Statistical uncertainty and error propagation

This lecture is about some of the basics of uncertainty: the use of variances and covariances to express statistical uncertainty (“error bars”, error ellipses); we are concentrating on the uncertainties of geographic co-ordinates. This makes it necessary to talk about geodetic datums – alternative ways of fixing the starting point(s) used for fixing geodetic co-ordinates in a network solution. It also makes it desirable to discuss absolute (single point) and relative (between pairs of points) co-ordinates and their uncertainties. We follow up by discussing some more esoteric concepts; these sections are provided as reading material, but we will discuss them only conceptually, to get the ideas across. The learning objective of this is, that you will not be completely surprised if in future work, these concepts turn up; you will be somewhat prepared to read up on these subjects and use them in your work. The subjects are (in blue): 1. Criterion matrices for modelling spatial variance structures 2. Stochastic processes as a means of modelling time series behaviour statistically; signal and noise processes 3. Some even more esoteric subjects: