17-21 November 2025

The course will introduce spatial statistical methods with emphasis on spatial sampling, point pattern analysis, geostatistical analysis, mixed linear and non-linear regression models, and machine learning methods applied to spatial variables. Underlying problems such as handling very large datasets and using large scale satellite imagery will be discussed. Theory will be explained and illustrated by practical applications that can be reproduced by the participants. Exercises will be provided to participants for developing an independent command of the materials.

This course is aimed at higher degree research students and early career researchers working with or with an interest in spatial data and applying spatial statistical methods, with emphasis on the biology and ecology domains. Some familiarity with R, R package sf, and the tidyverse is assumed. Familiarity with basic statistics, linear regression, standard errors, confidence intervals and prediction will be very useful.

 - Understanding of the different spatial statistical data types (point patterns, geostatistical data, lattice data)

- Understanding of spatial dependence, and its role in analysing spatial data

- Hands-on experience with spatial statistical methods and software in R, and a number of R spatial packages

- Understanding of the challenges of using big spatial datasets, and ways to handle them

Daily on-line meetings,  14:00-18:00 CET; offline communication through slack. Daily blocks will be scheduled as follows:
14:00 - 14:45 lecture
14:45 - 15:30 practical exercises (break-out groups)
15:30 - 15:45 discussion of exercises
15:45 - 16:15 break
16:15 - 17:00 lecture
17:00 - 17:45 practical exercises (break-out groups)
17:45 - 18:00 discussion of exercises

Day 1: Introduction to spatial data

Introduction to spatial data, support, coordinate reference systems
Introduction to spatial statistical data types: point patterns, geostatistical data, lattice data
Is spatial dependence a fact? And is it a curse, or a blessing?
Spatial sampling, design-based and model-based inference
Intro to point patterns and point processes: observation window, first and second order properties


Day 2: Point Pattern data

Point patterns, density functions
Interactions of point processes
Simulating point process
Modelling density as a function of external variables


Day 3: Geostatistical data
Stationarity of mean, stationarity of covariance
Estimating spatial covariance and semivariance
Modelling the variogram
Kriging interpolation
Conditional simulation


Day 4: Lattice data

Lattice data: origin, representations
Neighbourhood lists, spatial weights
Spatial correlation: Moran’s I, local Moran’s I
Models for lattice data
Count data, disease data

Day 5: Machine Learning methods; big spatial datasets

ML: coverages as predictors
ML pitfalls: independence, known predictors, clustered data
Model assessment, cross validation strategies
What is big?
Large vector and raster datasets, image collections and data cubes
Cloud solutions, cloud platforms, platform lock-in