 Master in Mathematical Engineering BAYESIAN INFERENCE

Lecturers

Conchi Ausín & Michael P. Wiper, Department of Statistics, UC3M

Lecture notes

·      Chapter 0: Course outline

·      Chapter 1: Introduction: Bayesian basics

·      Chapter 2: Conjugate models

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§  Other methods: Approximate Bayesian computation

·      Chapter 4: Regression & hierarchical models

·      Chapter 5: Model selection

Software

R codes (txt files)

·      Monty Hall with at least 3 doors via simulation (Ch1).

·      Inference with binomial data and TN prior via R2WinBUGS (Ch1).

§  Associated WinBUGS code for use in the above (save this file on c: or d: as binomialnc.bug).

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·      Beta binomial inference with a mixture prior (Ch2).

·      Bayesian and classical inference and prediction for exponential data (Ch2).

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·      Software reliability data (Ch2, Ch5).

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·      Bayesian and classical inference for normal data (Ch2).

·      Dirichlet process examples with continuous and discrete data (Ch2).

·      Importance and rejection sampling examples (Ch3).

·      Markov Chain Monte Carlo method examples (Ch3).

§   Save file: gamma.bug

·      ABC method with discrete data examples (Ch3).

·      ABC method with continuous data examples (Ch3).

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·      Normal and generalized linear model examples (Ch4).

§  Save files: Anova.buglogistic.bug

·       A First order polynomial DLM example (Ch4).

·      Testing for a fair coin (Ch5).

·      Calculating the marginal likelihood for different software reliability models (Ch5).

WinBUGS (txt files)

·      Inference with binomial data with beta and TN priors (Ch1).

·      One and two sample inference for a normal distribution (Ch2).

·      A logistic regression example (Ch4).

§  Another example.

§  Another example.

·      A hierarchical one-way ANOVA (Ch4).

§  Another example.

·      A hierarchical Poisson regression model (Ch4).

·      Model comparison using DIC for two independent normal samples (Ch5).

·      “Crib sheet” for Winbugs