Course content

Parameter estimation, simulation and applications of Gaussian random fields, point fields and
discrete Markov random fields. Examples from image analysis, and environmental and natural
resource applications.

Learning outcome

1. Knowledge. The student has knowledge about basic concepts of the theory about Gaussian random fields, including spatial interpolation by various types of kriging, and algorithms for unconditional and conditional simulation. The student has also knowledge about basic
concepts of the theory of point random fields, including K- and L-statistics, spatial Poisson, Cox and hard-core fields, and simulation of such point fields. Moreover, the student has knowledge about basic concepts of the theory of discrete Markov random fields, including
simulation of Markov random fields by MCMC algorithms. Lastly, the student has knowledge of parameter estimation in spatial random fields.

2. Skills. The student can formulate statistical models for simple spatial phenomena, and perform parameter estimation under these models by use of suitable computer software. Moreover, the student can evaluate conditional models by stochastic simulation.

Learning methods and activities

Lectures and works (projects). Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (70%) and works (projects) (30%). The results for the constituent parts are
to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination. The lectures may be given in English. If the course is taught in English, the exam may be given only in English. Students are free to choose Norwegian or English for written assessments.

Compulsory assignments

• Work

Recommended previous knowledge

TMA4240/TMA4245 Statistics and TMA4300 Computer Intensive Statistical Methods (may
be taken as a parallel), or equivalent. The subject requires a mature understanding of statistics and we also recommend TMA4265 Stochastic Processes and TMA4267 Linear Statistical Models.

Course materials

Will be announced at the start of the course.

Credit reductions