What this book covers
Chapter 1, Thinking Probabilistically – A Bayesian Inference Primer, tells us about Bayes' theorem and its implications for data analysis. We then proceed to describe the Bayesian-way of thinking and how and why probabilities are used to deal with uncertainty. This chapter contains the foundational concepts used in the rest of the book.
Chapter 2, Programming Probabilistically – A PyMC3 Primer, revisits the concepts from the previous chapter, this time from a more computational perspective. The PyMC3 library is introduced and we learn how to use it to build probabilistic models, get results by sampling from the posterior, diagnose whether the sampling was done right, and analyze and interpret Bayesian results.
Chapter 3, Juggling with Multi-Parametric and Hierarchical Models, tells us about the very basis of Bayesian modeling and we start adding complexity to the mix. We learn how to build and analyze models with more than one parameter and how to put structure into models, taking advantages of hierarchical models.
Chapter 4, Understanding and Predicting Data with Linear Regression Models, tells us about how linear regression is a very widely used model per se and a building block of more complex models. In this chapter, we apply linear models to solve regression problems and how to adapt them to deal with outliers and multiple variables.
Chapter 5, Classifying Outcomes with Logistic Regression, generalizes the the linear model from previous chapter to solve classification problems including problems with multiple input and output variables.
Chapter 6, Model Comparison, discusses the difficulties associated with comparing models that are common in statistics and machine learning. We will also learn a bit of theory behind the information criteria and Bayes factors and how to use them to compare models, including some caveats of these methods.
Chapter 7, Mixture Models, discusses how to mix simpler models to build more complex ones. This leads us to new models and also to reinterpret models learned in previous chapters. Problems, such as data clustering and dealing with count data, are discussed.
Chapter 8, Gaussian Processes, closes the book by briefly discussing some more advanced concepts related to non-parametric statistics. What kernels are, how to use kernelized linear regression, and how to use Gaussian processes for regression are the central themes of this chapter.
