STAT301: Simulation and Computation Techniques Using S-Plus
The S-Plus code was created by the instructor, Athanasios Micheas. I don't know if this code appears anywhere to my knowledge, I never looked for it. The theory that accompanies the code however, provides the appropriate references where needed. You may use the code at will, just mention the instructor and the course. May, 2004
Topic 1: Creating Pseudo Random Numbers
Random Number Generators: Introduction
Using S-Plus to create Random Number Generators
Topic 2: Generating Discrete Random Variables
Reference for Theory: Sheldon Ross, Chapter 4
Using S-Plus to generate discrete r.v.'s using Inverse Transform Method
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The Acceptance-Rejection Method
Using S-Plus to generate discrete r.v.'s using Acceptance-Rejection Method
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Using S-Plus to generate discrete r.v.'s using the Composition Method
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Generating Discrete Random Vectors: Conditional Approach
Using S-Plus to generate discrete random vectors
Topic 3: Generating Continuous Random Variables
Reference for Theory: Sheldon Ross, Chapter 5
Using S-Plus to generate continuous r.v.'s using Inverse Transform Method
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The Acceptance-Rejection Method
Using S-Plus to generate continuous r.v.'s using Acceptance-Rejection Method
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Using S-Plus to generate discrete mixtures of continuous p.d.f's
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Generating a Bivariate Normal: Polar Method and Conditional Approach
Using S-Plus to generate a Bivariate Normal using the Polar Method or Conditional Approach
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Generating a Multivariate Normal: Choleski Decomposition
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Using generated values to obtain credible sets and HPD's
Topic 4: Monte Carlo Methods
Introduction to Monte Carl Numerical Approximation of Integrals and computation of means of r.v.'s
Using S-Plus to approximate any integral or the mean of any function of a random variable
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Computation of Probabilities and Powers of Statistical Tests
Topic 5: Computing Roots of equations using the Newton-Raphson Method
Idea behind Newton-Raphson Method
Using S-Plus to apply Newton-Raphson Algorithm to calculate roots of equations (e.g., MLE's)
Topic 6: Bootstrap Techniques
Reference: Sheldon Ross, Chapter 7
Introduction to Bootstrap Techniques
Using S-Plus to apply Bootstrap Method in estimating MSE's
Topic 7: Markov Chain Monte Carlo Techniques
Reference: Sheldon Ross, Chapter 10
Introduction to Markov Chains and Markov Chain Monte Carlo (MCMC)
Using S-Plus to generate from Markov Chains with given transition probabilities
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Using S-Plus to apply Metropolis-Hastings Algorithm
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Introduction to Gibbs Sampling
Using S-Plus to perform the Gibbs Sampler
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Introduction to Simulated Annealing
Using S-Plus to apply Simulated Annealing approach
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