# STAT 221: Monte Carlo Methods

© 2004 2005 2006 2007 2008 2009 2010 2011 Raazesh Sainudiin. © 2008 2009 2010 2011 Dominic Lee.

**About this course**

This is a course about **computational statistical experiments** with Monte Carlo methods.

Official Description:
This course is about the generation of random numbers and their uses, including computer simulations to mimic and contrast random real-world phenomena. It will provide an intuitive and practical understanding of the basic methods in computational statistics, and show how to implement statistical algorithms to manipulate, visualise and comprehend various aspects of real-world data.

**Who does computational statistical experiments?**

A *statistical experimenter* is a person who conducts a *statistical experiment*. Roughly, an experiment is an action with an empirically observable outcome (data) that cannot necessarily be predicted with certainty (in the sense that a repetition of the experiment may result in a different outcome). An experimenter attempts to learn about a phenomenon through the outcome of an experiment. An experimenter is often a decision-maker, scientist or engineer.

Recent technological advances are facilitating computationally intensive statistical experiments based on possibly massive amounts of empirical observations, in a manner that was not viable a decade ago. Hence, a successful decision-maker, scientist or engineer in most specialisations today is a **computational statistical experimenter**. Now hear Chief Economist at Google talk about statistics being the dream job for 2010's.

A computational statistical experimenter has to *tell a machine what to do* with the data, i.e. *program the machine*. In addition, statistical experimenters use a mathematically formal way of thinking about their experiments. They use set theory, probability theory and other branches of pure and applied mathematics through established statistical theory to reach their administrative, scientific and engineering decisions from their data.

This course is designed to help you take the first steps along this path.

**What is Sage and why are we using it?**

We will be using Sage for our *hands-on* work in this course. Sage is a free open-source mathematics software system licensed under the GPL. Sage can be used to study mathematics and statistics, including algebra, calculus, elementary to very advanced number theory, cryptography, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra, optimization, interactive data visualization, randomized or Monte Carlo algorithms, scientific and statistical computing and much more. It combines various software packages into an integrative learning, teaching and research experience that is well suited for novice as well as professional researchers.

Sage is a set of software libraries built on top of Python, a widely used general purpose programming language. Sage greatly enhance Python's already mathematically friendly nature. It is one of the languages used at Google, US National Aeronautic and Space Administration (NASA), US Jet Propulsion Laboratory (JPL), Industrial Light and Magic, YouTube, and other leading entities in industry and public sectors (read more...). Scientists, engineers, and mathematicians often find it well suited for their work. Obtain a more thorough rationale for Sage from Why Sage? and Success Stories, Testimonials and News Articles. Jump start your motivation by taking a Sage Feature Tour right now!

**Expected Learning Outcomes**

The course assumes very little and starts from scratch.
The course has three contact hours per week. Lectures and computer labs are fully intertwined in this course.
You are expected to spend 4 to 6 hours each week to keep up with the material
(as per 200 level course requirements in Maths and Stats Department).
The course will give you skills to think from first principles to become an independent 'computational statistical experimenter'.
You will learn to program each concept you learn in python, a popular programming language via the Department's remotely accessible Sage Notebook Server. No prior programming knowledge is assumed.

# Course history and archive from 2009, 2008 and 2007

See STAT 218: Computational Methods in Statistics.

CC: This work (all of its contents) is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 New Zealand License.

Last modified on Friday, 02-Sep-2016 15:00:33 MST and served on Saturday, 16-Oct-2021 15:19:38 MST.