Bayesian Inference of State Space Models

1. Front Matter

   Pages i-xv

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2. State Space Models

   • Kostas Triantafyllopoulos

   Pages 1-20

3. Matrix Algebra, Probability and Statistics

   • Kostas Triantafyllopoulos

   Pages 21-61

4. The Kalman Filter

   • Kostas Triantafyllopoulos

   Pages 63-109

5. Model Specification and Model Performance

   • Kostas Triantafyllopoulos

   Pages 111-208

6. Multivariate State Space Models

   • Kostas Triantafyllopoulos

   Pages 209-261

7. Non-Linear and Non-Gaussian State Space Models

   • Kostas Triantafyllopoulos

   Pages 263-339

8. The State Space Model in Finance

   • Kostas Triantafyllopoulos

   Pages 341-402

9. Dynamic Systems and Control

   • Kostas Triantafyllopoulos

   Pages 403-475

10. Back Matter

    Pages 477-495

    PDF

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.

• State space models
• Bayesian estimation
• Financial time series
• Stochastic volatility
• Sequential Monte Carlo
• Dynamic models
• Non Gaussian time series
• Volatility models
• State space in dynamic systems
• Bayesian forecasting
• Control theory
• Systems stability

“The idea of this book is to bring together the mentioned models and make them available to a broad audience. The book is written from a statistician’s perspective. It uses a number of data sets from a wide range of disciplines. … It is aimed at students at the higher end of undergraduate or graduate level but also at scientists for self-study.” (Wolfgang Näther, zbMATH 1480.62003, 2022)

• School of Mathematics, University of Sheffield, Sheffield, UK

  Kostas Triantafyllopoulos

Kostas Triantafyllopoulos is a Senior Lecturer at the School of Mathematics and Statistics of the University of Sheffield. He holds a PhD in Statistics from the University of Warwick and prior to Sheffield worked as a Research Associate at the University of Bristol and as a Lecturer at the University of Newcastle upon Tyne. His research interests include Bayesian inference of time series models and statistical process control. He has published widely and is involved in research grants including the Nuffield Foundation, the NHS and the Engineering and Physical Sciences Research Council (UK). He has wide teaching experience in statistics and has supervised a number of doctoral students and postdoctoral fellows.

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