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Full Description
With the increasing prevalence of big data and sparse data, and rapidly growing data-centric approaches to scientific research, students must develop effective data analysis skills at an early stage of their academic careers. This detailed guide to data modeling in the sciences is ideal for students and researchers keen to develop their understanding of probabilistic data modeling beyond the basics of p-values and fitting residuals. The textbook begins with basic probabilistic concepts, models of dynamical systems and likelihoods are then presented to build the foundation for Bayesian inference, Monte Carlo samplers and filtering. Modeling paradigms are then seamlessly developed, including mixture models, regression models, hidden Markov models, state-space models and Kalman filtering, continuous time processes and uniformization. The text is self-contained and includes practical examples and numerous exercises. This would be an excellent resource for courses on data analysis within the natural sciences, or as a reference text for self-study.
Contents
Part I. Concepts from Modeling, Inference, and Computing: 1. Probabilistic modeling and inference; 2. Dynamical systems and Markov processes; 3. Likelihoods and latent variables; 4. Bayesian inference; 5. Computational inference; Part II. Statistical Models: 6. Regression models; 7. Mixture models; 8. Hidden Markov models; 9. State-space models; 10. Continuous time models*; Part III. Appendix: Appendix A: Notation and other conventions; Appendix B: Numerical random variables; Appendix C: The Kronecker and Dirac deltas; Appendix D: Memoryless distributions; Appendix E: Foundational aspects of probabilistic modeling; Appendix F: Derivation of key relations; References; Index.
