Allen B. Downey
Think Bayes: Bayesian Statistics Made Simple
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Contents
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Think Bayes is an introduction to Bayesian statistics using computational methods.

The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics.

Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops.

The author thinks this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.

Order print editions of Think Bayes from Green Tea Press

Language
English
ISBN
Unknown
Preface
My theory, which is mine
Modeling and approximation
Working with the code
Code style
Prerequisites
Bayes's Theorem
Conditional probability
Conjoint probability
Bayes's theorem
The diachronic interpretation
The M&M problem
The Monty Hall problem
Discussion
Computational Statistics
Distributions
The Bayesian framework
The Monty Hall problem
Encapsulating the framework
The M&M problem
Discussion
Exercises
Estimation
The dice problem
The locomotive problem
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
The odds form of Bayes's theorem
Oliver's blood
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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