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

periodic solutions for nonlinear second order difference equations abstract this paper is devoted to introduce a new approach to investigate the existence of periodic solutions for nonlinear difference equations transforming a second order nonlinear difference equation on a finite discrete segment with periodic boundary conditions into a continuous system we obtain the existence conditions of periodic solutions of the equation the proof relies on coincidence degree theory and matrix theory without using green s function

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

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

the foundations of finite sample estimation in stochastic processes generally in the literature on stochastic processes estimation is investigated in terms of asymptotic properties in this paper we establish some finite sample optimal estimation let y1 y2 be a discrete stochastic process since we will be discussing results for samples of finite size n we restrict the process to r in the following the term parameter is used in the same broad sense as by godambe thompson 1984 let y be a class of probability distributions f on r and 0 0 f f e jz be a real parameter let hi be a real function of y 1 yi and 0 be such that

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

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

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

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

some results on the problems of decentralized reliable stabilization concerns the problems of decentralized reliable control in linear time invariant multivariable control systems by the stable factorization approach decentralized reliable control is defined as the problem in which the closed loop system remains stable in spite of failure in the interconnection between the subplants based on the decentralized parametric characterization developed by desoer and gundes in 1988 a necessary and sufficient condition for the decentralized version of the strong stabilization problem is first proposed next it is shown that the decentralized reliable stabilization problem is solvable if and only if the augmented plant is decentralized strongly stabilizable moreover it is concluded that the problem of centralized reliable multiple control can be viewed as the problem of decentralized reliable stabilization of an augmented plant

bayesian approach of nearfield acoustic reconstruction with particle filters this paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the bayesian approach of parameter estimation in particular the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method esm a state space model is formulated in light of the esm the parameters to estimate are amplitudes and locations of the equivalent sources the parameters constitute the state vector which follows a first order markov process with the transition matrix being the identity for every frequency domain data frame filtered estimates of the state vector obtained are assigned weights adaptively the implementation of recursive bayesian filters involves a sequential monte carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function pmf which evolves with iteration the weight update equation governs the evolution of this pmf and depends primarily on the likelihood function and the prior distribution it is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation

algebraic aspects of linear control system stability after formulating the problem of linear control system stability in very general terms the problem is resolved by 1 establishing a necessary and sufficient condition for stability 2 exploring in some detail the nature of this condition and 3 developing a parametric characterization of all controllers which stabilize a given plant the problem formulation is based on a ring theoretic setting for linear systems and is distinguished by the use of a novel control system configuration any interconnection of two distinct systems can be represented in terms of this configuration while preserving the distinction between the two systems furthermore no other configuration has this property several benefits and extensions are accrued as a result of using this configuration first a completely general yet physically meaningful problem formulation results consequently state space and operator theoretic approaches to linear control system stability are thoroughly reconciled this reconciliation embraces continuous time as well as discrete time systems lumped as well as distributed systems and 1 d as well as n d systems second the controller parametrization affords four degrees of freedom two more than any existing parametrization the additional degrees of freedom make explicit the design opportunity associated with controller implementation and thus determine several important control system characteristics this result is expected to provide a theoretical basis for the development of comprehensive control system design methodologies wherein design considerations related to controller implementation are addressed

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

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

on existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations the existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second order ordinary differential equations the arguments are based only upon the positivity of the green s functions and the krasnosel skii fixed point theorem as an example a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity

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

extending the state space model to accommodate missing values in responses and covariates this article proposes an extended state space model for accommodating multivariate panel data the novel aspect of this contribution is an adjustment to the classical model for multiple subjects that allows missingness in the covariates in addition to the responses missing covariate data are handled by a second state space model nested inside the first to represent unobserved exogenous information relevant kalman filter equations are derived and explicit expressions are provided for both the e and m steps of an expectation maximization em algorithm to obtain maximum gaussian likelihood estimates of all model parameters in the presence of missing data the resulting em algorithm becomes computationally intractable but a simplification of the m step leads to a new procedure that is shown to be an expectation conditional maximization ecm algorithm under exogeneity of the covariates simulation studies reveal that the approach appears to be relatively robust to moderate percentages of missing dat

existence of a pair of periodic solutions of an o d e generalizing a problem in nonlinear elasticity via variational methods on considere l existence des solutions t periodiques de l equation differentielle x g t x ou g r r r est continue et t periodique en t sous certaines conditions sur g on demontre l existence d au moins deux solutions t periodiques on utilise une methode variationnelle

dynamic rating curve assessment in unstable rivers using ornstein uhlenbeck processes 1 the procedure of fitting rating curves in channels where the stage discharge relationship is subject to changes driven by morphological processes remains one of the major unsolved problems in hydrometry this paper addresses this issue by formulating the stage discharge relationship as a steady flow one segmented power law model with parameters that are viewed as stochastic processes with characteristics associated with the temporal instabilities of the channel elements governing the stage discharge relationship a bayesian analysis with informative priors and time stage discharge measurements as forcing data is used to determine the most plausible model and its posterior parameter distributions using markov chain monte carlo simulation techniques and particle filtering the proposed framework is applied to data from gauging stations in two unstable rivers and one stable river in norway

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a class of two point boundary value problems we improve the results obtained by the first author in a recent paper where a problem raised by a ambrosetti h brezis and g cerami concerning the exact structure of the set of solutions for a class of two point boundary value problems was solved here we study a more general problem and get more detailed results

characterization of controllers in simultaneous stabilization this paper gives a convenient parametrization for the class of all stabilizing controllers for two or more plants the result represent a generalization of the youla parametrization of the class of all stabilizing controllers in terms of an arbitrary stable proper transfer function although as expected the additional constraints for simultaneous stabilization are not readily incorporated into h h2 optimization procedures as in the standard case there is immediate application of the theory for reduction of controllers which simultaneously stabilize two or more plants

algebraic theory of linear time invariant feedback systems with two input two output plant and compensator this paper present an algebraic theory for linear time invariant multi input multi output systems with two input two output plant and compensator using the factorization approach this system configuration considered by doyle and nett is most general in that any interconnection of two systems can be represented in terms of this scheme other system configurations encountered in compensator design problems are special cases of this system configuration the analysis and synthesis applies to continuous time as well as discrete time systems and to lumped as well as distributed systems since the algebraic setting is completely general the compensator parametrization has four degrees of freedom the paper is self contained and is tutorial in the sense that it develops the main results of nett without introducing the concept of containment

convex saturated particle filter in many systems the state variables are defined on a compact set of the state space to estimate the states of such systems the constrained particle filters have been used with some success the performance of the standard particle filters can be improved if the measurement information is used during the importance sampling of the filtering phase it has been shown that the particles obtained in such a way approximate the true state of the system more accurately the measurement is incorporated into the filtering algorithm through a user specified detection function which aims to detect the saturation as it occurs the algorithm derived from the aforementioned principle is called the saturated particle filter spf in our previous work we have derived a complete spf framework for the class of systems with one dimensional constraints in this paper we derive a novel convex spf that extends our method to multidimensional systems with convex constraints the effectiveness of the new method is demonstrated using an illustrative example

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

extension of the stein estimating procedure through the use of estimating functions abstract this article extends the stein method through the use of estimating functions godambe 1960 to address the simultaneous estimation of k population parameters 1 k in a mixed model setting the procedure generalizes the stein method by a allowing us to deal effectively with complications such as inequality of population variances that may arise in non gaussian mixed models b being appropriate for estimating i in populations of varying sizes and in particular populations of small sizes and c applying to situations where it cannot be assumed that the i s have unbiased estimators or even estimators of finite moment the focus of the article is on the quadratic variance function exponential family morris 1983b estimators for the parameters of the mixed model are developed in a regression model setting in which the i s are allowed to vary with a vector of covariates an application to incidence rates for the iceland breast cancer incidence data is presented for illustra

radially symmetric systems with a singularity and asymptotically linear growth abstract we prove the existence of infinitely many periodic solutions for radially symmetric systems with a singularity of repulsive type the nonlinearity is assumed to have a linear growth at infinity being controlled by two constants which have a precise interpretation in terms of the dancer fucik spectrum our result generalizes an existence theorem by del pino et al 1992 4 obtained in the case of a scalar second order differential equation

exact number of solutions of a class of two point boundary value problems involving concave and convex nonlinearities in this paper exact number of solutions are obtained for a class of two point boundary value problems involving concave and convex nonlinearities moreover some properties of the solutions are studied in details

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

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

dynamic linear models with switching abstract the problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time varying independent random process we derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process a maximum likelihood estimation procedure is given that uses a pseudo expectation maximization algorithm in the initial stages and nonlinear optimization we relate the models to those considered previously in the literature and give an application involving the tracking of multiple targets

existence of two positive solutions of a singular nonlinear periodic boundary value problem abstract we consider the singular periodic boundary value problem for the second order scalar differential equation x f t x x under the assumption that f has the repulsive singularity at x 0 we present sufficient conditions for the existence of at least two different positive solutions of the problem we use the lower and upper solutions method here

weighted multiscale cumulative residual renyi permutation entropy of financial time series abstract in this paper based on cumulative residual entropy cre and renyi permutation entropy rpe multiscale cumulative residual renyi permutation entropy mcrrrpe and weighted multiscale cumulative residual renyi permutation entropy wmcrrpe are proposed as novelty measures to quantify the uncertainty of the nonlinear time series first the mcrrpe and wmcrrpe methods are performed on the synthetic data and the impact of the changes to parameters is discussed then the mcrrpe and wmcrrpe methods are applied to the closing prices of the us european and chinese stock markets we analyze the statistics and draw some conclusions from the comparison the stock markets can be divided into four categories 1 nasdaq and ftse100 2 s p500 dji and hsi 3 dax30 and cac40 and 4 sse and szse the standard deviation has a certain relationship with wmcrrpe compared with the mcrrpe method the wmcrrpe method can distinguish these financial stock markets effectively and better estimate the complexity of the time series containing amplitude information

a higher order correlation unscented kalman filter abstract many nonlinear extensions of the kalman filter e g the extended and the unscented kalman filter reduce the state densities to gaussian densities this approximation gives sufficient results in many cases however these filters only estimate states that are correlated with the observation therefore sequential estimation of diffusion parameters e g volatility which are not correlated with the observations is not possible while other filters overcome this problem with simulations we extend the measurement update of the gaussian two moment filters by a higher order correlation measurement update we explicitly state formulas for a higher order unscented kalman filter within a continuous discrete state space we demonstrate the filter in the context of parameter estimation of an ornstein uhlenbeck process

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

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

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

state space modeling of animal movement and mortality with application to salmon a stochastic model for the movement and eventual mortality of an individual animal is formulated as a combination of three components initial spatial location survival status at any point in time and spatial translation between points in time alternative theories about survival and migration can be expressed in terms of different models for any of the three components the model can be extended to groups of animals spatially and or temporally aggregated by appropriate integration when information about animal counts is partial or inexact as from mark recapture or harvest data state space models are a natural framework for estimating both unknown parameters and animal abundance as an example a multivariate linear normal state space model that explicitly incorporates each of the three individual animal components is formulated for the migration and harvest of pacific coho salmon oncorhynchus kisutch using recoveries of tagged coho salmon caught in ocean fisheries and associated measures of fishing effort the kalman filter and maximum likelihood are used to estimate parameters of the processes and the kalman smooth is used to estimate abundances given estimated parameters and current harvest and effort data real time management of exploited populations could be improved by using the kalman prediction algorithm

practical filtering with sequential parameter learning summary the paper develops a simulation based approach to sequential parameter learning and filtering in general state space models our approach is based on approximating the target posterior by a mixture of fixed lag smoothing distributions parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms we avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling the method is illustrated by using two examples a benchmark auto regressive model with observation error and a high dimensional dynamic spatiotemporal model we show that the method provides accurate inference in the presence of outliers model misspecification and high dimensionality

a robust reliable stabilization scheme for single input single output systems using transcendental methods abstract a stabilization scheme reliable against a single controller failure originally proposed by vidyasagar and viswanadham is analysed a connection between the problem of robust reliable stabilization and the problem of stabilization by a stable minimum phase compensator is established via interpolation theory

on scale mixtures of normal distributions summary the exponential power family of distributions of box tiao 1973 is shown to be a subset of the class of scale mixtures of normals the corresponding mixing distributions are explicitly obtained identifying a close relationship between the exponential power family and a further class of normal scale mixtures namely the stable distributions

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

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 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

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