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Bayesian Analysis with Python

Bayesian Analysis with Python - Third Edition

By : Osvaldo Martin
4.6 (21)
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Bayesian Analysis with Python

Bayesian Analysis with Python

4.6 (21)
By: Osvaldo Martin

Overview of this book

The third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection. In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets. By the end of this book, you’ll understand probabilistic modeling and be able to design and implement Bayesian models for data science, with a strong foundation for more advanced study. *Email sign-up and proof of purchase required
Table of Contents (15 chapters)
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Preface
12
Bibliography
13
Other Books You May Enjoy
14
Index

4.9 Multiple linear regression

So far, we have been working with one dependent variable and one independent variable. Nevertheless, it is not unusual to have several independent variables that we want to include in our model. Some examples could be:

  • Perceived quality of wine (dependent) and acidity, density, alcohol level, residual sugar, and sulfates content (independent variables)

  • A student’s average grades (dependent) and family income, distance from home to school, and mother’s education level (categorical variable)

We can easily extend the simple linear regression model to deal with more than one independent variable. We call this model multiple linear regression or, less often, multivariable linear regression (not to be confused with multivariate linear regression, the case where we have multiple dependent variables).

In a multiple linear regression model, we model the mean of the dependent variable as follows:

μ = 𝛼 + 𝛽1X1 + 𝛽2X2 + ⋅⋅⋅+ 𝛽kXk

Using linear algebra notation, we can write a shorter...

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