book

Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference

Name: Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference
Author: Cameron Davidson-Pilon
ISBN: 9780133902914

by Cameron Davidson-Pilon

October 2015

Beginner to intermediate

300 pages

7h 19m

English

Addison-Wesley Professional

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About This eBook
Title Page
Copyright Page
Dedication Page
Contents
Foreword
Preface
Acknowledgments
About the Author
1. The Philosophy of Bayesian Inference
1.1 Introduction1.1.1 The Bayesian State of Mind1.1.2 Bayesian Inference in Practice1.1.3 Are Frequentist Methods Incorrect?1.1.4 A Note on “Big Data”1.2 Our Bayesian Framework1.2.1 Example: Mandatory Coin-Flip1.2.2 Example: Librarian or Farmer?1.3 Probability Distributions1.3.1 Discrete Case1.3.2 Continuous Case1.3.3 But What Is λ?1.4 Using Computers to Perform Bayesian Inference for Us1.4.1 Example: Inferring Behavior from Text-Message Data1.4.2 Introducing Our First Hammer: PyMC1.4.3 Interpretation1.4.4 What Good Are Samples from the Posterior, Anyway?1.5 Conclusion1.6 Appendix1.6.1 Determining Statistically if the Two λs Are Indeed Different?1.6.2 Extending to Two Switchpoints1.7 Exercises1.7.1 Answers1.8 References

2. A Little More on PyMC
2.1 Introduction2.1.1 Parent and Child Relationships2.1.2 PyMC Variables2.1.3 Including Observations in the Model2.1.4 Finally. . .2.2 Modeling Approaches2.2.1 Same Story, Different Ending2.2.2 Example: Bayesian A/B Testing2.2.3 A Simple Case2.2.4 A and B Together2.2.5 Example: An Algorithm for Human Deceit2.2.6 The Binomial Distribution2.2.7 Example: Cheating Among Students2.2.8 Alternative PyMC Model2.2.9 More PyMC Tricks2.2.10 Example: Challenger Space Shuttle Disaster2.2.11 The Normal Distribution2.2.12 What Happened the Day of the Challenger Disaster?2.3 Is Our Model Appropriate?2.3.1 Separation Plots2.4 Conclusion2.5 Appendix2.6 Exercises2.6.1 Answers2.7 References
3. Opening the Black Box of MCMC
3.1 The Bayesian Landscape3.1.1 Exploring the Landscape Using MCMC3.1.2 Algorithms to Perform MCMC3.1.3 Other Approximation Solutions to the Posterior3.1.4 Example: Unsupervised Clustering Using a Mixture Model3.1.5 Don’t Mix Posterior Samples3.1.6 Using MAP to Improve Convergence3.2 Diagnosing Convergence3.2.1 Autocorrelation3.2.2 Thinning3.2.3 pymc.Matplot.plot()3.3 Useful Tips for MCMC3.3.1 Intelligent Starting Values3.3.2 Priors3.3.3 The Folk Theorem of Statistical Computing3.4 Conclusion3.5 References
4. The Greatest Theorem Never Told
4.1 Introduction4.2 The Law of Large Numbers4.2.1 Intuition4.2.2 Example: Convergence of Poisson Random Variables4.2.3 How Do We Compute Var(Z)?4.2.4 Expected Values and Probabilities4.2.5 What Does All This Have to Do with Bayesian Statistics?4.3 The Disorder of Small Numbers4.3.1 Example: Aggregated Geographic Data4.3.2 Example: Kaggle’s U.S. Census Return Rate Challenge4.3.3 Example: How to Sort Reddit Comments4.3.4 Sorting!4.3.5 But This Is Too Slow for Real-Time!4.3.6 Extension to Starred Rating Systems4.4 Conclusion4.5 Appendix4.5.1 Derivation of Sorting Comments Formula4.6 Exercises4.6.1 Answers4.7 References
5. Would You Rather Lose an Arm or a Leg?
5.1 Introduction5.2 Loss Functions5.2.1 Loss Functions in the Real World5.2.2 Example: Optimizing for the Showcase on The Price Is Right5.3 Machine Learning via Bayesian Methods5.3.1 Example: Financial Prediction5.3.2 Example: Kaggle Contest on Observing Dark Worlds5.3.3 The Data5.3.4 Priors5.3.5 Training and PyMC Implementation5.4 Conclusion5.5 References
6. Getting Our Priorities Straight
6.1 Introduction6.2 Subjective versus Objective Priors6.2.1 Objective Priors6.2.2 Subjective Priors6.2.3 Decisions, Decisions . . .6.2.4 Empirical Bayes6.3 Useful Priors to Know About6.3.1 The Gamma Distribution6.3.2 The Wishart Distribution6.3.3 The Beta Distribution6.4 Example: Bayesian Multi-Armed Bandits6.4.1 Applications6.4.2 A Proposed Solution6.4.3 A Measure of Good6.4.4 Extending the Algorithm6.5 Eliciting Prior Distributions from Domain Experts6.5.1 Trial Roulette Method6.5.2 Example: Stock Returns6.5.3 Pro Tips for the Wishart Distribution6.6 Conjugate Priors6.7 Jeffreys Priors6.8 Effect of the Prior as N Increases6.9 Conclusion6.10 Appendix6.10.1 Bayesian Perspective of Penalized Linear Regressions6.10.2 Picking a Degenerate Prior6.11 References
7. Bayesian A/B Testing
7.1 Introduction7.2 Conversion Testing Recap7.3 Adding a Linear Loss Function7.3.1 Expected Revenue Analysis7.3.2 Extending to an A/B Experiment7.4 Going Beyond Conversions: t-test7.4.1 The Setup of the t-test7.5 Estimating the Increase7.5.1 Creating Point Estimates7.6 Conclusion7.7 References
Glossary
Index
Code Snippets

Content preview from Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference

Index

Symbols and Numbers

α See Alpha (α) hyperparameter

β See Beta

Γ See Gamma

φ (phi) cumulative distribution, 123

μ See Mu (μ) mean

ν (nu) parameter, in t-tests, 204–207

θ (theta), Jeffreys priors and, 185–189

σ (sigma), standard deviation, in t-tests, 204–207

τ (tau) See Tau (τ) parameter

Ψ (psi), Jeffreys priors and, 185–187

λ See Lambda (λ) unknown parameter

95% least plausible value, 115–117

A

AAPL (Apple, Inc.) stock returns, 177–181

A/B testing

adding linear loss function, 196–197

BEST t-test and, 204–207

conversions and, 195–198

creating point estimates, 210–211

estimating increase in, 207–210

expected revenue analysis, 198–204

PyMC stategies for, 14–17

value of, 38

Absolute loss function, 128

Aggregated geographic data, Law of Large ...

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Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference

by Cameron Davidson-Pilon