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Bayesian Analysis with Python

You're reading from   Bayesian Analysis with Python A practical guide to probabilistic modeling

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Product type Paperback
Published in Jan 2024
Publisher Packt
ISBN-13 9781805127161
Length 394 pages
Edition 3rd Edition
Languages
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Author (1):
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Osvaldo Martin Osvaldo Martin
Author Profile Icon Osvaldo Martin
Osvaldo Martin
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Table of Contents (15) Chapters Close

Preface
1. Chapter 1 Thinking Probabilistically 2. Chapter 2 Programming Probabilistically FREE CHAPTER 3. Chapter 3 Hierarchical Models 4. Chapter 4 Modeling with Lines 5. Chapter 5 Comparing Models 6. Chapter 6 Modeling with Bambi 7. Chapter 7 Mixture Models 8. Chapter 8 Gaussian Processes 9. Chapter 9 Bayesian Additive Regression Trees 10. Chapter 10 Inference Engines 11. Chapter 11 Where to Go Next 12. Bibliography
13. Other Books You May Enjoy
14. Index

4.10 Summary

In this chapter, we have learned about linear regression, which aims to model the relationship between a dependent variable and an independent variable. We have seen how to use PyMC to fit a linear regression model and how to interpret the results and make plots that we can share with different audiences.

Our first example was a model with a Gaussian response. But then we saw that this is just one assumption and we can easily change it to deal with non-Gaussian responses, such as count data, using a NegativeBinomial regression model or a logistic regression model for binary data. We saw that when doing so we also need to set an inverse link function to map the linear predictor to the response variable. Using a Student’s t-distribution as the likelihood can be useful for dealing with outliers. We spent most of the chapter modeling the mean as a linear function of the independent variable, but we learned that we can also model other parameters, like the variance. This...

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