

a new extrapolation algorithm for band limited signals using the regularization method the ill posedness of the extrapolation problem in the presence of noise is considered a stable algorithm is constructed by solving a fredholm equation based on a regularization method the algorithm appears relatively robust since the noise eta sub delta t is taken as a function in l sup 2 t t t 0 such that the error energy integral mod eta sub delta t mod sup 2 dt

automatic smoothing of regression functions in generalized linear models abstract we consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models nelder and wedderburn 1972 and present a generalized cross validation procedure for empirically assessing an appropriate amount of smoothing in these estimates asymptotic arguments and numerical simulations are used to show that the generalized cross validatory procedure preforms well from the point of view of a weighted mean squared error criterion the methodology adds to the battery of graphical tools for model building and checking within the generalized linear model framework included are two examples motivated by medical and horticultural applications

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

tracking of time varying mobile radio channels 1 the wiener lms algorithm adaptation algorithms with constant gains are designed for tracking smoothly time varying parameters of linear regression models in particular channel models occurring in mobile radio communications in a companion paper an application to channel tracking in the is 136 tdma system is discussed the proposed algorithms are based on two key concepts first the design is transformed into a wiener filtering problem second the parameters are modeled as correlated arima processes with known dynamics this leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information the algorithms can be realized as wiener filters called learning filters or as lms newton updates complemented by filters that provide predictions or smoothing estimates the simplest algorithm named the wiener lms is presented all parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known the computational complexity is of the same order of magnitude as that of lms for regressors which are either white or have autoregressive statistics the tracking performance is however substantially improved

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

microstatistic lms filtering adaptive microstatistic filters are developed for applications in which the second order statistics of the thresholded signals are not known or may be nonstationary a multilevel threshold decomposition such that real valued stochastic processes can be filtered is used and the computational complexity of the algorithm can be arbitrarily specified by the designer the adaptation uses the least mean squares error approach of the least mean square lms algorithm the convergence of the adaptive algorithm is proved due to the nonhomogeneous statistical characteristic of the threshold signals a different step size adaptation parameter can be assigned to each threshold level simple design guidelines are developed for finding the set of nonhomogeneous step sizes which in practice yield better convergence characteristics

a variable step size lms algorithm a least mean square lms adaptive filter with a variable step size is introduced the step size increases or decreases as the mean square error increases or decreases allowing the adaptive filter to track changes in the system as well as produce a small steady state error the convergence and steady state behavior of the algorithm are analyzed the results reduce to well known results when specialized to the constant step size case simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual lms algorithm and another variable step size algorithm they show that its performance compares favorably with these existing algorithms

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

convergence analysis of adaptive linear estimation for dependent stationary processes the convergence properties of an adaptive linear mean square estimator that uses a modified lms algorithm are established for generally dependent processes bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated it is shown that the mean square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation the present findings extend earlier results in the literature obtained for independent and m dependent input data

a continuum of paired comparisons models summary an approach to building models for paired comparisons experiments based on com parisons of gamma random variables is considered the probability that one object is preferred to a second object is taken to be the probability that one gamma random variable with shape parameter r is less than a second independent gamma random variable with the same shape parameter but a different scale parameter this is motivated by considering a point scoring competition as the basis for each paired comparison different values of r provide different paired comparisons models including the bradley terry model having r equal to one and the thurstone mosteller model achieved as r tends to infinity applications of the models to data sets are discussed the most common analysis of paired comparisons experiments associates a parameter with each object in the experiment such that the probability that one object is preferred to a second object is a function of the difference between the associated parameters this linear model approach is described in detail by david 1988 some nonparametric techniques are discussed by kendall babington smith 1939 remage thompson 1966 and gokhale beaver and sirotnick 1983 a bibliography of the paired com parisons literature is given by davidson farquhar 1976 the present paper considers a subset of the linear models which are obtained from a physical model of the comparison procedure we suppose that the outcome of a paired comparison is determined by comparing the waiting time for r events to occur in each of the two processes being compared gamma random variables are used to describe these waiting times the resulting models include the bradley terry bradley terry 1952 and thurstone mosteller thurstone 1927 mosteller 1951 linear models the following section provides a motivation for models based on gamma random variables an independent increments gamma process extends the range of applicable models by permitting noninteger as well as integer values of r the models which are developed for particular values of r are described in 3 relationships with currently used methodologies are described wherever possible section 4 describes inference under the gamma model including estimation procedures and goodness of fit measures the gamma approach is applied to several paired comparisons data sets in 5

on extended j j lossless factorization abstract the extended j j lossless factorization for discrete time rational matrix functions with zeros on the unit circle is considered a necessary and sufficient condition for the existence of the extended j j lossless factorization is obtained the condition is given in terms of the original system parameters in the form of a generalized eigenvalue problem and a discrete time algebraic riccati equation state space representations for the extended j j lossless factorization are provided

performance analysis of the deficient length lms adaptive algorithm in almost all analyzes of the least mean square lms finite impulse response fir adaptive algorithm it is assumed that the length of the adaptive filter is equal to that of the unknown system impulse response however in many practical situations a deficient length adaptive filter whose length is less than that of the unknown system is employed and analysis results for the sufficient length lms algorithm are not necessarily applicable to the deficient length case therefore there is an essential need to accurately quantify the behavior of the lms algorithm for realistic situations where the length of the adaptive filter is deficient in this paper we present a performance analysis for the deficient length lms adaptive algorithm for correlated gaussian input data and using the common independence assumption exact expressions that completely characterize the transient and steady state mean square performances of the algorithm are developed which lead to new insights into the statistical behavior of the deficient length lms algorithm simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm

recursive nonlinear system identification by a stochastic gradient algorithm stability performance and model nonlinearity considerations a parameter estimation problem in a class of nonlinear systems is considered where the input output relation of a nonlinear system is approximated by a polynomial model e g a volterra series a least mean squares lms type algorithm is utilized for the recursive estimation of the polynomial coefficients and its resulting mean square error mse convergence properties are investigated conditions for the algorithm stability in the mean square sense are established steady state mse bounds are obtained and the convergence rate is discussed in addition modeling accuracy versus steady state performance is examined it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance that is yielding a larger steady state mse linear system identification is studied as a special case

constrained adaptive filtering algorithms asymptotic convergence properties for dependent data the convergence properties of constrained adaptive filtering algorithms are established the constraint is in the form of a bounded set in which the filter s coefficients must lie a recursive procedure that converges to the deterministic solution of the constrained linear mean square estimation problem is obtained using an appropriate contraction mapping the recursion is used to derive the adaptive algorithm for the filter coefficients bounds on the mean square error of the coefficients bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated the algorithms use a moving window of size n on the data from one adaptation step to the next however tighter bounds can be obtained when a skipped sampling mechanism is used

a robust variable step size lms type algorithm analysis and simulations a number of time varying step size algorithms have been proposed to enhance the performance of the conventional lms algorithm experimentation with these algorithms indicates that their performance is highly sensitive to the noise disturbance this paper presents a robust variable step size lms type algorithm providing fast convergence at early stages of adaptation while ensuring small final misadjustment the performance of the algorithm is not affected by existing uncorrelated noise disturbances an approximate analysis of convergence and steady state performance for zero mean stationary gaussian inputs and for nonstationary optimal weight vector is provided simulation results comparing the proposed algorithm to current variable step size algorithms clearly indicate its superior performance for cases of stationary environments for nonstationary environments our algorithm performs as well as other variable step size algorithms in providing performance equivalent to that of the regular lms algorithm