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Book Description

Table of Contents

- Preface
- My theory, which is mine
- Modeling and approximation
- Working with the code
- Code style
- Prerequisites

- Bayes's Theorem
- Conditional probability
- Conjoint probability
- The cookie problem
- Bayes's theorem
- The diachronic interpretation
- The M&M problem
- The Monty Hall problem
- Discussion

- Computational Statistics
- Distributions
- The cookie problem
- The Bayesian framework
- The Monty Hall problem
- Encapsulating the framework
- The M&M problem
- Discussion
- Exercises

- Estimation
- The dice problem
- The locomotive problem
- What about that prior?
- An alternative prior
- Credible intervals
- Cumulative distribution functions
- The German tank problem
- Discussion
- Exercises

- More Estimation
- The Euro problem
- Summarizing the posterior
- Swamping the priors
- Optimization
- The beta distribution
- Discussion
- Exercises

- Odds and Addends
- Odds
- The odds form of Bayes's theorem
- Oliver's blood
- Addends
- Maxima
- Mixtures
- Discussion

- Decision Analysis
- The Price is Right problem
- The prior
- Probability density functions
- Representing PDFs
- Modeling the contestants
- Likelihood
- Update
- Optimal bidding
- Discussion

- Prediction
- The Boston Bruins problem
- Poisson processes
- The posteriors
- The distribution of goals
- The probability of winning
- Sudden death
- Discussion
- Exercises

- Observer Bias
- The Red Line problem
- The model
- Wait times
- Predicting wait times
- Estimating the arrival rate
- Incorporating uncertainty
- Decision analysis
- Discussion
- Exercises

- Two Dimensions
- Paintball
- The suite
- Trigonometry
- Likelihood
- Joint distributions
- Conditional distributions
- Credible intervals
- Discussion
- Exercises

- Approximate Bayesian Computation
- The Variability Hypothesis
- Mean and standard deviation
- Update
- The posterior distribution of CV
- Underflow
- Log-likelihood
- A little optimization
- ABC
- Robust estimation
- Who is more variable?
- Discussion
- Exercises

- Hypothesis Testing
- Back to the Euro problem
- Making a fair comparison
- The triangle prior
- Discussion
- Exercises

- Evidence
- Interpreting SAT scores
- The scale
- The prior
- Posterior
- A better model
- Calibration
- Posterior distribution of efficacy
- Predictive distribution
- Discussion

- Simulation
- The Kidney Tumor problem
- A simple model
- A more general model
- Implementation
- Caching the joint distribution
- Conditional distributions
- Serial Correlation
- Discussion

- A Hierarchical Model
- The Geiger counter problem
- Start simple
- Make it hierarchical
- A little optimization
- Extracting the posteriors
- Discussion
- Exercises

- Dealing with Dimensions
- Belly button bacteria
- Lions and tigers and bears
- The hierarchical version
- Random sampling
- Optimization
- Collapsing the hierarchy
- One more problem
- We're not done yet
- The belly button data
- Predictive distributions
- Joint posterior
- Coverage
- Discussion

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