Think Bayes: Bayesian Statistics in Python, 2nd Edition
- Length: 300 pages
- Edition: 2
- Language: English
- Publisher: O'Reilly Media
- Publication Date: 2021-09-14
- ISBN-10: 149208946X
- ISBN-13: 9781492089469
- Sales Rank: #257528 (See Top 100 Books)
If you know how to program with Python, you’re ready to tackle Bayesian statistics. With this book, you’ll learn how to solve statistical problems with Python code instead of mathematical formulas, using discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems.
Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start.
- Use your existing programming skills to learn and understand Bayesian statistics
- Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing
- Get started with simple examples, using coins, dice, and a bowl of cookies
- Learn computational methods for solving real-world problems
Preface Who Is This Book For? Modeling Working with the Code Installing Jupyter Conventions Used in This Book O’Reilly Online Learning How to Contact Us Contributor List 1. Probability Linda the Banker Probability Fraction of Bankers The Probability Function Political Views and Parties Conjunction Conditional Probability Conditional Probability Is Not Commutative Condition and Conjunction Laws of Probability Theorem 1 Theorem 2 Theorem 3 The Law of Total Probability Summary Exercises 2. Bayes’s Theorem The Cookie Problem Diachronic Bayes Bayes Tables The Dice Problem The Monty Hall Problem Summary Exercises 3. Distributions Distributions Probability Mass Functions The Cookie Problem Revisited 101 Bowls The Dice Problem Updating Dice Summary Exercises 4. Estimating Proportions The Euro Problem The Binomial Distribution Bayesian Estimation Triangle Prior The Binomial Likelihood Function Bayesian Statistics Summary Exercises 5. Estimating Counts The Train Problem Sensitivity to the Prior Power Law Prior Credible Intervals The German Tank Problem Informative Priors Summary Exercises 6. Odds and Addends Odds Bayes’s Rule Oliver’s Blood Addends Gluten Sensitivity The Forward Problem The Inverse Problem Summary More Exercises 7. Minimum, Maximum, and Mixture Cumulative Distribution Functions Best Three of Four Maximum Minimum Mixture General Mixtures Summary Exercises 8. Poisson Processes The World Cup Problem The Poisson Distribution The Gamma Distribution The Update Probability of Superiority Predicting the Rematch The Exponential Distribution Summary Exercises 9. Decision Analysis The Price Is Right Problem The Prior Kernel Density Estimation Distribution of Error Update Probability of Winning Decision Analysis Maximizing Expected Gain Summary Discussion More Exercises 10. Testing Estimation Evidence Uniformly Distributed Bias Bayesian Hypothesis Testing Bayesian Bandits Prior Beliefs The Update Multiple Bandits Explore and Exploit The Strategy Summary More Exercises 11. Comparison Outer Operations How Tall Is A? Joint Distribution Visualizing the Joint Distribution Likelihood The Update Marginal Distributions Conditional Posteriors Dependence and Independence Summary Exercises 12. Classification Penguin Data Normal Models The Update Naive Bayesian Classification Joint Distributions Multivariate Normal Distribution A Less Naive Classifier Summary Exercises 13. Inference Improving Reading Ability Estimating Parameters Likelihood Posterior Marginal Distributions Distribution of Differences Using Summary Statistics Update with Summary Statistics Comparing Marginals Summary Exercises 14. Survival Analysis The Weibull Distribution Incomplete Data Using Incomplete Data Light Bulbs Posterior Means Posterior Predictive Distribution Summary Exercises 15. Mark and Recapture The Grizzly Bear Problem The Update Two-Parameter Model The Prior The Update The Lincoln Index Problem Three-Parameter Model Summary Exercises 16. Logistic Regression Log Odds The Space Shuttle Problem Prior Distribution Likelihood The Update Marginal Distributions Transforming Distributions Predictive Distributions Empirical Bayes Summary More Exercises 17. Regression More Snow? Regression Model Least Squares Regression Priors Likelihood The Update Marathon World Record The Priors Prediction Summary Exercises 18. Conjugate Priors The World Cup Problem Revisited The Conjugate Prior What the Actual? Binomial Likelihood Lions and Tigers and Bears The Dirichlet Distribution Summary Exercises 19. MCMC The World Cup Problem Grid Approximation Prior Predictive Distribution Introducing PyMC3 Sampling the Prior When Do We Get to Inference? Posterior Predictive Distribution Happiness Simple Regression Multiple Regression Summary Exercises 20. Approximate Bayesian Computation The Kidney Tumor Problem A Simple Growth Model A More General Model Simulation Approximate Bayesian Computation Counting Cells Cell Counting with ABC When Do We Get to the Approximate Part? Summary Exercises Index
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