# 2018/2019

## Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledge obtained by the module Statistical Inference for Linear Models from the Bachelor of Science (BSc) in Engineering (Mathematical Engineering)

## Content, progress and pedagogy of the module

The course deals with Markov chain Monte Carlo methods as well as one or more of the three main topics within spatial statistics.

### Learning objectives

#### Knowledge

• know the fundamental models and methods within the chosen main topics (geostatistics, lattice processes or spatial point processes) as well as Markov chain Monte Carlo.
• have knowledge about the following subjects within the chosen main topic(s)
• Geostatistics:
Theory for second order stationary processes, variograms/covariograms, prediction and kriging, as well as model based geostatistics
• Lattice processes:
Markov fields, Brook's factorisation and Hammersley-Clifford's theorem and likelihood based statistical analysis
• Spatial point processes:
Poisson processes, Cox processes and Markov point processes, as well as statistical analyses based on non-parametric methods (summary statistics) and likelihood based methods
• Markov chain Monte Carlo:
Fundamental theory of Markov chains with a view to simulation, Markov chain Monte Carlo methods for simulation of distributions, including the Metropolis-Hastings algorithm and the Gibbs sampler

#### Skills

• are able to explain the main theoretical results from the course
• are able to perform statistical analyses of concrete datasets
• are able to simulate the examined models

#### Competences

• are able to interpret a spatial statistical model in relation to a concrete dataset and give an account of the limitations of the model with respect to describing the variation in the dataset using the theoretical results within spatial statistics
• are able to simulate distributions using Markov chain Monte Carlo methods and evaluate the output of the Markov chain

### Type of instruction

As described in §17.

This is a 5 ECTS course module and the work load is expected to be 150 hours for the student.

## Exam

### Prerequisite for enrollment for the exam

• For students on the master level: In order to participate in the exam, students must have actively participated in course progress by way of one or several independent oral and/or written contributions.

### Exams

 Name of exam Spatial Statistics and Markov Chain Monte Carlo Methods Type of exam Written or oral exam Individual oral or written exam, or individual ongoing evaluation. ECTS 5 Assessment Passed/Not Passed Type of grading Internal examination Criteria of assessment As stated in the Joint Programme Regulations. http:/​/​www.engineering.aau.dk/​uddannelse/​Studieadministration/​