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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

8.6 Gaussian process regression with PyMC

The gray line in Figure 8.4 is a sin function. We are going to assume we don’t know this function and instead, all we have is a set of data points (dots). Then we use a Gaussian process to approximate the function that generated those data points.

PIC

Figure 8.4: Synthetic data (dots) generated from a known function (line)

GPs are implemented in PyMC as a series of Python classes that deviate a little bit from what we have seen in previous models; nevertheless, the code is still very PyMConic. I have added a few comments in the following code to guide you through the key steps of defining a GP with PyMC.

Code 8.3

# A one-dimensional column vector of inputs. 
X = x[:, None] 
 
with pm.Model() as model_reg: 
    # hyperprior for lengthscale kernel parameter 
    ℓ = pm.InverseGamma("ℓ", 7, 17) 
    # instanciate...
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