energy distribution of maxima and minima in a one dimensional random system we study the energy distribution of maxima and minima of a simple one dimensional disordered hamiltonian we find that in systems with short range correlated disorder there is energy separation between maxima and minima such that at fixed energy only one kind of stationary points is dominant in number over the other on the other hand in the case of systems with long range correlated disorder maxima and minima are completely mixed

partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

a single saddle model for the β relaxation in supercooled liquids we analyse the relaxational dynamics of a system close to a saddle of the potential energy function within an harmonic approximation our main aim is to relate the topological properties of the saddle as encoded in its spectrum to the dynamical behaviour of the system in the context of the potential energy landscape approach this represents a first formal step to investigate the belief that the dynamical slowing down at tc is related to the vanishing of the number of negative modes found at the typical saddle point in our analysis we keep the description as general as possible using the spectrum of the saddle as an input we prove the existence of a timescale t which is uniquely determined by the spectrum but is not simply related to the fraction of negative eigenvalues the mean square displacement develops a plateau of length t such that a two step relaxation is obtained if t diverges at tc we analyse different spectral shapes and outline the conditions under which the mean square displacement exhibits a dynamical scaling identical to the relaxation regime of mode coupling theory with a power law approach to the plateau and power law divergence of t at tc

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

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

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

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

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

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

stochastic model specification search for gaussian and partial non gaussian state space models model specification for state space models is a difficult task as one has to decide which components to include in the model and to specify whether these components are fixed or time varying to this aim a new model space mcmc method is developed in this paper it is based on extending the bayesian variable selection approach which is usually applied to variable selection in regression models to state space models for non gaussian state space models stochastic model search mcmc makes use of auxiliary mixture sampling we focus on structural time series models including seasonal components trend or intervention the method is applied to various well known time series

persistence of embedded eigenvalues we consider conditions under which an embedded eigenvalue of a self adjoint operator remains embedded under small perturbations in the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m infinity we show that in favorable situations the set of small perturbations of a suitable banach space which do not remove the eigenvalue form a smooth submanifold of codimension in we also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite

convergence of a stochastic approximation version of the em algorithm the expectation maximization em algorithm is a powerful computational technique for locating maxima of functions it is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models in certain situations however this method is not applicable because the expectation step cannot be performed in closed form to deal with these problems a novel method is introduced the stochastic approximation em saem which replaces the expectation step of the em algorithm by one iteration of a stochastic approximation procedure the convergence of the saem algorithm is established under conditions that are applicable to many practical situations moreover it is proved that under mild additional conditions the attractive stationary points of the saem algorithm correspond to the local maxima of the function presented to support our findings

bayesian forecasting of an inhomogeneous poisson process with applications to call center data a call center is a centralized hub where customer and other telephone calls are handled by an organization in today s economy call centers have become the primary points of contact between customers and businesses thus accurate predictions of call arrival rates are indispensable to help call center practitioners staff their call centers efficiently and cost effectively this article proposes a multiplicative model for modeling and forecasting within day arrival rates to a u s commercial bank s call center markov chain monte carlo sampling methods are used to estimate both latent states and model parameters one day ahead density forecasts for the rates and counts are provided the calibration of these predictive distributions is evaluated through probability integral transforms furthermore 1 day ahead forecasts comparisons with classical statistical models are given our predictions show significant improvements of up to 25 over these standards a sequential monte carlo algorithm is also proposed

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

likelihood based estimation of latent generalized arch structures garch models are commonly used as latent processes in econometrics financial economics and macroeconomics yet no exact likelihood analysis of these models has been provided so far in this paper we outline the issues and suggest a markov chain monte carlo algorithm which allows the calculation of a classical estimator via the simulated em algorithm or a bayesian solution in o t computational operations where t denotes the sample size we assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 uk sectorial stock returns and compare it to existing approximate solutions

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

bayesian inference for linear dynamic models with dirichlet process mixtures using kalman techniques it is possible to perform optimal estimation in linear gaussian state space models here we address the case where the noise probability density functions are of unknown functional form a flexible bayesian nonparametric noise model based on dirichlet process mixtures is introduced efficient markov chain monte carlo and sequential monte carlo methods are then developed to perform optimal batch and sequential estimation in such contexts the algorithms are applied to blind deconvolution and change point detection experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts

eigenfunctions and eigenvalues for a scalar riemann hilbert problem associated to inverse scattering a complete set of eigenfunctions is introduced within the riemann hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations in particular we consider the time independent and time dependent schrodinger problems which are related to the kdv and kpi equations possessing solitons and lumps respectively non standard scalar products orthogonality and completeness relations are derived for these problems the complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations we classify two different types of bifurcations of new eigenvalues and analyze their characteristic features one type corresponds to thresholdless generation of solitons in the kdv equation while the other predicts a threshold for generation of lumps in the kpi equation

diagnosing shocks in time series abstract efficient means of modeling aberrant behavior in times series are developed our methods are based on state space forms and allow test statistics for various interventions to be computed from a single run of the kalman filter smoother the approach encompasses existing detection methodologies departures commonly observed in practice such as outlying values level shifts and switches are readily dealt with new diagnostic statistics are proposed implications for structural models autoregressive integrated moving average models and models with explanatory variables are given

time series with additive noise summary we put forward a state space model where the unobservable state variable can be any gaussian stochastic process we discuss both maximum likelihood estimation and bayesian inference for this generalised model the methodology developed in this paper is particularly important for the class of long memory plus noise models armed with the simulation smoother introduced in this paper we can estimate a class of non gaussian measurement time series models with long memory in the state equation

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

monte carlo smoothing for nonlinear time series we develop methods for performing smoothing computations in general state space models the methods rely on a particle representation of the filtering distributions and their evolution through time using sequential importance sampling and resampling ideas in particular novel techniques are presented for generation of sample realizations of historical state sequences this is carried out in a forward filtering backward smoothing procedure that can be viewed as the nonlinear non gaussian counterpart of standard kalman filter based simulation smoothers in the linear gaussian case convergence in the mean squared error sense of the smoothed trajectories is proved showing the validity of our proposed method the methods are tested in a substantial application for the processing of speech signals represented by a time varying autoregression and parameterized in terms of time varying partial correlation coefficients comparing the results of our algorithm with those from a simple smoother based on the filte

nonlinear stability of time periodic viscous shocks in order to understand the nonlinear stability of many types of time periodic travelling waves on unbounded domains one must overcome two main difficulties the presence of embedded neutral eigenvalues and the time dependence of the associated linear operator this problem is studied in the context of time periodic lax shocks in systems of viscous conservation laws using spatial dynamics and a decomposition into separate floquet eigenmodes it is shown that the linear evolution for the time dependent operator can be represented using a contour integral similar to that of the standard time independent case by decomposing the resulting green s distribution the leading order behavior associated with the embedded eigenvalues is extracted sharp pointwise bounds are then obtained which are used to prove that time periodic lax shocks are linearly and nonlinearly stable under the necessary conditions of spectral stability and minimal multiplicity of the translational eigenvalues the latter conditions hold for example for small oscillation time periodic waves that emerge through a supercritical hopf bifurcation from a family of time independent lax shocks of possibly large amplitude

stability of the gibbs sampler for bayesian hierarchical models we characterize the convergence of the gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions we show that the convergence can be uniform geometric or subgeometric depending on the relative tail behavior of the error distributions and on the parametrization chosen our theory is applied to characterize the convergence of the gibbs sampler on latent gaussian process models we indicate how the theoretical framework we introduce will be useful in analyzing more complex models

bayesian estimation of switching arma models abstract switching arma processes have recently appeared as an efficient modelling to nonlinear time series models because they can represent multiple or heterogeneous dynamics through simple components the levels of dependence between the observations are double at a first level the parameters of the model are selected by a markovian procedure at a second level the next observation is generated according to a standard time series model when the model involves a moving average structure the complexity of the resulting likelihood function is such that simulation techniques like those proposed by shephard 1994 biometrika 81 115 131 and billio and monfort 1998 journal of statistical planning and inference 68 65 103 are necessary to derive an inference on the parameters of the model we propose in this paper a bayesian approach with a non informative prior distribution developed in mengersen and robert 1996 bayesian statistics 5 oxford university press oxford pp 255 276 and robert and titterington 1998 statistics and computing 8 2 145 158 in the setup of mixtures of distributions and hidden markov models respectively the computation of the bayes estimates relies on mcmc techniques which iteratively simulate missing states innovations and parameters until convergence the performances of the method are illustrated on several simulated examples this work also extends the papers by chib and greenberg 1994 journal of econometrics 64 183 206 and chib 1996 journal of econometrics 75 1 79 97 which deal with arma and hidden markov models respectively

perturbations of embedded eigenvalues for the planar bilaplacian operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task and the persistence properties of such eigenvalues are linked intimately to the multiplicity of the essential spectrum in this paper we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite dimensional manifold with infinite codimension in an appropriate space of potentials

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

stochastic volatility with leverage fast and efficient likelihood inference this paper is concerned with the bayesian analysis of stochastic volatility sv models with leverage specifically the paper shows how the often used kim et al 1998 stochastic volatility likelihood inference and comparison with arch models review of economic studies 65 361 393 method that was developed for sv models without leverage can be extended to models with leverage the approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten component mixture of bivariate normal distributions the resulting posterior distribution is summarized by mcmc methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure the overall procedure is fast and highly efficient we illustrate the ideas on daily returns of the tokyo stock price index finally extensions of the method are described for superposition models where the log volatility is made up of a linear combination of heterogenous and independent autoregressions and heavy tailed error distributions student and log normal

smoothing and interpolation with the state space model abstract a new result dealing with smoothing and interpolation in the state space model is developed and explored the result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages the connection to signal extraction and interpolation is explored and diffuse specifications are considered

markov chain monte carlo methods for stochastic volatility models this paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy tailed student t distributions with unknown degrees of freedom and exogenous variables in the observation and volatility equations and a jump component in the observation equation by building on the work of kim shephard and chib rev econom stud 65 1998 361 we develop efficient markov chain monte carlo algorithms for estimating these models the paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods computation of the marginal likelihood by the method of chib j amer statist assoc 90 1995 1313 is also considered the methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the s p 500 index where several stochastic volatility models are formally compared under different priors on the parameters

modeling and inference with υ spherical distributions abstract a new class of continuous multivariate distributions on n is proposed we define these so called spherical distributions through properties of the density function in a location scale context we derive conditions for properness of spherical distributions and discuss how to generate them in practice the name spherical is motivated by the fact that these distributions generalize the classes of spherical when is the l 2 norm and l q spherical when is the l q norm distributions isodensity sets are still always situated around the location parameter but exchangeability and axial symmetry are no longer imposed as is illustrated in some examples as an important special case we define a class of distributions suggested by independent sampling from a generalization of exponential power distributions this allows us to model skewness interestingly all the robustness results found previously for spherical and l q spherical models carry over directly to spherical mo

approximating hidden gaussian markov random fields summary gaussian markov random field gmrf models are frequently used in a wide variety of applications in most cases parts of the gmrf are observed through mutually independent data hence the full conditional of the gmrf a hidden gmrf hgmrf is of interest we are concerned with the case where the likelihood is non gaussian leading to non gaussian hgmrf models several researchers have constructed block sampling markov chain monte carlo schemes based on approximations of the hgmrf by a gmrf using a second order expansion of the log density at or near the mode this is possible as the gmrf approximation can be sampled exactly with a known normalizing constant the markov property of the gmrf approximation yields computational efficiency the main contribution in the paper is to go beyond the gmrf approximation and to construct a class of non gaussian approximations which adapt automatically to the particular hgmrf that is under study the accuracy can be tuned by intuitive parameters to nearly any precision these non gaussian approximations share the same computational complexity as those which are based on gmrfs and can be sampled exactly with computable normalizing constants we apply our approximations in spatial disease mapping and model based geostatistical models with different likelihoods obtain procedures for block updating and construct metropolized independence samplers

nonlinear state space models with state dependent variances nonlinear state space models with state dependent variances sdvs are commonly used in financial time series important examples include stochastic volatility sv and affine term structure models we propose a methodology for state smoothing in this class of models our smoothing technique is simulation based and uses an auxiliary mixture model key features of the auxiliary mixture model are the use of state dependent weights and efficient block sampling algorithms to jointly update all unobserved states given latent mixture indicators conditional on latent indicator variables the auxiliary mixture model reduces to a normal dynamic linear model we illustrate our methodology with two time series applications first we show how to construct the auxiliary model for a logarithmic sv model and compare the performance of our methodology with the current literature next we implement a square root sv model with jumps for short term interest rates in hong kong

stationarity of multivariate markov switching arma models in this article we consider multivariate arma models subject to markov switching in these models the parameters are allowed to depend on the state of an unobserved markov chain a natural idea when estimating these models is to impose local stationarity conditions i e stationarity within each regime in this article we show that the local stationarity of the observed process is neither sufficient nor necessary to obtain the global stationarity we derive stationarity conditions and we compute the autocovariance function of this nonlinear process interestingly it turns out that the autocovariance structure coincides with that of a standard arma some examples are proposed to illustrate the stationarity conditions using monte carlo simulations we investigate the consequences of accounting for the stationarity conditions in statistical inference

perturbations of embedded eigenvalues for a magnetic schrodinger operator on a cylinder perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum in this paper we study a perturbation problem for embedded eigenvalues for a magnetic schrodinger operator when the underlying domain is a cylinder the magnetic potential is c2 with an algebraic decay rate as the unbounded variable of the cylinder tends to in particular no analyticity of the magnetic potential is assumed we also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer thus avoiding the thresholds of the continuous spectrum of the unperturbed operator we show that the set of nearby potentials for which a simple embedded eigenvalue persists forms a smooth manifold of finite codimension

phase space geometry and slow dynamics we describe a non arrhenius mechanism for the slowing down of dynamics that is inherent to the high dimensionality of the phase space we show that such a mechanism is at work both in a family of mean field spin glass models without any domain structure and in the case of ferromagnetic domain growth the marginality of spin glass dynamics as well as the existence of a quasi equilibrium regime can be understood within this scenario we discuss the question of ergodicity in an out of equilibrium situation

estimation and comparison of multiple change point models this paper provides a new bayesian approach for models with multiple change points the centerpiece of the approach is a formulation of the change point model in terms of a latent discrete state variable that indicates the regime from which a particular observation has been drawn this state variable is specified to evolve according to a discrete time discrete state markov process with the transition probabilities constrained so that the state variable can either stay at the current value or jump to the next higher value this parameterization exactly reproduces the change point model the model is estimated by markov chain monte carlo methods using an approach that is based on chib 1996 this methodology is quite valuable since it allows for the fitting of more complex change point models than was possible before methods for the computation of bayes factors are also developed all the techniques are illustrated using simulated and real data sets

filtering and forecasting with misspecified arch models i getting the right variance with the wrong model this paper investigates the properties of the conditional covariance estimates generated by a misspecified arch model for example suppose that we observe a diffusion process at discrete time intervals of length h for each h we use a garch 1 1 model to estimate the instantaneous conditional covariance matrix of the diffusion under mild regularity conditions the difference between these conditional covariance estimates and the true conditional covariance converges to zero in probability as h 0 many other arch models for example exponential arch have similar consistency properties this may well account for the success of arch models in short term forecasting using high frequency data since even misspecified arch models can produce good estimates of volatility

exact score for time series models in state space form the full text of this article is not currently available in ora citation koopman s j shephard n 1992 exact score for time series models in state space form biometrika 79 40 823 826 available at http biomet oxfordjournals org

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

particle filtering for partially observed gaussian state space models summary solving bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models a large number of algorithms based on particle filtering methods also known as sequential monte carlo algorithms have recently been proposed to solve these problems we propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed gaussian state space models this algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms it differs from previous algorithms which were only applicable to conditionally linear gaussian state space models computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models

testing mode coupling theory for a supercooled binary lennard jones mixture i the van hove correlation function we report the results of a large scale computer simulation of a binary supercooled lennard jones liquid we find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time td t where d t is the diffusion constant the time range for which these curves follow the master curve is identified with the ensuremath alpha relaxation regime of mode coupling theory mct this master curve is fitted well by a functional form suggested by mct in accordance with idealized mct d t shows a power law behavior at low temperatures the critical temperature of this power law is the same for both types of particles and also the critical exponents are very similar however contrary to a prediction of mct these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function phys rev lett 73 1376 1994 at low temperatures the van hove correlation function self as well as distinct part shows almost no sign of relaxation in a time interval that extends over about three decades in time this time interval can be interpreted as the ensuremath beta relaxation regime of mct from the investigation of these correlation functions we conclude the hopping processes are not important on the time scale of the ensuremath beta relaxation for this system and for the temperature range investigated we test whether the factorization property predicted by mct holds and find that this is indeed the case for all correlation functions investigated the distance dependences of the critical amplitudes are in qualitative agreement with the ones predicted by mct for some other mixtures the non gaussian parameter for the self part of the van hove correlation function for different temperatures follows a master curve when plotted against time t

exponential family state space models based on a conjugate latent process summary this paper introduces non linear and non gaussian state space models with analytic updating recurnions for filtering and prediction this new class of models involves some well known results in the theory of exponential models and of exponential dispersion models and the latent process is defined in such a way that both the filtering and the prediction distributions turn out to be conjugate to the observation distribution at each step the corresponding analytic and inferential properties are investigated and some simple examples are presented

markov chain monte carlo estimation of classical and dynamic switching and mixture models bayesian estimation of a very general model class where the distribution of the observations depends on a latent process taking values in a discrete state space is discussed in this article this model class covers finite mixture modeling markov switching autoregressive modeling and dynamic linear models with switching the consequences the unidentifiability of this type of model has on markov chain monte carlo mcmc estimation are explicitly dealt with joint bayesian estimation of all latent variables model parameters and parameters that determine the probability law of the latent process is carried out by a new mcmc method called permutation sampling the permutation sampler first samples from the unconstrained posterior which often can be done in a convenient multimove manner and then applies a permutation of the current labeling of the states of the latent process in a first run the random permutation sampler used selected the permutation randomly the mcmc output of the random permutation s

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

role of saddles in mean field dynamics above the glass transition recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy here we further develop this approach in the context of a mean field model by analytically studying the properties of the closest saddle point to an equilibrium configuration of the system we prove that when the glass transition is approached the energy of the closest saddle goes to the threshold energy defined as the energy level below which the degree of instability of the typical stationary points vanishes moreover we show that the distance between a typical equilibrium configuration and the closest saddle is always very small and that surprisingly it is almost independent of the temperature

efficient bayesian inference for dynamic mixture models abstract a bayesian approach is presented for estimating a mixture of linear gaussian state space models such models are used to model interventions in time series and nonparametric regression markov chain monte carlo sampling is usually necessary to obtain the posterior distributions of such mixture models because it is difficult to obtain them analytically the methodological contribution of the article is to derive a set of recursions for dynamic mixture models that efficiently implement a markov chain monte carlo sampling scheme that converges rapidly to the posterior distribution the methodology is illustrated by fitting an autoregressive model subject to interventions to zinc concentration in sludge

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

markov chain monte carlo in conditionally gaussian state space models summary a bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values a sequence of indicator variables determines which components the errors belong to and the values of the coefficients the computation is carried out using markov chain monte carlo with the indicator variables generated without conditioning on the states previous approaches use the gibbs sampler to generate the indicator variables conditional on the states in many problems however there is a strong dependence between the indicator variables and the states causing the gibbs sampler to converge unacceptably slowly or even not to converge at all the new sampler is implemented in o n operations where n is the sample size permitting an exact bayesian analysis of problems that previously had no computationally tractable solution we show empirically that the new sampler can be much more efficient than previous approaches and illustrate its applicability to robust nonparametric regression with discontinuities and to a time series change point problem

testing for integration using evolving trend and seasonals models a bayesian approach in this paper we make use of state space models to investigate the presence of stochastic trends in economic time series a model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation tests based on the former are analogous to dickey fuller tests of unit roots while the latter are analogous to kpss tests of trend stationarity we use bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends we extend these ideas to the problem of testing for integration at seasonal frequencies and show how our techniques can be used to carry out bayesian variants of either the hegy or canova hansen test stochastic integration rules based on markov chain monte carlo as well as deterministic integration rules are used strengths and weaknesses of each approach are indicated

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

disturbance smoother for state space models summary this paper develops a method to evaluate the smoothed estimator of the disturbance vector in a state space model together with its mean squared error matrix this disturbance smoother also leads to an efficient smoother for the state vector applications include a method to calculate auxiliary residuals for unobserved components time series models and an em algorithm for estimating covariance parameters in a state space model

statistical analysis of ion channel data using hidden markov models with correlated state dependent noise and filtering a hidden markov model that describes ion channel data including correlated state dependent noise and filter characteristics and a markov chain monte carlo algorithm that enables bayesian inference under this model are presented the method provides parameter estimates and an estimate of the noiseless signal it was tested on simulated data and applied to real recordings to estimate the model parameters modeling the noise and filter correctly turned out to be crucial for the analyzed data sets the assumption of white noise is too simple and negligence of the smoothing effect of the low pass filter leads to errors in the detection of rapid transitions the hidden markov model that we propose treats these effects simultaneously

quasi equilibrium interpretation of ageing dynamics we develop an interpretation of the off equilibrium dynamical solution of mean field glassy models in terms of quasi equilibrium concepts we show that the relaxation of the thermo remanent magnetization follows a generalized version of the onsager regression postulate of induced fluctuations we then find the rationale for the equality between the fluctuation dissipation ratio and the rate of growth of the configurational entropy close to the asymptotic state found empirically in mean field solutions

semiparametric bayesian inference for time series with mixed spectra summary a bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms the periodic terms may have known or unknown frequencies the advantage of our approach is that different features of the data such as the regression parameters the spectral density unknown frequencies and missing observations are combined in a hierarchical bayesian framework and estimated simultaneously a bayesian test to detect deterministic components in the data is also constructed by using an asymptotic approximation to the likelihood the computation is carried out efficiently using the markov chain monte carlo method in o mn operations where n is the sample size and m is the number of iterations we show empirically that our approach works well on real and simulated samples

bifurcations of new eigenvalues for the benjamin ono equation a criterion for the emergence of new eigenvalues is found for the linear scattering problem associated with the benjamin ono bo equation this bifurcation occurs due to perturbations of nongeneric potentials which include the soliton solutions of the bo equation the asymptotic approximation of an exponentially small new eigenvalue is derived the method is based on the expansion of a localized function through a complete set of unperturbed eigenfunctions explicit expressions are obtained for the soliton potentials

exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders in applications solitary wave solutions of semilinear elliptic equations u g u u 0 x y r in infinite cylinders frequently arise as travelling waves of parabolic equations as such their bifurcations are an interesting issue interpreting elliptic equations on infinite cylinders as dynamical systems inxhas proved very useful still there are major obstacles in obtaining for instance bifurcation results similar to those for ordinary differential equations in this article persistence and continuation of exponential dichotomies for linear elliptic equations is proved with this technique at hands lyapunov schmidt reduction near solitary waves can be applied as an example existence of shift dynamics near solitary waves is shown if a perturbation h x u u periodic inxis added

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

local scale models state space alternative to integrated garch processes state space alternative to autoregressive conditional heteroskedasticity models are proposed the initial model which is labelled the gaussian local scale model has a measurement density which is gaussian conditional on the unobservable precision the precision is assumed to be a gamma variable which evolves by being scaled by a beta variable the resulting forecast is a student s t random variable with a scale which is approximately an exponentially weighted moving average ewma of the squares of the past observations the degrees of freedom of the student s t distribution is controlled by the size of the discount parameter of the ewma procedure the gaussianity of the measurement density is potentially inadequate when the model is applied to heavy tailed finance data instead this assumption can be replaced by an exponential power density which allows the observed excess kurtosis to be modelled the choice of the exponential power means that the model still maintains conjugacy so allowing the derivation of an exact filter and likelihood function this model is called the generalised local scale model it has been used to model two exchange rate series

probabilistic forecasts calibration and sharpness summary probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions we propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only a simple theoretical framework allows us to distinguish between probabilistic calibration exceedance calibration and marginal calibration we propose and study tools for checking calibration and sharpness among them the probability integral transform histogram marginal calibration plots the sharpness diagram and proper scoring rules the diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the stateline wind energy centre in the us pacific northwest in combination with cross validation or in the time series context our proposal provides very general nonparametric alternatives to the use of information criteria for model diagnostics and model selection

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

a signal extraction approach to modeling hormone time series with pulses and a changing baseline abstract hormones serve as regulating signals for many biological processes in recent years it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern in addition to the absolute concentration level is important in regulating biological processes consequently it is necessary to characterize the latent secretion patterns from measurements of concentration levels the characterization is complicated by the presence of a biological circadian rhythm when hormone concentrations are plotted over time the resultant time series usually exhibits occasional short rises superimposed on a slowly changing baseline this is a result of a mixture of pulsatile secretions and a circadian rhythm in this article we present a signal extraction approach to model simultaneously a slowly changing component and a pulsatile component of a time series a smoothing spline is used to model the baseline and a multiprocess dynamic linear model is used to model the pulsati

indirect estimation of large conditionally heteroskedastic factor models with an application to the dow 30 stocks we derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a kalman filter approximation with inequality constraints on the auxiliary model parameters we also propose alternative indirect estimators for large scale models and explain how to apply our procedures to many other dynamic latent variable models we analyse the small sample behaviour of our indirect estimators and several likelihood based procedures through an extensive monte carlo experiment with empirically realistic designs finally we apply our procedures to weekly returns on the dow 30 stocks

non gaussian seasonal adjustment abstract a non gaussian state space modeling of time series with trend and seasonality is shown an observed time series is decomposed into trend seasonal and observational noise each component is expressed by a smoothness prior model which is expressed by a stochastic linear difference equation the essential difference from the previous methods is the use of non gaussian distributions namely the white noise input to each component and the observational noise are not necessarily gaussian this allows for the possible existence of jump of the trend or seasonal component and of the outliers thus by the use of this non gaussian state space model seasonal time series with possible existence of outliers and sudden structural changes can be automatically handled without any special treatment the filtering and smoothing formulas for the non gaussian state space model is realized by using gaussian mixture approximation to the involved densities numerical examples are shown to contrast with gaussian modeling