a dynamic approach to the statistical analysis of point processes summary an approach to the analysis of point processes based on sequential analysis of successive intervals assuming a piecewise constant intensity rate is presented bayesian inference for processes with explanatory variables is derived in terms of on line estimation filtering and prediction limiting equations for the time continuous intensity rate are obtained and solved for the no covariates case examples are provided and the approach is applied in a numerical example similar approaches include the work of koch spreij 1983 and snyder 1975 6 which also use a dynamic model with a system equation these approaches based on filtering theory for time continuous processes provide good probabilistic descriptions their main problem is the difficulty in applying the results in the presence of covariates even in simple problems the purpose of this paper is to provide tractable yet reasonable solutions to the inference problem of point processes with explanatory variables azzalini 1982 warns about the complications of exact calculations required by filtering theory even in the absence of covariates the approach is based on and to some extent generalizes work on survival data gamerman 1991 inference is considered in terms of on line and smoothed or filtered estimation of model parameters and prediction of future occurrences based on past information in 2 the model is stated and inference procedures derived in 3 the model with no covariates is considered in detail and limiting equations for any continuous rate

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

lower bounds for generalized eigenvalues of the quasilinear systems abstract in this paper we establish several new lyapunov type inequalities for two classes of one dimensional quasilinear elliptic systems of resonant type which generalize or improve all related existing ones then we use the lyapunov type inequalities obtained in this paper to derive a better lower bound for the generalized eigenvalues of the one dimensional quasilinear elliptic system with the dirichlet boundary conditions

particle filters for state space models with the presence of unknown static parameters particle filters for dynamic state space models handling unknown static parameters are discussed the approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered such a marginalization can always be applied however real time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low dimensional sufficient statistics such sufficient statistics are present in many of the commonly used state space models marginalizing the static parameters avoids the problem of impoverishment which typically occurs when static parameters are included as part of the state vector the filters are tested on several different models with promising results

generalized autoregressive moving average models a class of generalized autoregressive moving average garma models is developed that extends the univariate gaussian arma time series model to a flexible observation driven model for non gaussian time series data the dependent variable is assumed to have a conditional exponential family distribution given the past history of the process the model estimation is carried out using an iteratively reweighted least squares algorithm properties of the model including stationarity and marginal moments are either derived explicitly or investigated using monte carlo simulation the relationship of the garma model to other models is shown including the autoregressive models of zeger and qaqish the moving average models of li and the reparameterized generalized autoregressive conditional heteroscedastic garch model providing the formula for its fourth marginal moment not previously derived the model is demonstrated by the application of the garma model with a negative binomial conditional distribution to

stability criteria for linear periodic impulsive hamiltonian systems in this paper we obtain stability criteria for linear periodic impulsive hamiltonian systems a lyapunov type inequality is established our results improve also the ones previously obtained for systems without impulse effect

theory and methods abstract a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

robust locally optimal filters kalman and bayesian estimation theory this paper presents a unified approach to local optimality robustness and bayesian estimation theory concepts in deriving kalman filtering equations in the case of non gaussian observation noise in most of these derivations an approximation criterion proposed by masreliez is used the prediction error density is approximately gaussian it is shown that locally optimal kalman filters are equivalent to one step map iterative procedures the introduction of nonlinear iterative techniques adds a new dimension to the analysis of recursive non gaussian estimation moreover to estimate the parameters of the kalman model a direct solution of map equations is obtained through an m interval piecewise linear approximation mipla of the locally optimal nonlinearity score function robustness is achieved by proper modification and approximation of the score function finally the performance of the filters in question are tested under intensive monte carlo simulations satisfactory results are obtained even in the case of extremely impulsive observation noise cauchy contaminated gaussian

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

lyapunov type inequalities for second order half linear differential equations in this paper we establish some new lyapunov type inequalities for second order half linear differential equations which almost generalize and extend all related existing results in the literature

a neural net model for prediction abstract in this article we introduce a neural net designed for nonlinear statistical prediction the net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions a bayesian inferential procedure for this model based on the kalman filter is derived the resulting learning algorithm generalizes the so called onedimensional newton method an updating algorithm currently popular in the neural net literature a numerical study concerning the prediction of a noisy chaotic time series is presented and the greater predictive accuracy of the new algorithm with respect to the newton algorithm is exhibited

prediction rules for exponential family state space models summary we state and prove a simple and general expression for the marginal mean in an exponential family state space model with conjugate state density we then discuss implications of this result on the choice of parameterization of the observation density on the interpretation of the predictive density for steady models and on exponentially weighted moving average and trend free forecasting

bandwidth enhancement inverse q filtering or time varying wiener deconvolution abstractdispersion and attenuation corrections can improve the resolution of seismic data this significantly facilitates interpretation in principle inverse q filtering and the time varying wiener deconvolution can achieve this inverse q filtering is a deterministic process that requires knowledge of the quality factor q whereas the time varying wiener deconvolution is a statistical approach based on the estimation of the nonstationary propagating wavelet dispersion corrections based on phase only inverse q filtering is an inherently stable method that is robust in the presence of noise attenuation corrections via amplitude only inverse q filtering on the other hand is likely to lead to noise amplification as well as bandwidth enhancement dispersion corrections via the time varying wiener deconvolution are challenging because these require estimation of a nonstationary frequency dependent nonminimum phase wavelet fortunately attenuation corrections via the wiener deconvolution need only esti

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

mixture based extension of the ar model and its recursive bayesian identification an extension of the autoregressive ar model is studied which allows transformations and distortions on the regressor to be handled many important signal processing problems are amenable to this extended ar i e ear model it is shown that bayesian identification and prediction of the ear model can be performed recursively in common with the ar model itself the ear model does however require that the transformation be known when it is unknown the associated transformation space is represented by a finite set of candidates what follows is a mixture based ear model i e the mear model an approximate identification algorithm for mear is developed using a restricted variational bayes vb method this restores the elegant recursive update of sufficient statistics the mear model is applied to the robust identification of ar processes corrupted by outliers and burst noise respectively and to click removal for speech

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

prior elicitation variable selection and bayesian computation for logistic regression models summary bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models specifying a prior distribution on the model space and computations we address these three issues for the logistic regression model for the first we propose an informative prior distribution for variable selection several theoretical and computational properties of the prior are derived and illustrated with several examples for the second we propose a method for specifying an informative prior on the model space and for the third we propose novel methods for computing the marginal distribution of the data the new computational algorithms only require gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models several properties of the algorithms are also derived the prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction yo for the response vector and a quantity ao quantifying the uncertainty in yo then yo and ao are used to specify a prior for the regression coefficients semi automatically examples using real data are given to demonstrate the methodology

robust recursive estimation in the presence of heavy tailed observation noise a first order approximation is derived for the conditional prior distribution of the state of a discrete time stochastic linear dynamic system in the presence of contaminated normal observation noise this distribution is then used to derive a first order approximation of the conditional mean minimum variance estimator if the observation noise distribution can be represented as a member of the e contaminated normal neighborhood then the conditional prior is also to first order an analogous perturbation from a normal distribution whose first two moments are given by the kalman filter moreover the perturbation is itself of a special form combining distributions whose parameters are given by banks of parallel kalman filters and optimal smoothers

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

lyapunov type inequalities for a certain class of nonlinear systems in this paper we state and prove some new lyapunov type inequalities for a class of nonlinear systems special cases of which contain the well known hamiltonian system emden fowler half linear and linear differential equations of second order our results improve and generalize these types of inequalities related to all existing ones

forecasting turning points in international output growth rates using bayesian exponentially weighted autoregression time varying parameter and pooling techniques abstract in this paper two variants of an autoregressive leading indicator arli model are employed to forecast turning points in the growth rates of 18 countries annual real output for the years 1974 1986 bayesian predictive densities have been employed to compute probabilities of downturns and upturns and they have been employed in a bayesian decision theoretic framework to obtain optimal turning point forecasts various versions of the arli model with and without pooling of data across countries produced about 70 to 80 percent correct forecasts for 158 turning points time varying parameter models performed slightly better than others the performance of the arli models in forecasting turning points is shown to be considerably better than that of four naive methods of forecasting turning points

robust sequential approximate bayesian estimation summary an approximation to the sequential updating of the distribution of location parameters of a linear time series model is developed for non normal observations the behaviour of the resulting non linear recursive filtering algorithm is examined and shown to have certain desirable properties for a variety of non normal error distributions illustrative examples are given and relationships with previous work on robustness and sequential estimation are mentioned we consider here the problem of sequential estimation of the location vector of a linear time series model termed the dynamic linear model by harrison and stevens 1976 the straightforward exact analysis obtained by assuming normal error and prior structure is generally lost when alternative error distributions are adopted and yet considerations of realism or robustness may strongly suggest such non normal assumptions the multi state model of harrison and stevens provides an approximate analysis based on a discrete variance mixture of normal distributions an approach which has been extensively investigated in the engineering literature under the name of gaussian sum approximations see for example alspach and sorenson 1971 our aim in this paper is to provide an approximate tractible recursive updating procedure for the location parameters which is applicable to a wide range of symmetric unimodal error distributions and is both more realistic and more elegant than the discrete gaussian sum approach in particular for heavy tailed distributions our procedures provide approximate bayesian methods for time series analysis which extend considerably the work of masreliez and martin 1977 and have close connections with classical robustness ideas such as m estimation and influence functions

a non gaussian state space model and application to prediction of records on developpe une classe de modeles qui generalisent le travail de smith 1979 et bathes 1975 pour des donnees censurees

filtering and smoothing via estimating functions abstract we consider the problem of filtering and smoothing in state space models which include nonlinear and non gaussian models we do not make any distributional assumptions about the processes involved our approach to these problems is based on the theory of estimating functions filter and smoother are obtained as solutions of estimating equations that are optimal in appropriate classes we illustrate our procedures by simulation studies of a model where the observational variance depends on the state and a binomial logit model with a covariate in non gaussian cases procedures based on estimating equations often perform considerably better than the existing semiparametric procedures

robustification of kalman filter models abstract kalman filter models based on the assumption of multivariate gaussian distributions are known to be nonrobust this means that when a large discrepancy arises between the prior distribution and the observed data the posterior distribution becomes an unrealistic compromise between the two in this article we discuss a rationale for how to robustify the kalman filter specifically we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered and we point out that this can be achieved by assuming a multivariate distribution with student t marginals to achieve fully robust results of the kind desired it becomes necessary to forsake an exact distribution theory approach and adopt an approximation method involving poly t distributions a recursive mechanism for implementing the multivariate t based kalman filter is described its properties are discussed and the procedure is illustrated by an example

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

a non gaussian model for time series with pulses abstract a non gaussian autoregressive like model is presented for time series that exhibit occasional large increases in value termed pulses and exponential decay between pulses the model differs from a first order autoregressive process in its incorporation of feedback between the distribution of the current innovation and the history of the process likelihood based methods of inference for the model are developed and an application to endocrinological data is given

dynamic modelling and penalized likelihood estimation for discrete time survival data summmary this paper describes a dynamic or state space approach for analyzing discrete time or grouped survival data simultaneous estimation of baseline hazard functions and of timevarying covariate effects is based on maximization of posterior densities or equivalently a penalized likelihood leading to kalman type smoothing algorithms data driven choice of unknown smoothing parameters is possible via an em type procedure the methods are illustrated by applications to real data

inference from accelerated life tests using filtering in coloured noise summary we present a new approach for inference from accelerated life tests our approach formulates such problems as inference under kalman filter models with correlated observation errors we restrict attention to exponential life distributions and the power rule as a time transformation function extensions to other time transformation functions are straightforward however extensions to other distributions involve non linear filtering and are not considered the advantages of our formulation are that we are able to incorporate uncertainty in the time transformation function and also are able to allow it to change with the stress to validate our approach we consider some simulated data to give it a sense of reality we apply it to actual data

a non gaussian kalman filter with application to the estimation of vehicular speed single inductive loop detectors ilds which provide online measurements of traffic volume and occupancy are widely used devices in road systems because of the nature of traffic flow fast estimation and forecasting of vehicular speed using the data collected by an ild are crucial to online road traffic management here we formulate statistical inference for vehicular speed as a dynamic generalized linear model with a reciprocal inverse gaussian observational distribution the formulation motivates us to extend the gaussian kalman filter to this non gaussian scenario this results in a set of simple recursive formulas in which the current estimate of the parameter of interest is updated as a weighted harmonic average of the previous estimate and the current observation by applying the developed non gaussian kalman filter to analyze traffic data collected by an ild we provide a competitive alternative for estimating vehicular speed at a minimum computational cost

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

on liapunov type inequality for third order differential equations abstract in this paper a liapunov type inequality has been derived for a class of third order differential equations of the form y p t y 0 wherepis a real valued continuous function on 0 the nature of the distance between consecutive two zeros or three zeros has been studied with the help of the inequality

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

lyapunov type inequalities for nonlinear systems in this paper by using elementary analysis we establish some new lyapunov type inequalities for nonlinear systems of differential equations special cases of which contain the well known equations such as emden fowler type and half linear equations the inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations

lyapunov inequalities for discrete linear hamiltonian systems abstract in this paper we present some lyapunov type inequalities for discrete linear scalar hamiltonian systems when the coefficient c t is not necessarily nonnegative valued and when the end points are not necessarily usual zeros but rather generalized zeros applying these inequalities we obtain some disconjugacy and stability criteria for discrete hamiltonian systems

bayesian forecasting of multinomial time series through conditionally gaussian dynamic models abstract we consider inference in the class of conditionally gaussian dynamic models for nonnormal multivariate time series in such models data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series a key example the main focus here is time series of multinomial observations a common occurrence in sociological and demographic studies involving categorical count data however we present this development in a more general setting as the resulting methods apply beyond the multinomial context we discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing markov chain monte carlo algorithms for normal dynamic linear models and including metropolis hastings components we develop an analysis of time series of flows of students in the italian secondary education system as an illustration of the models and methods

auxiliary mixture sampling for parameter driven models of time series of counts with applications to state space modelling we consider parameter driven models of time series of counts where the observations are assumed to arise from a poisson distribution with a mean changing over time according to a latent process estimation of these models is carried out within a bayesian framework using data augmentation and markov chain monte carlo methods we suggest a new auxiliary mixture sampler which possesses a gibbsian transition kernel where we draw from full conditional distributions belonging to standard distribution families only emphasis lies on application to state space modelling of time series of counts but we show that auxiliary mixture sampling may be applied to a wider range of parameter driven models including random effects models and panel data models based on the poisson distribution

moments for the canonical parameter of an exponential family under a conjugate distribution summary for exponential families the moment generating function of a conjugate exponential family distribution for the canonical parameter can be conveniently written in terms of the corresponding normalising constant for the conjugate densities this result can be used to find the moments of the canonical parameter and certain functions thereof this is illustrated for the class of natural exponential families having a simple quadratic variance function two applications are outlined the first is concerned with the analysis of dynamic generalised linear models as put forward by west harrison migon 1985 the second refers to the calculations of the expected logarithmic divergence for exponential families under a conjugate distribution

generalized linear models with varying dispersion summary generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean it is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately mean and dispersion submodels are formulated for this the dependent variable for the dispersion submodel being the deviance components of the mean submodel the fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests estimation algorithms are proposed which have good convergence properties the results apply mainly to the normal inverse gaussian and gamma distributions but can be extended to discrete distributions by using quasi likelihoods the methods developed are applied to a well known data set

sparse reflectivity inversion for nonstationary seismic data abstractconventional reflectivity inversion methods are based on a stationary convolution model and theoretically require stationary seismic traces as input i e those free of attenuation and dispersion effects reflectivity inversion for nonstationary data which is typical for field surveys requires us to first compensate for the earth s q filtering effects by inverse q filtering however the attenuation compensation for inverse q filtering is inherently unstable and offers no perfect solution thus we presented a sparse reflectivity inversion method for nonstationary seismic data we referred to this method as nonstationary sparse reflectivity inversion nsri it makes the novel contribution of avoiding intrinsic instability associated with inverse q filtering by integrating the earth s q filtering operator into the stationary convolution model nsri also avoids time variant wavelets that are typically required in time variant deconvolution although nsri is initially designed for nonstationary

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

lyapunov inequality for linear hamiltonian systems on time scales the principal aim of this paper is to state and prove some lyapunov inequalities for linear hamiltonian system on an arbitrary time scale t so that the well known case of differential linear hamiltonian systems t r and the recently developed case of discrete hamiltonian systems t z are unified applying these inequalities a disconjugacy criterion for hamiltonian systems on time scales is obtained

linear growth curve analysis based on exponential dispersion models the paper introduces a class of linear growth curve models based on combinations of exponential dispersion models the models have three components namely a latent markov growth process with stationary and independent increments a noise component and a component describing variation between subjects the models allow a wide range of continuous discrete and mixed distributions estimation for the models is based on an estimating equation derived from an em like algorithm combined with kalman smoothing

a simple risk adjusted exponentially weighted moving average in such contexts as medical monitoring there is a need for a simple procedure to estimate the level of a smoothly changing dynamic process while adjusting for risk factors associated with heterogeneous nonnormal observations standard methods exist for when the data are normal and simple methods have been developed for nonnormal data without covariates the dynamic generalized linear model dglm may be considered a standard for nonnormal data with covariates but perhaps one that is overcomplicated for many contexts we propose adapting the standard exponentially weighted moving average ewma to take into account the effect of risk factors by approximating the correct exponential family likelihood we derive a risk adjusted ewma ra ewma that is essentially a standard ewma applied to pseudo observations which are the original observations adjusted for differential risk the ra ewma can be expressed as a type of filter in which current estimate previous estimate discounted predictive error we

disconjugacy via lyapunov and vallee poussin type inequalities for forced differential equations in the case of oscillatory potentials we present some new lyapunov and vallee poussin type inequalities for second order forced differential equations no sign restriction is imposed on the forcing term the obtained inequalities generalize and compliment the existing results in the literature

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

bayesian model monitoring on presente une approche bayesienne basee sur des comparaisons des predictions a partir du modele standard avec celles d un modele alternatif simple

multiregression dynamic models multiregression dynamic models are defined to preserve certain conditional independence structures over time across a multivariate the series they are non gaussian and yet they can often be updated in closed form the first two moments of their one step ahead forecast distribution can tie easily calculated furthermore they can be built to contain all the features of the univariate dynamic linear model and promise more efficient identification of causal structures in a time series than has been possible in the past

on liapunov type inequality for certain higher order differential equations in this paper we generalize the well known liapunov type inequality for a class of third order differential equations without damping force to 2n 1 order differential equations

semiparametric bayesian analysis of survival data abstract this review article investigates the potential of bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function the nonparametric part of every model is assumed to be a realization of a stochastic process the parametric part which may include a regression parameter or a parameter quantifying the heterogeneity of a population is assumed to have a prior distribution with possibly unknown hyperparameters careful applications of some recently popular computational tools including sampling based algorithms are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures the methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies here we focus on univariate survival data in the presence of fixed and time dependent covariates multiple event time data for repeated nonfatal events

outlier models and prior distributions in bayesian linear regression summary bayesian inference in regression models is considered using heavy tailed error distri butions to accommodate outliers the particular class of distributions that can be con structed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in bayesian linear modelling includ ing simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters the modelling of outliers in nominally normal linear regression models using alternative error distributions which are heavy tailed relative to the normal provides an automatic means of both detecting and accommodating possibly aberrant observations such realistic models do however often lead to analytically intractable analyses with complex posterior distributions in several dimensions that are difficult to summarize and understand in this paper we consider a special yet rather wide class of heavy tailed unimodal and symmetric error distributions for which the analyses though apparently intractable can be examined in some depth by exploiting certain properties of the assumed error form the distributions concerned are those that can be con structed as scale mixtures of normal distributions in his paper concerning location parameters de finetti 1961 discusses such distributions and suggests the hypothetical interpretation that each observation is taken using an instrument with normal error but each time chosen at random from a collection of instruments of different precisions the distribution of the

sensitivity of the dispersion correction to q error a controlled phase acquisition and processing methodology for our company has been described by trantham 1994 he pointed out that it is careful attention to wavelet phase that leads to improved well ties and a more geologically accurate seismic image in addition we prefer zero phase wavelets on our seismic sections for a given amplitude spectrum they have the simplest shape and the highest peak further the peak occurs at the reflection time of the event this alignment is important since the seismic wavelet generally broadens with increasing depth with a zero phase wavelet remaining symmetrical about the event time our experience has been that a true zero phase section can be tied over the entire length of a synthetic trace without having to slide the synthetic trace to tie different time zones

estimation of median income of four person families a bayesian time series approach abstract this article develops a general methodology for small domain estimation based on data from repeated surveys the results are directly applied to the estimation of median income of four person families for the 50 states and the district of columbia these estimates are needed by the u s department of health and human services hhs to formulate its energy assistance program for low income families the u s bureau of the census by an informal agreement has provided such estimates to hhs through a linear regression methodology since the latter part of the 1970s the current method is an empirical bayes method eb that uses the current population survey cps estimates as well as the most recent decennial census estimates updated by the per capita income estimates of the bureau of economic analysis however with the existing methodology standard errors associated with these estimates are not easy to obtain the eb estimates when used naively can lead to underestimation of standard errors mo

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

prediction using partly conditional time varying coefficients regression models summary data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts in this paper we propose a method for estimating predictive functions the method uses an extension of the marginal regression analysis methods of liang and zeger 1986 biometrika73 13 22 and is implemented using simple estimating equations a key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions we suggest methods for evaluating the diagnostic accuracy sensitivity and specificity of such rules using cross validation the method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient s current and past clinical status

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

covariance matrix and transfer function of dynamic generalized linear models statistical inference for dynamic generalized linear models dglms is challenging due to the time varying nature of the unknown parameters in these models in this paper we focus on the covariance matrix and the transfer function the two key components in dglms we first establish some convergence results for the covariance matrix estimation we then provide an in depth study of the transfer function on its stability and fourier transformation which is necessary for parameter estimation in dglms implications of our results on estimation in dglms are illustrated in the paper through a simulation study and a real data example our understanding on dglms has substantially improved though this study

a state space model for multivariate longitudinal count data summary we propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma markov process the poisson counts are assumed to be conditionally independent given the latent process both over time and across categories we consider a regression model where time varying covariates may enter via either the poisson model or the latent gamma process estimation is based on the kalman smoother and we consider analysis of residuals from both the poisson model and the latent process a reanalysis of zeger s 1988 polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long term decrease in the rate of u s polio infection

a generalization of the kalman filter for models with state dependent observation variance abstract the kalman filter is generalized to cover state space models in which the variance of the observation error depends on the state vector derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints linear bayes theory and gauss markov theory the results are applied to a model for which y t t 1 2 n follow a poisson distribution with corresponding intensities t t 1 2 n that are assumed to follow an autoregressive process of order 1 namely the steady state generalized kalman filter algorithm in the case for which 1 gives a generalization of exponential smoothing for a poisson process with time varying intensity

non homogeneous autoregressive processes for tracking software reliability growth and their bayesian analysis summary we motivate a non homogeneous autoregressive process as a model for reliability growth and consider two formulations both bayesian which alleviate a limitation that least squares estimators for such processes of order greater than 1 exist only when repeated measurements of the time series are available in one formulation the prior assumption involves exchangeability of coefficients whereas in the other an autoregressive structure is imposed on them both formulations enable us to cast the resulting processes in state space form for which the kalman filter algorithm can be used the first formulation involves an adaptation of standard techniques whereas the second results in a new methodology for adaptive filtering which is facilitated by an approximation due to lindley the procedures are demonstrated via a consideration of some data on software failures

a discrete analogue of lyapunov type inequalities for nonlinear systems in this paper by using elementary analysis we establish some new lyapunov type inequalities for nonlinear systems of difference equations when the coefficent b 2 t is not necessarily nonnegative valued and when the end points are not necessarily usual zeros but rather generalized zeros applying these inequalities we obtain a disconjugacy criterion and boundedness for the solution of our system some special cases of our results contain recently developed lyapunov inequalities for discrete linear hamiltonian systems the inequalities obtained here can be used as handy tools in the study of the qualitative behaviour of solutions of the associated equations

lyapunov type integral inequalities for certain higher order differential equations in this paper first we will give a short survey of the most basic results on lyapunov inequality and next we obtain this type integral inequalities for certain higher order differential equations our results are sharper than some results of yang 2003 20

a self organizing state space model a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method

on the linearity of bayesian interpolators for non gaussian continuous time ar 1 processes bayesian estimation problems involving gaussian distributions often result in linear estimation techniques nevertheless there are no general statements as to whether the linearity of the bayesian estimator is restricted to the gaussian case the two common strategies for non gaussian models are either finding the best linear estimator or numerically evaluating the bayesian estimator by monte carlo methods in this paper we focus on bayesian interpolation of non gaussian first order autoregressive ar processes where the driving innovation can admit any symmetric infinitely divisible distribution characterized by the levy khintchine representation theorem we redefine the bayesian estimation problem in the fourier domain with the help of characteristic forms by providing analytic expressions we show that the optimal interpolator is linear for all symmetric stable distributions the bayesian interpolator can be expressed in a convolutive form where the kernel is described in terms of exponential splines we also show that the limiting case of levy type ar 1 processes the system of which has a pole at the origin always corresponds to a linear bayesian interpolator made of a piecewise linear spline irrespective of the innovation distribution finally we show the two mentioned cases to be the only ones within the family for which the bayesian interpolator is linear

time series of continuous proportions summary a vector of continuous proportions consists of the proportions of some total accounted for by its constituent components an example is the proportions of world motor vehicle production by japan the usa and all other countries we consider the situation where time series data are available and where interest focuses on the proportions rather than the actual amounts reasons for analysing such times series include estimation of the underlying trend estimation of the effect of covariates and interventions and forecasting we develop a state space model for time series of continuous proportions conditionally on the unobserved state the observations are assumed to follow the dirichlet distribution often considered to be the most natural distribution on the simplex the state follows the dirichlet conjugate distribution which is introduced here thus the model although based on the dirichlet distribution does not have its restrictive independence properties covariates trends seasonality and interventions may be incorporated in a natural way the model has worked well when applied to several examples and we illustrate with components of world motor vehicle production

smoothing serial count data through a state space model a method is proposed for smoothing serial poisson count data through state space modeling recursive formulas for evaluating the exact likelihood are given the exact likelihood yields the likelihood ratio test for homogeneity of the poisson means the method is versatile enough to permit various extensions including that for serial binomial data the proposed method is applied to three sets of weekly disease incidence data

lyapunov type inequality for a class of even order differential equations in this paper we generalize the well known lyapunov type inequality for second order linear differential equations to a class of even order linear differential equations the results of this paper are new and generalize some known inequalities in the literatures

gaussian particle filtering sequential bayesian estimation for nonlinear dynamic state space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations this paper introduces a new filter called the gaussian particle filter it is based on the particle filtering concept and it approximates the posterior distributions by single gaussians similar to gaussian filters like the extended kalman filter and its variants it is shown that under the gaussianity assumption the gaussian particle filter is asymptotically optimal in the number of particles and hence has much improved performance and versatility over other gaussian filters especially when nontrivial nonlinearities are present simulation results are presented to demonstrate the versatility and improved performance of the gaussian particle filter over conventional gaussian filters and the lower complexity than known particle filters

on inequalities of lyapunov type we generalize the classical lyapunov inequality for second order linear differential equations to nonlinear differential equations of second order and then to higher order linear differential equations

the scan sampler for time series models summary an algorithm called the scan sampler is developed and discussed the scan sampler has a variety of uses for time series analysis based on the state space model with nongaussian observations the algorithm is based on the kalman filter smoothing algorithm it can be used for bayesian inference using markov chain monte carlo and to find posterior modes

stability criteria for linear hamiltonian systems under impulsive perturbations abstract stability criteria are given for planar linear periodic hamiltonian systems with impulse effect by making use of a lyapunov type inequality a disconjugacy criterion is also established the results improve the related ones in the literature for such systems

using historical controls to adjust for covariates in trend tests for binary data abstract historical data often play an important role in helping interpret the results of a current study this article is motivated primarily by one specific application the analysis of data from rodent carcinogenicity studies by proposing a suitable informative prior distribution on the relationship between control outcome data and covariates we derive modified trend test statistics that incorporate historical control information to adjust for covariate effects frequentist and fully bayesian methods are presented and novel computational techniques are developed to compute the test statistics several attractive theoretical and computational properties of the proposed priors are derived in addition a semiautomatic elicitation scheme for the priors is developed our approach is used to modify a widely used prevalence test for carcinogenicity studies the proposed methodology is applied to data from a national toxicology program carcinogenicity experiment and is shown to provide helpful insight on t

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

a new perspective on priors for generalized linear models abstract this article deals with specifications of informative prior distributions for generalized linear models our emphasis is on specifying distributions for selected points on the regression surface the prior distribution on regression coefficients is induced from this specification we believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model dependent regression coefficients previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression we expand on the idea of conditional means priors and extend these to arbitrary generalized linear models we also consider data augmentation priors where the prior is of the same form as the likelihood we show that data augmentation priors are special cases of conditional means priors with current monte carlo methodology such as importance sampling and gibbs sampling our priors result in

some properties and generalizations of non negative bayesian time series models we study the most basic bayesian forecasting model for exponential family time series the power steady model psm of smith in terms of observable properties of one step forecast distributions and sample paths the psm implies a constraint between location and spread of the forecast distribution including a scale parameter in the models does not always give an exact solution free of this problem but it does suggest how to define related models free of the constraint we define such a class of models which contains the psm we concentrate on the case where observations are non negative probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant making them unsuitable for modelling in many situations the results apply more generally to non negative models defined in terms of exponentially weighted moving averages we use these and related results to motivate define and apply very simple models based on directly specifying the forecast distributions

on lyapunov type inequalities for certain higher order differential equations in this paper we derive lyapunov type inequalities for certain higher order differential equations which relate the points at which the solutions and their certain derivatives have zeros the inequalities obtained here can be used to study the qualitative behavior of solutions of the corresponding differential equations