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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
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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 FREE CHAPTER 2. Chapter 2 Programming Probabilistically 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

4.6 Logistic regression

The logistic regression model is a generalization of the linear regression model, which we can use when the response variable is binary. This model uses the logistic function as an inverse link function. Let’s get familiar with this function before we move on to the model:

logistic(z) = ---1--- 1+ e−z

For our purpose, the key property of the logistic function is that irrespective of the values of its argument z, the result will always be a number in the [0-1] interval. Thus, we can see this function as a convenient way to compress the values computed from a linear model into values that we can feed into a Bernoulli distribution. This logistic function is also known as the sigmoid function because of its characteristic S-shaped aspect, as we can see from Figure 4.10.

PIC

Figure 4.10: Logistic function

4.6.1 The logistic model

We have almost all the elements to turn a simple linear regression into a simple logistic regression. Let’s begin with the case of only two classes...

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