2023VT

Status Active - open for registrations IDA-gemensam (IDA) STIMA Frank Miller http://www.adoptdesign.de/frankmillereu/adcompstat2023.html

## Course plan

#### Recommended for

The course is intended for Ph.D. students from Statistics or a related field (e.g. Mathematical Statistics, Engineering Science, Quantitative Finance, Computer Science).

#### The course was last given

In this form, the course is new. The optimisation part of this course is a part of the course Optimisation Algorithms in Statistics given in Fall 2020 and Spring 2021.

#### Intended Learning Oucomes

On completion of the course, the student is expected to be able to:
• Demonstrate knowledge of principles of computational statistics
• Explain theoretical and empirical methods to compare different algorithms
• Design and organize algorithms for optimisation, integration, and simulation of distributions
• Solve statistical computing problems using advanced algorithms
• Adapt a given optimisation, integration, or simulation method to a specific problem
• Assess, compare and contrast properties of alternative optimisation, integration, and simulation methods
• Critically judge different methods for optimisation, integration, and simulation
• Ability to choose an adequate method for a given statistical problem

#### Prerequisites

Accepted to a doctoral program in Sweden in Statistics or a related field. Knowledge about Statistical Inference (e.g. from the
Master's level) and familiarity with a programming language (e.g. with R) is required.

#### Content

The course contains fundamental principles of computational statistics. Focus is on:
• Principles of gradient based and gradient free optimisation including stochastic optimisation and constrained optimisation
• Introduction to convergence analysis for stochastic optimisation algorithms
• Statistical problem-solving using optimisation, including maximum likelihood, regularized least squares, and optimal experimental designs
• Principles of numerical integration
• Principles of statistical simulation
• The bootstrap method
• Statistical problem-solving using simulation techniques including generation of Monte Carlo estimates, their confidence intervals, and posterior distributions

#### Literature

• Givens GH, Hoeting JA (2013). Computational Statistics, 2nd edition. John Wiley & Sons, Inc., Hoboken, New Jersey.
• Goodfellow I, Bengio Y, Courville A (2016). Deep Learning. MIT Press, http://www.deeplearningbook.org. Focus on Chapter 4, 5, and 8.
• Further literature including research articles and other learning material will be provided in the course

#### Lectures

Lectures and problem sessions will be partly in class (one session in Linköping, one in Stockholm) and partly online.

#### Examination

The Intended Learning Oucomes will be graded by a written exam and/or hand-in solutions to assignments. The grades given: Pass/Fail.

Frank Miller

#### Credits

7.5

Page responsible: Director of Graduate Studies