Data Modeling for the Sciences Applications Basics Computations 1st Edition by Steve Pressé, Ioannis Sgouralis ISBN 9781009098502 1009098500

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ISBN 10: 1009098500
ISBN 13: 9781009098502
Author: Steve Pressé, Ioannis Sgouralis

Data Modeling for the Sciences Applications Basics Computations 1st Edition Table of contents:

Part I Concepts from Modeling, Inference, and Computing

1 Probabilistic Modeling and Inference

1.1 Modeling with Data

1.2 Working with Random Variables

1.3 Data-Driven Modeling and Inference

1.4 Exercise Problems

Additional Reading

2 Dynamical Systems and Markov Processes

2.1 Why Do We Care about Stochastic Dynamical Models?

2.2 Forward Models of Dynamical Systems

2.3 Systems with Discrete State-Spaces in Continuous Time

2.4 Systems with Discrete State-Spaces in Discrete Time

2.5 Systems with Continuous State-Spaces in Discrete Time

2.6 Systems with Continuous State-Spaces in Continuous Time

2.7 Exercise Problems

Additional Reading

3 Likelihoods and Latent Variables

3.1 Quantifying Measurements with Likelihoods

3.2 Observations and Associated Measurement Noise

3.3 Exercise Problems

Additional Reading

4 Bayesian Inference

4.1 Modeling in Bayesian Terms

4.2 The Logistics of Bayesian Formulations: Priors

4.3 EM for Posterior Maximization

4.4 Hierarchical Bayesian Formulations and Graphical Representations

4.5 Bayesian Model Selection

4.6 Information Theory

4.7 Exercise Problems

Additional Reading

5 Computational Inference

5.1 The Fundamentals of Statistical Computation

5.2 Basic MCMC Samplers

5.3 Processing and Interpretation of MCMC

5.4 Advanced MCMC Samplers

5.5 Exercise Problems

Additional Reading

Part II Statistical Models

6 Regression Models

6.1 The Regression Problem

6.2 Nonparametric Regression in Continuous Space: Gaussian Process

6.3 Nonparametric Regression in Discrete Space: Beta Process Bernoulli Process

6.4 Exercise Problems

Additional Reading

7 Mixture Models

7.1 Mixture Model Formulations with Observations

7.2 MM in the Bayesian Paradigm

7.3 The Infinite MM and the Dirichlet Process

7.4 Exercise Problems

Additional Reading

8 Hidden Markov Models

8.1 Introduction

8.2 The Hidden Markov Model

8.3 The Hidden Markov Model in the Frequentist Paradigm

8.4 The Hidden Markov Model in the Bayesian Paradigm

8.5 Dynamical Variants of the Bayesian HMM

8.6 The Infinite Hidden Markov Model

8.7 A Case Study in Fluorescence Spectroscopy

8.8 Exercise Problems

Additional Reading

9 State-Space Models

9.1 State-Space Models

9.2 Gaussian State-Space Models

9.3 Linear Gaussian State-Space Models

9.4 Bayesian State-Space Models and Estimation

9.5 Exercise Problems

Additional Reading

10 Continuous Time Models

10.1 Modeling in Continuous Time

10.2 MJP Uniformization and Virtual Jumps

10.3 Hidden MJP Sampling with Uniformization and Filtering

10.4 Sampling Trajectories and Model Parameters

10.5 Exercise Problems

Additional Reading

Part III Appendices

Appendix A Notation and Other Conventions

A.1 Time and Other Physical Quantities

A.2 Random Variables and Other Mathematical Notions

A.3 Collections

Appendix B Numerical Random Variables

B.1 Continuous Random Variables

B.2 Discrete Random Variables

Appendix C The Kronecker and Dirac Deltas

C.1 Kronecker Delta

C.2 Dirac delta

Appendix D Memoryless Distributions

Appendix E Foundational Aspects of Probabilistic Modeling

E.1 Outcomes and Events

E.2 The Measure of Probability

E.3 Random Variables

E.4 The Measurables

E.5 A Comprehensive Modeling Overview

Additional Reading

Appendix F Derivation of Key Relations

F.1 Relations in

F.2 Relations in

F.3 Relations in

F.4 Relations in

F.5 Relations in

F.6 Relations in

F.7 Relations in

F.8 Relations in

Index

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Tags: Steve Pressé, Ioannis Sgouralis, Data Modeling, Sciences Applications, Basics Computations