Variograms, Kriging and BLUP Flashcards
What is the variogram
Also known as the semi-variogram of the strcture function
It is the gamma parameter from the definition of intrinsic stationarity
Given a convariance function how do you find it’s variogram
gamma(h) = sigma^2 - C(h)
When des a variogram have a covariance function
When the process is ergodic
What are 2 variograms without covariance fucntions
Linear + Power Law
What is Kriging
Using the variogram to interpolate between data
Give the 5 variations of Kriging we have seen
- Simple Kriging
- Ordinary Kriging
- Universal Kriging
- Block Kriging
- Robsut Kriging
What is Simple Kriging
In simple kriging the mean is assumed to be constant and known
Ordinary Kriging
The mean is estimated as well as the parameters in the variogram
Universal Kriging
The mean is a function of some covariates, usually but not
exclusively, spatial co-ordinates.
What is the BLUP
- Best - least squares
- Linear - Linear combination of the data
- Unbiased - Expected value = “truth”
How do you find BLUP
See Equation sheet
What are the Kriging Equations
See Equation sheet
What assumptions does Kriging make
Optimality and least squares implies normality
Explain in words why we need a ergodic process to get a covariance function from the variogram
If the process is not ergodic then the variogram might have a sill at infinity meaning the covariance function isn’t finite for lags going to infinity, hence it is not supported as we need finite variance
What is the process of finding a covariance function from a variogram
- First find c(0) by finding gamma(infinity) = c(0)
- Then find c(t) =c(0) - gamma(t)
