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

The Inverse Transform Method

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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The Composition Method

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

The Inverse Transform Method

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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The Composition Method

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

Using S-Plus to generate a Multivariate Normal random vector (and derivative distributions) using 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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Metropolis-Hastings Algorithm

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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The Sampling Importance Resampling (SIR) Algorithm

Using S-Plus to illustrate the SIR Algorithm