MATH 648 BAYESIAN INFERENCE

Examples with MINITAB output

• Chapter 1 - Background
• Example 1 (Bayes' rule): Learning about a student's ability.
• Example 2 (Bayes' rule): How many reds did I put in the bag?
• Example 3 (Bayes' rule): The car and goats problem.
• Chapter 2 - Single-parameter models
• Binomial Inference
  • Inference about a proportion using a discrete prior.
  • Predictive inference using a discrete prior.
  • Selecting a beta prior.
  • Summarizing a beta posterior distribution.
  • Summarizing a beta posterior by simulation.
  • Predictive inference using a beta prior.
  • Inference about a proportion using a nonconjugate prior.
• Normal Inference
  • Inference about a variance using simulation.
• Answers to selected exercises.
• Chapter 3 - Multiparameter models
• Comparing Two Proportions
  • Using discrete priors.
  • Using a discrete "testing" prior.
  • Using beta priors and simulation.
• Normal inference
  • Using the macro 'm_nchi' to learn about M and S.
  • Simulating from a normal-inverse-chi-squared distribution.
• A Poisson log-linear model (exercise 12)
  • A macro to compute the logarithm of the posterior density.
  • Summarizing the density by adaptive quadrature.
  • Summarizing the density by the Laplace method.
  • Simulating from the posterior by Gibbs sampling.
• Answers to selected exercises.
• Chapter 4 - Large sample methods
• Definition of log posterior for Cauchy problem (hw #2).
• Definition of log posterior for speed of light problem with t sampling model (hw #3)
• Chapter 5 - Hierarchical modeling
• Analyzing the rat tumour data using MATLAB.
• Comparing two simple hypotheses (Example: Is the machine working?)
• Comparing two composite hypotheses (Example: Do the two drugs have the same cure rates?)
• A Bayes factor to test a point null hypothesis (Example: Does Joe have an average IQ?)
• Bayes factors for comparing models (Example: Modeling Mike Schmidt's homerun data using Poisson and binomial distributions.)
• Use of the posterior predictive distribution.
• In predictive inference. (Example: Would Matt Williams have broken the season homerun in 1994 if the season were a full 162 games?)
• In model checking. (Example: Checking the normality assumption of Newcomb's speed of light data.)
• Bayesian computing
• An example of sampling-importance-resampling.
• Homework problem #2 (How many math-ed undergraduates are interested in graduate study in math?)