Bayesian modeling with PyMC3 and exploratory analysis of Bayesian models with ArviZ
Key Features
A step-by-step guide to conduct Bayesian data analyses using PyMC3 and ArviZ
A modern, practical and computational approach to Bayesian statistical modeling
A tutorial for Bayesian analysis and best practices with the help of sample problems and practice exercises.
Book Description
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.
What you will learn
Build probabilistic models using the Python library PyMC3
Analyze probabilistic models with the help of ArviZ
Acquire the skills required to sanity check models and modify them if necessary
Understand the advantages and caveats of hierarchical models
Find out how different models can be used to answer different data analysis questions
Compare models and choose between alternative ones
Discover how different models are unified from a probabilistic perspective
Think probabilistically and benefit from the flexibility of the Bayesian framework
Who this book is for
If you are a student, data scientist, researcher, or a developer looking to get started with Bayesian data analysis and probabilistic programming, this book is for you. The book is introductory so no previous statistical knowledge is required, although some experience in using Python and NumPy is expected.
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"In more than three centuries of science everything has changed except perhaps one thing: the love for the simple."
ā Jorge Wagensberg
Musicāfrom classical compositions to Sheena is a Punk Rocker by The Ramones, passing through the unrecognized hit from a garage band and Piazzolla's Libertangoāis made from recurring patterns. The same scales, combinations of chords, riffs, motifs, and so on appear over and over again, giving rise to a wonderful sonic landscape capable of eliciting and modulating the entire range of emotions humans can experience. In a similar fashion, the universe of statistics and machine learning (ML) is built upon recurring patterns, small motifs that appear now and again. In this chapter, we are going to look at one of the most popular and useful of them, the linear model (or motif, if you want). This is a very useful model on its own and also the building block of many other models. If you ever took a statistics course (even a non-Bayesian one), you may have heard of simple and multiple linear regression, logistic regression, ANOVA, ANCOVA, and so on. All these methods are variations of the same underlying motif, the linear regression model. In this chapter, we will cover the following topics:
Simple linear regression
Robust linear regression
Hierarchical linear regression
Polynomial regression
Multiple linear regression
Interactions
Variable variance
Simple linear regression
Many problems we find in science, engineering, and business are of the following form. We have a variable
and we want to model/predict a variable
. Importantly, these variables are paired like
. In the most simple scenario, known as simple linear regression, both
and
are uni-dimensional continuous random variables. By continuous, we mean a variable represented using real numbers (or floats, if you wish), and using NumPy, you will represent the variables
or
as one-dimensional arrays. Because this is a very common model, the variables get proper names. We call the
variables the dependent, predicted, or outcome variables, and the
variables the independent, predictor, or input variables. When
is a matrix (we have different variables), we have what is known as multiple linear regression. In this and the following chapter, we will explore these and other linear regression models.
Some typical situations where linear regression models can be used are:
Model the relationship between factors like rain, soil salinity, and the presence/absence of fertilizer in crop productivity. Then, answer questions such as: is the relationship linear? How strong is this relationship? Which factors have the strongest effect?
Find a relationship between average chocolate consumption by country and the number of Nobel laureates in that country, and then understand why this relationshi...
