MATH 648 BAYESIAN INFERENCE - SPRING 1998

The Reverend Thomas Bayes (1702-1761)

(updated March 19, 1998)

• Instructor: Jim Albert (email: albert@math.bgsu.edu)
  
• Texts:
  Albert, Bayesian Computation Using Minitab
  Albert and Johnson, Ordinal Data Analysis: A Bayesian Approach
  

Handouts and Matlab Labs

• Introduction to Matlab.
  
  

• Learning using Bayes' rule
  

  Matlab Lab 1 - Computing probabilities by simulation and using the Bayes toolbox.
  
  

• Proportion inference
  

  DATA for the homework on proportion inference.

  Example using Matlab function p_disc -- computing posterior using a discrete prior

  Example using Matlab function p_disc -- computing posterior using a discrete prior and finding posterior summaries

  Example using Matlab function p_disc_p -- computing predictive distribution using a discrete prior

  Example using Matlab function beta_sel -- selecting a beta prior using predictive statements

  Example using Matlab function p_beta_p -- computing predictive distribution using a beta prior

  Example using Matlab function p_beta_t -- a test for a binomial proportion

  Example using Matlab function p_hist_p -- computing posterior using a histogram prior
  
  

• Normal inference
  

  First Bayes software (zip file)

  Using Matlab function m_cont -- computing posterior using direct simulation
  
  

• Bayesian computation
  

  Illustration of Laplace, adaptive quadrature, and metropolis algorithms for one-parameter problem

  Illustration of Laplace, adaptive quadrature, and Gibbs algorithms for two-parameter problem
  
  

• Hierarchical modeling
  
  

  Matlab function for computing log posterior of hyperparameters for binomial/beta exchangeable model
  
  

  See a scatterplot of 5000 simulated sample values of (log(m/(1-m)), log(K)) for Efron and Morris baseball example
  
  

• Bayesian testing
  
  
• Binary response regression methods
  
  

  MATLAB Binary Regression Toolbox
  
  

• Ordinal response regression methods