Course Title: Spatio-temporal Statistical Modelling

The course handles the three main classes of spatial data and processes including time: geostatistical data, measured on spatially continuous processes, lattice data obtained from discrete processes, and point patterns obtained from point processes. Where appropriate, the time dimension is included. The course aims to present methods that are able to deal with all such data. Point of departure is that data are varying in space and in time, but data close to each other are more similar than data further away. Geostatistical methods include the semi-variogram and interpolation (kriging) in space and time. The methods will be extended and applied for data aggregated over contiguous regions.

Learning goals:

1. Conceptualize spatial data in relation to modelling spatial processes
2. Conceptualize and quantify spatial correlation of geostatistical data and relate its significance to spatial prediction and simulation
3. Explain and compare the principles of deterministic and stochastic spatial predictions and simulations of geostatistical data
4. Explain the concepts and assumptions of stationarity (second-order and intrinsic) and its role in spatial prediction and simulations
5. Implement the concept of spatial correlation for stochastic spatial prediction (kriging)
6. To design and set up a spatial data modeling problem, identity measurable objectives, and implement the modeling ideas

Content:

1. Spatial variation and spatio-temporal variation
2. Ordinary kriging, co-kriging, external drift kriging
3. Area to point kriging for lattice data
4. Conditional autoregressive (CAR) modelling of lattice data
5. Spatio-temporal simulation routines
6. Point patterns

Textbooks:

Webster, R. & Oliver, M. A. Geostatistics for environmental scientists. (John Wiley & Sons, 2001).

Olea, R. A. Geostatistics for Engineers and Earth Scientists. (Springer Science & Business Media, 2012).

Chilès, J.-P. & Delfiner, P. Geostatistics: Modeling Spatial Uncertainty. (Wiley, 2012).