There are several excellent text books in Bayesian statistics (see the reference section).  This page contains class notes from a leture sereies by Dan Goodman during Spring semester 2000 at Montana State University, Bozeman.  Lecture notes were typed up by students in this class (Dan Hennen, Lynn Kaeding, Jeremy Littell, Ed Luschei,  Matt Rinella, and me).  All lecture notes can be downloaded in pdf files.  Significant amount of time was spent in programming during the semester.  Majority of programs were written in Fortran and some were written in Matlab.  All codes are available but no guarantee that they will give you correct answers.  These programs are not limited to Bayesian statistics.  See our computer programs page for more.

There is a computer "package" that performs Bayesian analyses. The UNIX version of it is called BUGS (a bad name for a computer program...) and its Windows version is called WinBugs. These programs are available for free from BUGS homepage. Just for your information.

I started to use a program called R, which is a dialect of S and S+. I find it relatively easy to use. Best of all, it is free. It also accepts C and Fortran codes as dynamic libraries. I made some C-functions to work in R after spending several hours. Their manual was not very helpful in this regard. So, here is what my understanding of how it works.

INDEX:
Lecture 1: Introduction
Lecture 2: Binomial distribution
Lecture 3: Bayesian statistics in decision context
Lecture 4: Bayesian theory at work
Lecture 5: Binomial decision making continues
Lecture 6: Pre-posterior analysis
Lecture 7: Power analysis, bootstrapping, and introduction to conjugate functions
Lecture 8: Mark-recapture analysis and Smith-Gelfand algorithm
Lecture 9: Bayesian statistics and decision making with Monte-Carlo simulation
Lecture 10: Multidimensional parameter space and Metropolis algorithm
Lecture 11: Metropolis algorithm continues
Lecture 12: Gaussian (Normal) distribution
Lecture 13: Statistics, sufficient statistics, and Fisher's fiducial inference
Lecture 14: Prior distribution and Fisherian confidence principle
Lecture 15: Bayes Empirical Bayes (or hierarchical Bayes)
Lecture 16: Hypothesis testing and Bayesian model selection (sorry not available in pdf format yet)
Lecture 17: Multidimensional inference (sorry not available in pdf format yet)
Lecture 18: Sea otter problem continues (sorry not available in pdf format yet)
Final Project
Lecture from November 2001 on Line Transect

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Lecture 1: Introduction

• Estimating parameters
• Stochastic backward simulations
• Important probabitliy distributions
• Uniform
• Gaussian (Normal)
• Log-normal
• Poisson
• Exponential
• Gamma
• Chi-squared
• Binomial
• Hypergeometric
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• Binomial distribution
• Simple but effective binomial random number generator

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Lecture 3: Bayesian statistics in decision context

• Decisions and binomial events
• Expected utility
• Probabitliy assignment to events
• Inference
• Likelihood function
• Compound sampling

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Lecture 4: Bayesian theory at work

• An example of Bayesian approach and decision making
• Numerical approach
• Algebraic approach
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Lecture 5: Binomail decision making continues

• Playing a game with binomial decision (buy or sell)

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Lecture 6: Preposterior analysis

• Preposterior analysis in binomial situation

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Lecture 7: Power analysis, bootstrapping, and introduction to conjugate functions

• Power analysis nonsense
• Parametric bootstrapping
• Gamma function
• Beta distribution

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Lecture 8: Mark-recapture analysis and Smith-Gelfand algorithm

• Bayesian approach to mark-recapture analysis
• Smith-Gelfand algorithm

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Lecture 9: Bayesian statistics and decision making with Monte Carlo simulation

• Numerical approach to posterior distribution

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Lecture 10: Multidimensional parameter space and Metropolis algorithm

Metropolis algorithm
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Lecture 11: Metropolis algorithm continues

• Metropolis algorithm and its proof (quite simple)

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Lecture 12: Gaussin (Normal) distribution

• Normal distribution and its conjugacy
• Sea otter problem

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Lecture 13: Statitics, sufficient statistics, and Fisher's fiducial inference

• Normal likelihood
• Statistics and sufficient statistics
• Likelihood
• Fisher's fiducial inference

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Lecture 14: Prior distribution and Fisherian "confidence principle"

• Prior distribution
• Bayes empirical Bayes
• Confidence principle

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Lecture 15: Bayes empirical Bayes (or hierarchical Bayes)

• Bayes empirical Bayes

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Lecture 16: Hypothesis testing and Bayesian model selection (sorry not available in pdf format yet)

• Hypothesis testing and more on confidence
• Model selection

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Lecture 17: Multidimensional inference (sorry not available in pdf format yet)

• Marginal and joint distributions
• Primary and derived parameters

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• Parameter estimation in population dynamics models

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Final Project : I could not find all figures in the report. Sorry... (In a pdf file)

Line transect analysis with a Bayesian approach

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Selected reference

Gelman, A., J. B. Carlin, H. S. Stern, D. B. Rubin. 1995. Bayesian data analysis. Chapman and Hall, New York, NY. 526 pp.
Lee, P. M. 1997. Bayesian statistics. An introduction. Second edition. John Wiley and sons Inc. New York, NY 344 pp.
Press, S. J. 1988. Bayesian statistics: principles, models, and applications. Wiley Series in probability and mathematical statistics, John Wiley and Sons, Inc. New York, NT. 237 pp.
Robert, C. P. 1994. The Bayesian choice. Springer-Verlag, New York, NY. 436 pp.

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