Spatial modelling and Bayesian inference, Spring 2017


Teacher:  Jarno Vanhatalo

Scope: 5 cr

Type: Advanced studies

Teaching: course exercises and Exam

Topics: Gaussian process, its properties and use in spatial statistics. Inference and prediction with hierarchical Gaussian process models. Maximum a posterior and Markov chain Monte Carlo approaches for inference.

Prerequisites: At least intermediate level of probability and statistical inference, including Bayesian inference, courses as well as linear algebra and matrix calculation. The course includes computer exercises so programming skills with R or Matlab are required.


Tuesday 9.5. at 12-15.


Teaching schedule

The course takes place on period IV: 13.3.-7.5. The specific schedule is the following


  • Monday 10-12   room B221 in Exactum
  • Tuesday 14-16   room B321 in Exactum

Exercise classes:

  • Wednesday 14-16 room B221 in Exactum


Course assessment and grading

  • Grading: 1-5
    • [The final grade] = 0.5*[the grade from exercises] + 0.5*[the grade from the exam]
  • Exercises and their grading
    • <50% of weekly exercises correct = failed
    • >50% of weekly exercises correct = 1
    • >60% of weekly exercises correct = 2
    • >70% of weekly exercises correct = 3
    • >80% of weekly exercises correct = 4
    • >90% of weekly exercises correct = 5
  • Exam and their grading
    • Grading as with exercises
    • You can use pencil and eraser in the exam.
  • Learning diary
    • In order to pass the course you need to also write a learning diary (this will help in developing the course further)
    • bookkeeping  of time used for the course
    • discuss what was easy/hard, which areas too much/little time was devoted to, what more should have been included, what should have been left out, etc.
    • very informal, keep it short!

Course material

Various chapters from the book Gaussian processes in Machine Learning (Rasmussen and Williams, 2006), lecture notes and articles to be announced during the course. For additional reading the following book is suggested: Banerjee, S., Carlin, B. P. and Gelfand, A. (2015) Hierarchical Modeling and Analysis for Spatial Data, Second Edition, Chapman and Hall/CRC.

Useful links to R and Matlab and for their comparison:

Course Moodle page

The course information will now be distributed mainly through Moodle. The link to the course is:



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Lecture notes










Lectures and exercises

Week 11 (2 lecture days)

Introduction to spatial data problems and Gaussian processes

Week 12 (2 lecture days)

More on Gaussian processes. Including prediction and some valid covariance functions.

Review of Markov chain Monte Carlo methods and how they are used for Bayesian inference.

Week 13 (2 lecture days)

STAN and how to implement GP models in it.

Week 14 (2 lecture days)

Week 15 (2 lecture days)

Week 17 (2 lecture days)

Week 18 (1 lecture day, Vappu)

  • Lecture material
  • exercises


Exercise classes are on Wednesday 14-16 at .

Course feedback

Course feedback can be given at any point during the course. Click here.

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