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

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

mcmc maximum likelihood for latent state models abstract this paper develops a pure simulation based approach for computing maximum likelihood estimates in latent state variable models using markov chain monte carlo methods mcmc our mcmc algorithm simultaneously evaluates and optimizes the likelihood function without resorting to gradient methods the approach relies on data augmentation with insights similar to simulated annealing and evolutionary monte carlo algorithms we prove a limit theorem in the degree of data augmentation and use this to provide standard errors and convergence diagnostics the resulting estimator inherits the sampling asymptotic properties of maximum likelihood we demonstrate the approach on two latent state models central to financial econometrics a stochastic volatility and a multivariate jump diffusion models we find that convergence to the mle is fast requiring only a small degree of augmentation

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

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

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

use of the kalman filter for inference in state space models with unknown noise distributions the kalman filter is frequently used for state estimation in state space models when the standard gaussian noise assumption does not apply a problem arises however in that inference based on the incorrect gaussian assumption can lead to misleading or erroneous conclusions about the relationship of the kalman filter estimate to the true unknown state this note shows how inequalities from probability theory associated with the probabilities of convex sets have potential for characterizing the estimation error of a kalman filter in such a non gaussian distribution free setting

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

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

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

a new algorithm for latent state estimation in non linear time series models we consider the problem of optimal state estimation for a wide class of non linear time series models a modified sigma point filter is proposed which uses a new procedure for generating sigma points unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator the effectiveness of the new filtering procedure is assessed through simulation examples

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

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

on the nonlinear and nonnormal filter using rejection sampling a nonlinear and or nonnormal filter is proposed using rejection sampling generating random draws of the state vector directly from the filtering density the filtering estimate is simply obtained as the arithmetic average of the random draws in the proposed filter the random draws are recursively generated at each time monte carlo experiments indicate that the proposed nonlinear and nonnormal filter shows a good performance

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

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

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

bayesian inference in cyclical component dynamic linear models abstract dynamic linear models dlm s with time varying cyclical components are developed for the analysis of time series with persistent though time varying cyclical behavior the development covers inference on wavelengths of possibly several persistent cycles in nonstationary time series permitting explicit time variation in amplitudes and phases of component waveforms decomposition of stochastic inputs into purely observational noise and innovations that impact on the waveform characteristics with extensions to incorporate ranges of time varying time series and regression terms wihin the standard dlm context bayesian inference via iterative stochastic simulation methods is developed and illustrated some indications of model extensions and generalizations are given in addition to the specific focus on cyclical component models the development provides the basis for bayesian inference via stochastic simulation for state evolution matrix parameters and variance components in dlm s building o

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

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

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

markov switching time series models with application to a daily runoff series we consider a class of bayesian dynamic models that involve switching among various regimes as an example we produce a model for a runoff time series exhibiting pulsatile behavior this model is a mixture of three autoregressive models which accommodate rising falling and normal states in the runoff process the mechanism for switching among regimes is given by a three state markov chain whose transition probabilities are modeled on the basis both of past runoff values and of a time series of rainfall data we adopt the bayesian approach and use the gibbs sampler in the numerical analyses a study of a daily runoff series from lake taupo new zealand is given

a vertex model with an unbounded number of components a model which is an infinite component generalization of the six vertex model is proposed the method of solution is based on a random walk representation of states the bethe ansatz equations for periodic boundary conditions are obtained the partition function of the finite model with special arrow configurations at the boundary of a square is given in contrast to analogous solutions of korepin 1982 and baxter 1982 it has the form of an evaluable determinant

bayesian lasso regression summary the lasso estimate for linear regression corresponds to a posterior mode when independent double exponential prior distributions are placed on the regression coefficients this paper intro duces new aspects of the broader bayesian treatment of lasso regression a direct characterization of the regression coefficients posterior distribution is provided and computation and inference under this characterization is shown to be straightforward emphasis is placed on point estima tion using the posterior mean which facilitates prediction of future observations via the posterior predictive distribution it is shown that the standard lasso prediction method does not neces sarily agree with model based bayesian predictions a new gibbs sampler for bayesian lasso regression is introduced

bayesian model discrimination and bayes factors for linear gaussian state space models summary it is shown how to discriminate between different linear gaussian state space models for a given time series by means of a bayesian approach which chooses the model that minimizes the expected loss a practical implementation of this procedure requires a fully bayesian analysis for both the state vector and the unknown hyperparameters and is carried out by markov chain monte carlo methods an application to some non standard situations such as testing hypotheses on the boundary of the parameter space discriminating non nested models and discrimination of more than two models is discussed in detail

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

multinomial inverse regression for text analysis text data including speeches stories and other document forms are often connected to sentiment variables that are of interest for research in marketing economics and elsewhere it is also very high dimensional and difficult to incorporate into statistical analyses this article introduces a straightforward framework of sentiment sufficient dimension reduction for text data multinomial inverse regression is introduced as a general tool for simplifying predictor sets that can be represented as draws from a multinomial distribution and we show that logistic regression of phrase counts onto document annotations can be used to obtain low dimensional document representations that are rich in sentiment information to facilitate this modeling a novel estimation technique is developed for multinomial logistic regression with very high dimensional response in particular independent laplace priors with unknown variance are assigned to each regression coefficient and we detail an efficient routine for ma

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

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 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

matching hierarchical structures using association graphs it is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a derived association graph however it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized i e are trees since maximal cliques are not constrained to preserve the partial order we provide a solution to the problem of matching two trees by constructing the association graph using the graph theoretic concept of connectivity we prove that in the new formulation there is a one to one correspondence between maximal cliques and maximal subtree isomorphisms this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin straus theorem and we use replicator dynamical systems developed in theoretical biology to solve it such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations the framework is also extended to the matching of attributed trees by using weighted association graphs we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees

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

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

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and 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

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

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

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

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

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