Swedish web site
Advanced Computational Statistics2023VT
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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.
Examiner
Frank Miller
Credits
7.5
Page responsible: Director of Graduate Studies
