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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

9.4 Constant and linear response

By default, PyMC-BART will fit trees that return a single value at each leaf node. This is a simple approach that usually works just fine. However, it is important to understand its implications. For instance, this means that predictions for any value outside the range of the observed data used to fit the model will be constants. To see this, go back and check Figure 9.2. This tree will return 1.9 for any value below c1. Notice that this will still be the case if we, instead, sum a bunch of trees, because summing a bunch of constant values results in yet another constant value.

Whether this is a problem or not is up to you and the context in which you apply the BART model. Nevertheless, PyMC-BART offers a response argument that you pass to the BART random variable. Its default value is "constant". You can change it to "linear", in which case PyMC-BART will return a linear fit at each leaf node or "mix", which will propose...

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