Stochastic Modeling of Scientific Data

Peter Guttorp

• Publisher: Chapman and Hall/CRC
• Year: 2018
• eBook ISBN: 9781351413657
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• CHAPTER 1. Introduction
• CHAPTER 2. Discrete time Markov chains
• CHAPTER 3. Continuous time Markov chains
• CHAPTER 4. Markov random fields
• CHAPTER 5. Point processes
• CHAPTER 6. Brownian motion and diffusion
• APPENDIX A. Some statistical theory
• APPENDIX B. Linear difference equations with constant coefficients
• APPENDIX C. Some theory of partial differential equations
• References
• Index of results
• Applications and examples
• Index of notation
• Index of terms
• Data sets