For the first model, change the prior for the mean to a Gaussian distribution centered at the empirical mean and play with a couple of reasonable values for the standard deviation of this prior. How robust/sensitive are the inferences to these changes? What do you think of using a Gaussian, which is an unbounded distribution, to model bounded data like this? Remember we said is not possible to get values below 0 or above 100.
Using the data from the first example, compute the empirical mean and the standard deviation with and without outliers. Compare those results to the Bayesian estimation using the Gaussian and Student's t-distribution . Repeat the exercise adding more outliers.
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Modify the tips example to make it robust to outliers. Try with one shared
for all groups and also with one per group. Run posterior predictive checks to assess these three models.
Compute the probability of superiority directly from the posterior (without computing Cohen's d first). You can use the...
Bayesian Analysis with Python
Bayesian Analysis with Python
Overview of this book
The purpose of this book is to teach the main concepts of Bayesian data analysis. We will learn how to effectively use PyMC3, a Python library for probabilistic programming, to perform Bayesian parameter estimation, to check models and validate them. This book begins presenting the key concepts of the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems.
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Bayesian Analysis with Python
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Table of Contents (15 chapters)
Bayesian Analysis with Python
Credits
About the Author
About the Reviewer
www.PacktPub.com
Preface
Free Chapter
Thinking Probabilistically - A Bayesian Inference Primer
Programming Probabilistically – A PyMC3 Primer
Juggling with Multi-Parametric and Hierarchical Models
Understanding and Predicting Data with Linear Regression Models
Classifying Outcomes with Logistic Regression
Model Comparison
Mixture Models
Gaussian Processes
Index
Customer Reviews