فهرست مطالب

• Preface
• Chapter 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
• Summary
• Exercises
• Chapter 2: Bayes’s Theorem
• The Cookie Problem
• Diachronic Bayes
• Bayes Tables
• The Dice Problem
• The Monty Hall Problem
• Summary
• Exercises
• Chapter 3: Distributions
• Distributions
• Probability Mass Functions
• The Cookie Problem Revisited
• 101 Bowls
• The Dice Problem
• Updating Dice
• Summary
• Exercises
• Chapter 4: Estimating Proportions
• The Euro Problem
• The Binomial Distribution
• Bayesian Estimation
• Triangle Prior
• The Binomial Likelihood Function
• Bayesian Statistics
• Summary
• Exercises
• Chapter 5: Estimating Counts
• The Train Problem
• Sensitivity to the Prior
• Power Law Prior
• Credible Intervals
• The German Tank Problem
• Informative Priors
• Summary
• Exercises
• Chapter 6: Odds and Addends
• Odds
• Bayes’s Rule
• Oliver’s Blood
• Addends
• Gluten Sensitivity
• The Forward Problem
• The Inverse Problem
• Summary
• More Exercises
• Chapter 7: Minimum, Maximum, and Mixture
• Cumulative Distribution Functions
• Best Three of Four
• Maximum
• Minimum
• Mixture
• General Mixtures
• Summary
• Exercises
• Chapter 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
• Chapter 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
• Chapter 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
• Chapter 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
• Chapter 12: Classification
• Penguin Data
• Normal Models
• The Update
• Naive Bayesian Classification
• Joint Distributions
• Multivariate Normal Distribution
• A Less Naive Classifier
• Summary
• Exercises
• Chapter 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
• Chapter 14: Survival Analysis
• The Weibull Distribution
• Incomplete Data
• Using Incomplete Data
• Light Bulbs
• Posterior Means
• Posterior Predictive Distribution
• Summary
• Exercises
• Chapter 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
• Chapter 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
• Chapter 17: Regression
• More Snow?
• Regression Model
• Least Squares Regression
• Priors
• Likelihood
• The Update
• Marathon World Record
• The Priors
• Prediction
• Summary
• Exercises
• Chapter 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
• Chapter 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
• Chapter 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