Think Bayes: Bayesian Statistics Made Simple

Free

Description

Contents

Reviews

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

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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