The main idea discussed in this chapter is a rather simple one: in order to predict the mean of an output variable, we can apply an arbitrary function to a linear combination of input variables. I know I already said this at the beginning of the chapter, but repetition is important. We call that arbitrary function the inverse link function. The only restriction we have in choosing such a function is that the output has to be adequate to be used as a parameter of the sampling distribution (generally the mean). One situation in which we would like to use an inverse link function is when working with categorical variables, another is when the data can only take positive values, and yet another is when we need a variable in the [0, 1] interval. All these different variations become different models; many of those models are routinely used as statistical tools, and their application...
Bayesian Analysis with Python
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Bayesian Analysis with Python
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Overview of this book
The second edition of Bayesian Analysis with Python is an introduction to the main concepts of applied Bayesian inference and its practical implementation in Python using PyMC3, a state-of-the-art probabilistic programming library, and ArviZ, a new library for exploratory analysis of Bayesian models.
The main concepts of Bayesian statistics are covered using a practical and computational approach. Synthetic and real data sets are used to introduce several types of models, such as generalized linear models for regression and classification, mixture models, hierarchical models, and Gaussian processes, among others.
By the end of the book, you will have a working knowledge of probabilistic modeling and you will be able to design and implement Bayesian models for your own data science problems. After reading the book you will be better prepared to delve into more advanced material or specialized statistical modeling if you need to.
Table of Contents (11 chapters)
Preface
Free Chapter
Thinking Probabilistically
Programming Probabilistically
Modeling with Linear Regression
Generalizing Linear Models
Model Comparison
Mixture Models
Gaussian Processes
Inference Engines
Where To Go Next?
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