- Use the grid approach with other priors; for example, try with prior = (grid <= 0.5).astype(int) or prior = abs(grid - 0.5), or try defining your own crazy priors. Experiment with other data, such as increasing the total amount of data or making it more or less even in terms of the number of heads you observe.
- In the code we use to estimate π, keep N fixed and re-run the code a couple of times. Notice that the results are different because we are using random numbers, but also check that the errors are more or less in the same order. Try changing the number of N points and re-run the code. Can you guesstimate how the number of N points and the error are related? For a better estimation, you may want to modify the code to compute the error as a function of N. You can also run the code a few times with the same N and compute the mean error and standard deviation...
Bayesian Analysis with Python
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Bayesian Analysis with Python
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Overview of this book
The second edition of Bayesian Analysis with Python is an introduction to the main concepts of applied Bayesian inference and its practical implementation in Python using PyMC3, a state-of-the-art probabilistic programming library, and ArviZ, a new library for exploratory analysis of Bayesian models.
The main concepts of Bayesian statistics are covered using a practical and computational approach. Synthetic and real data sets are used to introduce several types of models, such as generalized linear models for regression and classification, mixture models, hierarchical models, and Gaussian processes, among others.
By the end of the book, you will have a working knowledge of probabilistic modeling and you will be able to design and implement Bayesian models for your own data science problems. After reading the book you will be better prepared to delve into more advanced material or specialized statistical modeling if you need to.
Table of Contents (11 chapters)
Preface
Free Chapter
Thinking Probabilistically
Programming Probabilistically
Modeling with Linear Regression
Generalizing Linear Models
Model Comparison
Mixture Models
Gaussian Processes
Inference Engines
Where To Go Next?
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