PhD Courses in Denmark

Objectives of the course:
The PhD students will be introduced to Bayesian hierarchical modelling, which are becoming increasingly popular for fitting ecological, environmental, and human disease models to temporal and spatial data. The aim of the course is to introduce the students to i) the applied use of likelihood functions and Bayesian statistics, ii) setting up advanced hierarchical statistical models with latent variables, iii) applying advanced statistical models, and iv) making quantitative predictions with a known degree of uncertainty.

Learning outcomes and competences:

At the end of the course, the student should be able to:

- assess the possible value of using advanced hierarchical statistical methods in the students own work

- critically evaluate scientific literature using advanced statistical models

Course parameters:

Language: English

Level of course: PhD course

Time of year: Spring 2025

No. of contact hours/hours in total incl. preparation, assignment or the like: 35/80

Capacity limits: 16 participants

Compulsory program: preparation, active participation, assignment

Course contents:

• Introduction to likelihood functions and Bayesian statistics
• Hierarchical models with latent variables
• Fitting models to data using Bayesian methods
• Model prediction

Prerequisites: Introductory probability and statistics courses

Name of lecturers: Christian Damgaard and Peter Borgen Sørensen

Type of course/teaching methods: Seminars and exercises using R

Literature: Before course start the student are expected to have read chapters 1, 3-7 in the electronic book: https://bayesball.github.io/BOOK/probability-a-measurement-of-uncertainty.html, and be familiar with the statistic software R (e.g. http://r.sund.ku.dk/)

We will use the software “RTMB” at the course - https://cran.rproject.org/web/packages/RTMB/vignettes/RTMB-introduction.html

Software: R, RStudio, RTMB

Course assessment: Personalized reports (approximately 10-30 pages, corresponding to a workload of 20 hours outside, and in the week after the end of the scheduled classes) must be completed and submitted for approval (pass/fail).

Special comments on this course: All expenses for accommodation and travel are paid by the student.

Time:  7-11 April 2025

Place: Department of Ecoscience, Aarhus University, Denmark

Registration: Deadline for registration is 1 April 2025 (first come, first served).

For registration: Please write an e-mail to Christian Damgaard, e-mail: cfd@ecos.au.dk

Course Program

The topics of the 5 days are as detailed below, and each topic starts with a lecture followed by computer exercises in R which are carried out in teams of two-three participants. Each participant must produce a personalized report of the exercises. During the course, the participants should be prepared to work outside the scheduled classes to complete the computer exercises.

Day 1

10:00 – 10:15                        Welcome, Introduction to Course

10:00 – 12:00                        Lecture 1: Probability theory – the logic of science

12:00 – 13:00                        Lunch

13:00 – 15:00                        Lecture 2: Probability distributions and likelihood functions, exercises in R

15:00 – 15:15                        Break

15:15 – 16:00                        Short plenum presentation of the student’s own data and methods.

Day 2

08:30 – 10:00                        Lecture 3: Bayesian statistics and MCMC, exercises in R

10:00 – 10:15                        Break

10:15 – 12:00                        Lecture 4: Laplace's approximation - RTMB

12:00 – 13:00                        Lunch

13:00 – 15:00                        Exercises in RTMB

15:00 – 15:15                        Break

15:15 – 16:00                        Exercises in RTMB

Day 3

08:30 – 10:00                        Lecture 5: Structural equation modelling

10:00 – 10:15                        Break

10:15 – 12:00                        Exercises in RTMB

12:00 – 13:00                        Lunch

13:00 – 15:00                        Exercises in RTMB

15:00 – 15:15                        Break

15:15 – 16:00                        Exercises in RTMB

Day 4

08:30 – 10:00                        Lecture 6: Prediction and uncertainties

10:00 – 10:15                        Break

10:15 – 12:00                        Exercises in RTMB

12:00 – 13:00                        Lunch

13:00 – 15:00                        Exercises in RTMB

15:00 – 15:15                        Break

15:15 – 16:00                        Exercises in RTMB

Day 5

08:30 – 10:00                        Exercises in RTMB

10:00 – 10:15                        Break

10:15 – 12:00                        Evaluation in plenum to identify relevant methods for students’ own data.

12:00 – 13:00                        Lunch

13:00 – 14:00                        Evaluation and departure

Within two weeks                   Submission of final report by e-mail to Christian Damgaard

If you have any questions, please contact Christian Damgaard or Peter Borgen Sørensen.