Course Overview

Topics

This is a master-level course in computational statistics, which roughly speaking means implementing statistical theory as computer code (and all of the different issues that arise in doing so). The course revolves around three overarching topics: smoothing, Monte-Carlo simulation, and optimization. Contents include the following:

  • Maximum-likelihood and numerical optimization
  • The EM-algorithm
  • Stochastic optimization algorithms
  • Simulation algorithms and Monte Carlo methods
  • Nonparametric density estimation
  • Bivariate smoothing
  • Numerical linear algebra in statistics. Sparse and structured matrices
  • Practical implementation of statistical computations and algorithms
  • R/C++ and RStudio statistical software development

Structure

The backbone of the course is made up of four topics in computational statistics:

  • Smoothing
  • Univariate Simulation
  • The EM Algorithm
  • Stochastic Optimization

For the oral exam you will draw a topic at random and present one of the two assignments of your own choice from the topic. This presentation will be individual. You will therefore need to prepare a total of four presentations. All eight assignments will, however, be covered by group presentations during the course, which are planned for weeks 3, 4, 6 and 7 of the course. Each group will consist of 2-3 students, and you need to register your group and which topic and assignment you will cover on Absalon.

Lectures

Every Tuesday and Thursday there will be a lecture on the course material. We recommend that you bring a laptop to these sessions since each lecture will end with a short exercise session.

Exercise Sessions

Each Thursday morning there will be an exercise session in which you can work on the exercises or assignments in the course. There will be a teaching assistant there to help you out. You need to bring your laptop to these sessions.

Assignment Presentations

On four Thursday afternoons (weeks 3, 4, 6, and 7 of the course) there will be group presentation sessions for the assignments. It is compulsory to hold one presentation of an assignment. After forming a group, you need to register for one of the presentation groups in the People section. The first four groups will present an assignment from the first topic in the first session, and so on.

Literature

The primary course literature for this course is Computational Statistics with R by professor Niels Richard Hansen. It is provided for free online at https://cswr.nrhstat.org. We will also use parts of the book Advanced R (second edition) by Hadley Wickham, which is also available for free online at https://adv-r.hadley.nz

R

The course will use R as a programming language. We expect you to have a basic grasp of R, but in case you feel the need to refresh your knowledge of the R basics, please take a look at Hands-On Programming with R by Garrett Grolemund, which is a short and beginner-friendly introduction to the basics of R. We also assume that you have a good grasp of the content of chapters 1-5 in Advanced R on data structures, subsetting and control flows. If not, please consider going over these sections before the course starts or during the first week.

If you haven’t already, you need to install R and RStudio on your computer. Instructions on how to do so can be found at here.

We will not enforce (nor teach) a specific coding style, but recommend that you take a look at the Tidyverse style guide, which is used widely throughout the R community. Using these simple rules consistently (this holds for the spacing rules for infix operators in particular) makes life a lot easier for everybody.

Examination

The course is graded on a 7-point scale. During the course a total of eight assignments will be given within four different topics. You need to select one assignment from each topic and prepare a solution for that assignment for the exam. That is, you need to prepare solutions of four assignments in total.

At the oral examination, we will randomly select one of the four topics and you will give the presentation that you have prepared for that topic (based on the assignment that you have chosen). The presentation is followed by a discussion with the examinator regarding the topics of the course. The grade is based on both the presentation itself and the discussion.

Learning Outcomes

Knowledge

Knowledge of

  • fundamental algorithms for statistical computations and
  • R packages that implement some of these algorithms or are useful for developing novel implementations.

Skills

Ability to implement, test, debug, benchmark, profile and optimize statistical software.

Competence

Ability to

  • select appropriate numerical algorithms for statistical computations and
  • evaluate implementations in terms of correctness, robustness, accuracy and memory and speed efficiency.