Course Syllabus for

# Monte Carlo Methods for Statistical Inference Monte Carlo-baserade statistiska metoder

## FMS092F, 7.5 credits

Valid from: Spring 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2014-01-13

## General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMS091
Teaching language: English

## Aim

The aim is that doctoral student shall gain proficiency with modern computer intensive 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). The purpose of the course is to give the doctoral student tools and knowledge to handle complex statistical problems and models in order to be able to use these in the doctoral student's own research. Further, the doctoral student should be able to assess the uncertainty of these estimates. The main aim lies in enhancing the scope of statistical problems that the doctoral student will be able to solve.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

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

Competences and Skills

For a passing grade the doctoral student must

• Given a stochastic model and problem formulation, be able to choose relevant quantities in a way that permits approximation using Monte Carlo methods.
• Given a (possibly multivariate) probability distribution, be able to 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, be able to approximate relevant probabilities and expectations as well as estimate the uncertainty in the approximated quantities.
• Given a model description and a statistical problem, be able to suggest a simple permutation test and implement it in a computer program.
• Given a model description and a statistical problem, be able to suggest a resampling procedure and implement it in a computer program.
• Be able to 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 doctoral student must Be able to identify and problemise the possibilities and limitations of statistical inference.

## Course Contents

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.

## Course Literature

Sköld, M.: Computer Intensive Statistical Methods.

## Instruction Details

Types of instruction: Lectures, laboratory exercises, project

## Examination Details

Examination format: Written report. Oral project presentation