Contents

1. Prologue
   1. Bayesian and Classical Statistics
   2. This Version of the Notes
   3. Assessment
2. Introduction
   1. Certainty, Uncertainty and Probability
3. First Examples
   1. The Bayes’ Box
      1. Likelihood
      2. Finding the Likelihood Values
      3. The Mechanical Part
      4. Interpretation
   2. Bayes’ Rule
   3. Phone Example
      1. Solution
   4. Important Equations
4. Parameter Estimation I: Bayes’ Box
   1. Parameter Estimation: Bus Example
      1. Sampling Distribution and Likelihood
      2. What is the “Data”?
   2. Prediction in the Bus Problem
   3. Bayes’ Rule, Parameter Estimation Version
5. Parameter Estimation: Analytical Methods
   1. ”~” Notation
   2. The Effect of Different Priors
      1. Prior 2: Emphasising the Extremes
      2. Prior 3: Already Being Well Informed
      3. The Beta Distribution
      4. A Lot of Data
6. Summarising the Posterior Distribution
   1. Point Estimates
      1. A Very Brief Introduction to Decision Theory
      2. Absolute Loss
      3. All-or-nothing Loss
      4. Invariance of Decisions
      5. Computing Point Estimates from a Bayes’ Box
      6. Computing Point Estimates from Samples
   2. Credible Intervals
      1. Computing Credible Intervals from a Bayes’ Box
      2. Computing Credible Intervals from Samples
   3. Confidence Intervals
7. Hypothesis Testing and Model Selection
   1. An Example Hypothesis Test
   2. The “Testing” Prior
   3. Some Terminology
   4. Hypothesis Testing and the Marginal Likelihood
8. Markov Chain Monte Carlo
   1. Monte Carlo
      1. Summaries
   2. Multiple Parameters
   3. The Metropolis Algorithm
      1. Metropolis, Stated
   4. A Two State Problem
   5. The Steady-State Distribution of a Markov Chain
   6. Tactile MCMC
9. Using JAGS
   1. Basic JAGS Example
   2. Checklist for Using JAGS
10. Regression
    1. A Simple Linear Regression Problem
    2. Interpretation as a Bayesian Question
    3. Analytical Solution With Known Variance
    4. Solution With JAGS
    5. Results for “Road” Data
    6. Predicting New Data
    7. Simple Linear Regression with Outliers
    8. Multiple Linear Regression and Logistic Regression
11. Replacements for t-tests and ANOVA
    1. A T-Test Example
       1. Likelihood
       2. Prior 1: Very Vague
       3. Prior 2: They might be equal!
       4. Prior 3: Alright, they’re not equal, but they might be close
    2. One Way Anova
       1. Hierarchical Model
       2. MCMC Efficiency
       3. An Alternative Parameterisation
12. Acknowledgements

A. R Background 1. Vectors 2. Lists 3. Functions 4. For Loops 5. Useful Probability Distributions

A. Probability 1. The Product Rule 1. Bayes’ Rule 2. The Sum Rule 3. Random Variables 1. Discrete Random Variables 2. Continuous Random Variables 3. Shorthand Notation 4. Useful Probability Distributions

A. Rosetta Stone

Mnemonics

figurative codes | base images | base images with figuarative codes | locations | helpful images

base images

location	base image
1
2
3 first examples
4 parameter	yellow house

locations for parameter estimation: bayes box

shiyakushokita street

link

• big brown building
• st micheal restaurant
• next restaurant
• petrol garage
• vending machines
• hospital 1
• hospiral 2
• red cars

• bridge

• parameter (yellow house)
• estimation
• 1
• Bayes Box
• Parameter ….. estimation bus example
• Prediction …… in the bus problem
• Bayes rule, parameter estimation version