Course syllabus

# Monte Carlo-baserade statistiska metoder

Monte Carlo and Empirical Methods for Stochastic Inference

## FMS091, 7,5 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

Admission requirements:## Reading list

## Contact and other information

Monte Carlo and Empirical Methods for Stochastic Inference

Valid for: 2013/14

Decided by: Education Board B

Date of Decision: 2013-04-10

Elective for: D4, F4, F4-bm, F4-fm, I4, I4-fir, Pi4, Pi4-bs, Pi4-bm, Pi4-fm, Pi4-mrk

Language of instruction: The course will be given in English on demand

The purpose of the course is to give the students tools and knowledge to handle complex statistical problems and models. The aim is that students shall gain proficiency with modern computer intencive statistical methods and use these to estimate quantities and parameters in complex models that arise in different applications (e.g. economics, signal processing, biology, climate, and environmental statistics). Further, the student should be able to assess the uncertainty of these estimates. The main aim lies in enhancing the scope of statistical problems that the student will be able to solve.

Knowledge and understanding

For a passing grade the student must

- describe fundamental principles of Monte Carlo integration and random variable generation.
- explain and use the concept of statistical uncertainty from a frequentist perspective as well as from a Bayesian perspective,
- describe fundamental principles of parametric and non-parametric resampling.

Competences and skills

For a passing grade the student must

- given a stochastic model and problem formulation, choose relevant quantities in a way that permits approximation using Monte Carlo methods,
- given a (possibly multivariate) probability distribution, suggest and implement in a computer program, a method for generation of random variables from this distribution,
- given a large number of generated random variables from a probability distribution, approximate relevant probabilities and expectations as well as estimate the uncertainty in the approximated quantities,
- given a model description and a statistical problem, suggest a simple permutation test and implement it in a computer program,
- given a model description and a statistical problem, suggest a resampling procedure and implement it in a computer program,
- present the course of action taken and conclusions drawn in the solution of a given statistical problem.

Judgement and approach

For a passing grade the student must

- be able to identify and problemise the possibilities and limitations of statistical inference.

Simulation based methods of integration and statistical analysis. Monte Carlo methods for sequential problems. Markov chain methods, e.g. Gibbs sampling and the Metropolis-Hastings algorithm, for simulation and inference. Bayesian modelling and inference. The re-sampling principle, both non-parametric and parametric. Methods for constructing confidence intervals using re-sampling. Simulation based tests as an alternative to asymptotic parametric tests.

Grading scale: TH

Assessment: Written and oral project presentation.

- FMS012 Mathematical Statistics, Basic Course or FMS032 Mathematical Statistics, Basic Course or FMS035 Mathematical Statistics, Basic Course or FMS086 Mathematical Statistics or FMS140 Mathematical Statistics, Basic Course

Required prior knowledge: At least one of Stationary stochastic processer or Markov processes. Some programming experience.

The number of participants is limited to: No

The course overlaps following course/s: MAS221, MASM11

- Sköld, M.: Computer Intensive Statistical Methods. 2006.

Director of studies: Studierektor Anna Lindgren, studierektor@matstat.lu.se

Course homepage: http://www.maths.lth.se/matstat/kurser/fms091/

Further information: The course is also given at the faculty of science with the code MASM11.