A Non Gaussian Family Of State Space Models With Exact Marginal Likelihood

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A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood

Author : Dani Gamerman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood by : Dani Gamerman

Download or read book A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood written by Dani Gamerman and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Gaussian assumption generally employed in many state-space models is usually not satisfied for real time series. Thus, in this work, a broad family of non-Gaussian models is defined by integrating and expanding previous work in the literature. The expansion is obtained at two levels: at the observational level, it allows for many distributions not previously considered, and at the latent state level, it involves an expanded specification for the system evolution. The class retains analytical availability of the marginal likelihood function, uncommon outside Gaussianity. This expansion considerably increases the applicability of the models and solves many previously existing problems such as long-term prediction, missing values and irregular temporal spacing. Inference about the state components can be performed because of the introduction of a new and exact smoothing procedure, in addition to filtered distributions. Inference for the hyperparameters is presented from the classical and Bayesian perspectives. The results seem to indicate competitive results of the models when compared with other non-Gaussian state-space models available. The methodology is applied to Gaussian and non-Gaussian dynamic linear models with time-varying means and variances and provides a computationally simple solution to inference in these models. The methodology is illustrated in a number of examples.

A Class of Non-Gaussian State Space Models with Exact Likelihood Inference

Author : Drew Creal
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis A Class of Non-Gaussian State Space Models with Exact Likelihood Inference by : Drew Creal

Download or read book A Class of Non-Gaussian State Space Models with Exact Likelihood Inference written by Drew Creal and published by . This book was released on 2014 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The likelihood function for general non-linear, non-Gaussian state space models is a high- dimensional integral with no closed-form solution. In this paper, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that includes stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a non-negative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the maximum likelihood estimator, I also show how to perform filtering and smoothing to estimate the latent variables in the model. Finally, it is also possible to take random draws from the joint posterior distribution of the latent states conditional on the data and the model's parameters, which is valuable for inference of more complex models.

Bayesian Inference of State Space Models

Author : Kostas Triantafyllopoulos
Publisher : Springer Nature
ISBN 13 : 303076124X
Total Pages : 503 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Bayesian Inference of State Space Models by : Kostas Triantafyllopoulos

Download or read book Bayesian Inference of State Space Models written by Kostas Triantafyllopoulos and published by Springer Nature. This book was released on 2021-11-12 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.

Handbook of Discrete-Valued Time Series

Author : Richard A. Davis
Publisher : CRC Press
ISBN 13 : 1466577746
Total Pages : 484 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Discrete-Valued Time Series by : Richard A. Davis

Download or read book Handbook of Discrete-Valued Time Series written by Richard A. Davis and published by CRC Press. This book was released on 2016-01-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model a Wide Range of Count Time Series Handbook of Discrete-Valued Time Series presents state-of-the-art methods for modeling time series of counts and incorporates frequentist and Bayesian approaches for discrete-valued spatio-temporal data and multivariate data. While the book focuses on time series of counts, some of the techniques discussed ca

State Space and Unobserved Component Models

Author : James Durbin
Publisher : Cambridge University Press
ISBN 13 : 9780521835954
Total Pages : 398 pages
Book Rating : 4.8/5 (359 download)

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Book Synopsis State Space and Unobserved Component Models by : James Durbin

Download or read book State Space and Unobserved Component Models written by James Durbin and published by Cambridge University Press. This book was released on 2004-06-10 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of developments in the theory and application of state space modeling, first published in 2004.

Building a Platform for Data-Driven Pandemic Prediction

Author : Dani Gamerman
Publisher : CRC Press
ISBN 13 : 1000457192
Total Pages : 382 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Building a Platform for Data-Driven Pandemic Prediction by : Dani Gamerman

Download or read book Building a Platform for Data-Driven Pandemic Prediction written by Dani Gamerman and published by CRC Press. This book was released on 2021-09-13 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about building platforms for pandemic prediction. It provides an overview of probabilistic prediction for pandemic modeling based on a data-driven approach. It also provides guidance on building platforms with currently available technology using tools such as R, Shiny, and interactive plotting programs. The focus is on the integration of statistics and computing tools rather than on an in-depth analysis of all possibilities on each side. Readers can follow different reading paths through the book, depending on their needs. The book is meant as a basis for further investigation of statistical modelling, implementation tools, monitoring aspects, and software functionalities. Features: A general but parsimonious class of models to perform statistical prediction for epidemics, using a Bayesian approach Implementation of automated routines to obtain daily prediction results How to interactively visualize the model results Strategies for monitoring the performance of the predictions and identifying potential issues in the results Discusses the many decisions required to develop and publish online platforms Supplemented by an R package and its specific functionalities to model epidemic outbreaks The book is geared towards practitioners with an interest in the development and presentation of results in an online platform of statistical analysis of epidemiological data. The primary audience includes applied statisticians, biostatisticians, computer scientists, epidemiologists, and professionals interested in learning more about epidemic modelling in general, including the COVID-19 pandemic, and platform building. The authors are professors at the Statistics Department at Universidade Federal de Minas Gerais. Their research records exhibit contributions applied to a number of areas of Science, including Epidemiology. Their research activities include books published with Chapman and Hall/CRC and papers in high quality journals. They have also been involved with academic management of graduate programs in Statistics and one of them is currently the President of the Brazilian Statistical Association.

Non gaussian state space models for count data: the durbin and koopman methodology

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (181 download)

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Book Synopsis Non gaussian state space models for count data: the durbin and koopman methodology by :

Download or read book Non gaussian state space models for count data: the durbin and koopman methodology written by and published by . This book was released on 1902 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: O objetivo desta tese é o de apresentar e investigar a metodologia de Durbin e Koopman (DK) usada para estimar o espaço de estado de modelos de séries temporais não-Gaussianos, dentro do contexto de modelos estruturais. A abordagem de DK está baseada na avaliação da verossimilhança usando uma eficiente simulação de Monte Carlo, por meio de amostragem por importância e técnicas de redução de variância, tais como variáveis antitéticas e variáveis de controle. Ela também integra conhecidas técnicas existentes no caso Gaussiano tais como o Filtro de Kalman Siavizado e o algoritmo de simulação suavizada. Uma vez que os hiperparâmetros do modelo são estimados, o estado, que contém as componentes do modelo, é estimado pela avaliação da moda a posteriori. Propomos então aproximações para avaliar a média e a variância da distribuição preditiva. São consideradas aplicações usando o modelo de Poisson.

A Family of Multivariate Non-Gaussian Time Series Models

Author : Tevfik Aktekin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis A Family of Multivariate Non-Gaussian Time Series Models by : Tevfik Aktekin

Download or read book A Family of Multivariate Non-Gaussian Time Series Models written by Tevfik Aktekin and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we propose a class of multivariate non-Gaussian time series models which include dynamic versions of many well-known distributions and consider their Bayesian analysis. A key feature of our proposed model is its ability to account for correlations across time as well as across series (contemporary) via a common random environment. The proposed modeling approach yields analytically tractable dynamic marginal likelihoods, a property not typically found outside of linear Gaussian time series models. These dynamic marginal likelihoods can be tied back to known static multivariate distributions such as the Lomax, generalized Lomax, and the multivariate Burr distributions. The availability of the marginal likelihoods allows us to develop efficient estimation methods for various settings using Markov chain Monte Carlo as well as sequential Monte Carlo methods. Our approach can be considered to be a multivariate generalization of commonly used univariate non-Gaussian class of state space models. To illustrate our methodology, we use simulated data examples and a real application of multivariate time series for modeling the joint dynamics of stochastic volatility in financial indexes, the VIX and VXN.

Time Series Analysis by State Space Methods

Author : James Durbin
Publisher : OUP Oxford
ISBN 13 : 0191627194
Total Pages : 369 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Time Series Analysis by State Space Methods by : James Durbin

Download or read book Time Series Analysis by State Space Methods written by James Durbin and published by OUP Oxford. This book was released on 2012-05-03 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition updates Durbin & Koopman's important text on the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbance terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions to this second edition include the filtering of nonlinear and non-Gaussian series. Part I of the book obtains the mean and variance of the state, of a variable intended to measure the effect of an interaction and of regression coefficients, in terms of the observations. Part II extends the treatment to nonlinear and non-normal models. For these, analytical solutions are not available so methods are based on simulation.

Time Series Analysis and Its Applications

Author : Robert H. Shumway
Publisher :
ISBN 13 : 9781475732627
Total Pages : 568 pages
Book Rating : 4.7/5 (326 download)

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Book Synopsis Time Series Analysis and Its Applications by : Robert H. Shumway

Download or read book Time Series Analysis and Its Applications written by Robert H. Shumway and published by . This book was released on 2014-01-15 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Importance Sampling for State Space Models

Author : Borus Martinus Johannes Petrus Jungbacker
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (255 download)

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Book Synopsis On Importance Sampling for State Space Models by : Borus Martinus Johannes Petrus Jungbacker

Download or read book On Importance Sampling for State Space Models written by Borus Martinus Johannes Petrus Jungbacker and published by . This book was released on 2005 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Time Series and Forecasting

Author : Peter J. Brockwell
Publisher : Springer Science & Business Media
ISBN 13 : 1475725264
Total Pages : 429 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Time Series and Forecasting by : Peter J. Brockwell

Download or read book Introduction to Time Series and Forecasting written by Peter J. Brockwell and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.

Bayesian Filtering and Smoothing

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 110703065X
Total Pages : 255 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä

Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Dynamic Linear Models with R

Author : Giovanni Petris
Publisher : Springer Science & Business Media
ISBN 13 : 0387772383
Total Pages : 258 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Dynamic Linear Models with R by : Giovanni Petris

Download or read book Dynamic Linear Models with R written by Giovanni Petris and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: State space models have gained tremendous popularity in recent years in as disparate fields as engineering, economics, genetics and ecology. After a detailed introduction to general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. Whenever possible it is shown how to compute estimates and forecasts in closed form; for more complex models, simulation techniques are used. A final chapter covers modern sequential Monte Carlo algorithms. The book illustrates all the fundamental steps needed to use dynamic linear models in practice, using R. Many detailed examples based on real data sets are provided to show how to set up a specific model, estimate its parameters, and use it for forecasting. All the code used in the book is available online. No prior knowledge of Bayesian statistics or time series analysis is required, although familiarity with basic statistics and R is assumed.

Journal of the American Statistical Association

Author :
Publisher :
ISBN 13 :
Total Pages : 1586 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Journal of the American Statistical Association by :

Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2000 with total page 1586 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gaussian Processes for Machine Learning

Author : Carl Edward Rasmussen
Publisher : MIT Press
ISBN 13 : 026218253X
Total Pages : 266 pages
Book Rating : 4.2/5 (621 download)

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Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen

Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Validation of State-Space Models from a Single Realization of Non-Gaussian Measurements

Author : James C. Spall
Publisher :
ISBN 13 :
Total Pages : 3 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Validation of State-Space Models from a Single Realization of Non-Gaussian Measurements by : James C. Spall

Download or read book Validation of State-Space Models from a Single Realization of Non-Gaussian Measurements written by James C. Spall and published by . This book was released on 1985 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: A methodology is presented for testing whether a dynamic model in linear state-space form accurately describes the system under consideration. Unlike existing procedures it is not necessary to assume that all of the random terms in the model are normally distributed. The methodology is based on a single realization of observations and is relatively easy to implement since it relies on a normalized Kalman filter state estimate. The testing procedure rests on an asymptotic distribution theory for the filter estimate. Control theory; Reprints. (jhd).