Course Information

Course Description

Computational statistics is a branch of mathematical sciences concerned with efficient methods for obtaining numerical solutions to statistically formulated problems. This course will introduce students to a variety of computationally intensive statistical techniques and the role of computation as a tool of discovery. Topics include numerical optimization in statistical inference [expectation-maximization (EM) algorithm, Fisher scoring, etc.], random number generation, Monte Carlo methods, randomization methods, jackknife methods, bootstrap methods, tools for identification of structure in data, estimation of functions (orthogonal polynomials, splines, etc.), and graphical methods. Additional topics may vary. Coursework will include computer assignments.

Prerequisites

Multivariate calculus, familiarity with basic matrix algebra and EN.625.603 Statistical Methods and Data Analysis.

Course Goal

To provide a background in the computationally intensive tools and methodologies relevant to statistical analysis and the visualization of complex data.

Course Objectives

• By the end of this course, you will be able to:
• Compare and contrast traditional and computational statistics, explaining the role of computation as a tool of discovery.

• Implement computational statistics techniques using the software R.

• Estimate statistical functions or parameters by selecting and implementing appropriate

computational statistics techniques.

• Evaluate the choice of applying a specific computational statistics technique to a given problem.

• Apply randomization techniques to extract information from large data sets.

• Generate graphical displays as a tool for analyzing both large data sets and computational

statistics techniques.

Syllabus

• The Role of Optimization in Inference
• Multivariate Optimization and the EM Algorithm
• Monte Carlo Methods 1: Simulation and MC Integration
• Monte Carlo Methods 2: Importance Sampling and Markov Chain Monte Carlo
• Monte Carlo Methods 3: More MCMC and Implementation Concerns
• Randomization and Data Partitioning
• Bootstrapping
• Function Estimation and Final Project Proposal
• Density Estimation
• Bi-variate Smoothing
• Graphical Methods in Computational Statistics

Student Assessment Criteria

 Example: Class Preparation and Participation 15% Example: Homework 30% Example: Class Project 15% Example: Final Exam 40%

Computer and Technical Requirements

R

You will need to install R on your computer (free!), by going to the R Project website (http://www.r- project.org/) and following the instructions provided. There are also instructions provided in Module 1.

Textbooks

Textbook information for this course is available online through the MBS Direct Virtual Bookstore.

Course Notes

There are no notes for this course.