Geod Sci 862 – Adjustment Computations for Random Processes

Professor: Burkhard Schaffrin

T.A: Yaron A. Felus

Random Effects Model, optimal and robust prediction, weak hypothesis testing, spatial processes, covariance function, variogram, homeogram, Kriging and alternative interpolators, quality measures.

Objectives and Syllabus:

The course makes students aware of adjustment techniques in so-called non-standard cases.

These include models with random effects as well as space processes. Kriging methods will be discussed along with some of their alternatives so that students should be able to make the right choice, no matter how complicated the data situation may be, for the adjustment.

1. Random Effects Model

1.1 Random effects versus fixed parameters

1.2 Prediction and estimation: inhomBLIP versus BLUUE

1.3 Robust collocation: homeBLIP and homBLUP

1.4 Least-squares approach within a modified Gauss-Markov Model

1.5 Hypothesis testing for random constraints

Lab1

2. Spatial Processes

2.1 Definition and typical examples

2.2 Ergodicity, homogeneity and isotropy

2.3 Covariance function, variogram and homeogram

2.4 Kriging and its variants, e.g., least squares collocation

2.5 Accuracy measures and test statistics

Lab2

References (recommended):

Cressie, N.: Statistics for Spatial Data, 2nd edition, Wiley: New York, etc., 1993.

Journel, A.G. and Ch.J. Huijbregts: Mining Geostatistics, latest printing, Academic Press: London, etc., 1990.

Koch, K. R., Parameter Estimation and Hypothesis Testing in Linear Models, New York: Springer, 1999, 2^nd edition.

Rao, C.R. and H. Toutenburg: Linear Models. Least Squares and Alternatives, Springer: New York, etc., 1999, 2^nd edition.

Chilès, J.P. and P. Delfiner: Geostatistics. Modeling Spatial Uncertainty, Wiley: New York, etc., 1999.

Web Resources:

AI-GEOSTATS: The Central Server for GIS & Spatial Statistics

OSU - Program in Spatial Statistics and Environmental Sciences

Electronic Statistics Textbook