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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

8.12 Exercises

  1. For the example in the Covariance functions and kernels section, make sure you understand the relationship between the input data and the generated covariance matrix. Try using other input such as data = np.random.normal(size=4).

  2. Rerun the code generating Figure 8.3 and increase the number of samples obtained from the GP prior to around 200. In the original figure, the number of samples is 2. What is the range of the generated values?

  3. For the generated plot in the previous exercise, compute the standard deviation for the values at each point. Do this in the following form:

    • Visually, just observing the plots

    • Directly from the values generated from pz.MVNormal(.).rvs

    • By inspecting the covariance matrix (if you have doubts go back to exercise 1)

    Did the values you get from these three methods match?

  4. Use test points np.linspace(np.floor(x.min()), 20, 100)[:,None] and re-run model_reg. Plot the results. What did you observe? How is this related to the specification...

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