Bayesian Modeling and Computation in Python 1st Edition by Osvaldo Martin, Ravin Kumar, Junpeng Lao ISBN 9780367894368 036789436X

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ISBN 10: 036789436X
ISBN 13: 9780367894368
Author: Osvaldo Martin, Ravin Kumar, Junpeng Lao

Bayesian Modeling and Computation in Python 1st Edition Table of contents:

1. Bayesian Inference

1.1. Bayesian Modeling

1.1.1. Bayesian Models

1.1.2. Bayesian Inference

1.2. A DIY Sampler, Do Not Try This at Home

1.3. Say Yes to Automating Inference, Say No to Automated Model Building

1.4. A Few Options to Quantify Your Prior Information

1.4.1. Conjugate Priors

1.4.2. Objective Priors

1.4.3. Maximum Entropy Priors

1.4.4. Weakly Informative Priors and Regularization Priors

1.4.5. Using Prior Predictive Distributions to Assess Priors

1.5. Exercises

2. Exploratory Analysis of Bayesian Models

2.1. There is Life After Inference, and Before Too!

2.2. Understanding Your Assumptions

2.3. Understanding Your Predictions

2.4. Diagnosing Numerical Inference

2.4.1. Effective Sample Size

2.4.2. Potential Scale Reduction Factor R

2.4.3. Monte Carlo Standard Error

2.4.4. Trace Plots

2.4.5. Autocorrelation Plots

2.4.6. Rank Plots

2.4.7. Divergences

2.4.8. Sampler Parameters and Other Diagnostics

2.5. Model Comparison

2.5.1. Cross-validation and LOO

2.5.2. Expected Log Predictive Density

2.5.3. Pareto Shape Parameter, k is Large

2.5.4. Interpreting p_loo When Pareto k

2.5.5. LOO-PIT

2.5.6. Model Averaging

2.6. Exercises

3. Linear Models and Probabilistic Programming Languages

3.1. Comparing Two (or More) Groups

3.1.1. Comparing Two PPLs

3.2. Linear Regression

3.2.1. Linear Penguins

3.2.2. Predictions

3.2.3. Centering

3.3. Multiple Linear Regression

3.3.1. Counterfactuals

3.4. Generalized Linear Models

3.4.1. Logistic Regression

3.4.2. Classifying Penguins

3.4.3. Interpreting Log Odds

3.5. Picking Priors in Regression Models

3.6. Exercises

4. Extending Linear Models

4.1. Transforming Covariates

4.2. Varying Uncertainty

4.3. Interaction Effects

4.4. Robust Regression

4.5. Pooling, Multilevel Models, and Mixed Effects

4.5.1. Unpooled Parameters

4.5.2. Pooled Parameters

4.5.3. Mixing Group and Common Parameters

4.6. Hierarchical Models

4.6.1. Posterior Geometry Matters

4.6.2. Predictions at Multiple Levels

4.6.3. Priors for Multilevel Models

4.7. Exercises

5. Splines

5.1. Polynomial Regression

5.2. Expanding the Feature Space

5.3. Introducing Splines

5.4. Building the Design Matrix using Patsy

5.5. Fitting Splines in PyMC3

5.6. Choosing Knots and Prior for Splines

5.6.1. Regularizing Prior for Splines

5.7. Modeling CO2 Uptake with Splines

5.8. Exercises

6. Time Series

6.1. An Overview of Time Series Problems

6.2. Time Series Analysis as a Regression Problem

6.2.1. Design Matrices for Time Series

6.2.2. Basis Functions and Generalized Additive Model

6.3. Autoregressive Models

6.3.1. Latent AR Process and Smoothing

6.3.2. (S)AR(I)MA(X)

6.4. State Space Models

6.4.1. Linear Gaussian State Space Models and Kalman filter

6.4.2. ARIMA, Expressed as a State Space Model

6.4.3. Bayesian Structural Time Series

6.5. Other Time Series Models

6.6. Model Criticism and Choosing Priors

6.6.1. Priors for Time Series Models

6.7. Exercises

7. Bayesian Additive Regression Trees

7.1. Decision Trees

7.1.1. Ensembles of Decision Trees

7.2. The BART Model

7.3. Priors for BART

7.3.1. Prior Independence

7.3.2. Prior for the Tree Structure Tj

7.3.3. Prior for the Leaf Values uij and Number of Trees m

7.4. Fitting Bayesian Additive Regression Trees

7.5. BART Bikes

7.6. Generalized BART Models

7.7. Interpretability of BARTs

7.7.1. Partial Dependence Plots

7.7.2. Individual Conditional Expectation

7.8. Variable Selection

7.9. Priors for BART in PyMC3

7.10. Exercises

8. Approximate Bayesian Computation

8.1. Life Beyond Likelihood

8.2. Approximating the Approximated Posterior

8.3. Fitting a Gaussian the ABC-way

8.4. Choosing the Distance Function, � and the Summary Statistics

8.4.1. Choosing the Distance

8.4.2. Choosing e

8.4.3. Choosing Summary Statistics

8.5. g-and-k Distribution

8.6. Approximating Moving Averages

8.7. Model Comparison in the ABC Context

8.7.1. Marginal Likelihood and LOO

8.7.2. Model Choice via Random Forest

8.7.3. Model Choice for MA Model

8.8. Choosing Priors for ABC

8.9. Exercises

9. End to End Bayesian Workflows

9.1. Workflows, Contexts, and Questions

9.1.1. Applied Example: Airlines Flight Delays Problem

9.2. Getting Data

9.2.1. Sample Surveys

9.2.2. Experimental Design

9.2.3. Observational Studies

9.2.4. Missing Data

9.2.5. Applied Example: Collecting Airline Flight Delays Data

9.3. Making a Model and Probably More Than One

9.3.1. Questions to Ask Before Building a Bayesian Model

9.3.2. Applied Example: Picking Flight Delay Likelihoods

9.4. Choosing Priors and Predictive Priors

9.4.1. Applied Example: Picking Priors for Flight Delays Model

9.5. Inference and Inference Diagnostics

9.5.1. Applied Example: Running Inference on Flight Delays Models

9.6. Posterior Plots

9.6.1. Applied Example: Posterior of Flight Delays Models

9.7. Evaluating Posterior Predictive Distributions

9.7.1. Applied Example: Posterior Predictive Distributions of Flight Delays

9.8. Model Comparison

9.8.1. Applied Example: Model Comparison with LOO of Flight Delays

9.9. Reward Functions and Decisions

9.9.1. Applied Example: Making Decisions Based on Flight Delays Modeling Results

9.10. Sharing the Results With a Particular Audience

9.10.1. Reproducibility of Analysis Workflow

9.10.2. Understanding the Audience

9.10.3. Static Visual Aids

9.10.4. Reproducible Computing Environments

9.10.5. Applied Example: Presenting Flight Delay Conclusions

9.11. Experimental Example: Comparing Between Two Groups

9.12. Exercises

10. Probabilistic Programming Languages

10.1. A Systems Engineering Perspective of a PPL

10.1.1. Example: Rainier

10.2. Posterior Computation

10.2.1. Getting the Gradient

10.2.2. Example: Near Real Time Inference

10.3. Application Programming Interfaces

10.3.1. Example: Stan and Slicstan

10.3.2. Example: PyMC3 and PyMC4

10.4. PPL Driven Transformations

10.4.1. Log Probabilities

10.4.2. Random Variables and Distributions Transformations

10.4.3. Example: Sampling Comparison between Bounded and Unbounded Random Variables

10.5. Operation Graphs and Automatic Reparameterization

10.6. Effect handling

10.6.1. Example: Effect Handling in TFP and Numpyro

10.7. Base Language, Code Ecosystem, Modularity and Everything Else

10.8. Designing a PPL

10.8.1. Shape Handling in PPLs

10.9. Takeaways for the Applied Bayesian Practitioner

10.10. Exercises

11. Appendiceal Topics

11.1. Probability Background

11.1.1. Probability

11.1.2. Conditional Probability

11.1.3. Probability Distribution

11.1.4. Discrete Random Variables and Distributions

11.1.5. Continuous Random Variables and Distributions

11.1.6. Joint, Conditional and Marginal Distributions

11.1.7. Probability Integral Transform (PIT)

11.1.8. Expectations

11.1.9. Transformations

11.1.10. Limits

11.1.11. Markov Chains

11.2. Entropy

11.3. Kullback-Leibler Divergence

11.4. Information Criterion

11.5. LOO in Depth

11.6. Jeffreys’ Prior Derivation

11.6.1. Jeffreys’ Prior for the Binomial Likelihood in Terms of θ

11.6.2. Jeffreys’ Prior for the Binomial Likelihood in Terms of k

11.6.3. Jeffreys’ Posterior for the Binomial Likelihood

11.7. Marginal Likelihood

11.7.1. The Harmonic Mean Estimator

11.7.2. Marginal Likelihood and Model Comparison

11.7.3. Bayes Factor vs WAIC and LOO

11.8. Moving out of Flatland

11.9. Inference Methods

11.9.1. Grid Method

11.9.2. Metropolis-Hastings

11.9.3. Hamiltonian Monte Carlo

11.9.4. Sequential Monte Carlo

11.9.5. Variational Inference

11.10. Programming References

11.10.1. Which Programming Language?

11.10.2. Version Control

11.10.3. Dependency Management and Package Repositories

11.10.4. Environment Management

11.10.5. Text Editor vs Integrated Development Environment vs Notebook

11.10.6. The Specific Tools Used for this Book

Glossary

Bibliography

Index

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