Geostatistics: Kriged Estimate

Sir Ronald A Fisher (1890-1962), a statistician and geneticist, was familiar with the distance-weighted average long before it metamorphosed into a kriged estimate in recognition of the groundbreaking work of Professor D A Krige, Honorary Research Fellow, University of the Witwatersrand, South Africa, and the first plotter of kriged estimates in a gold deposit.


	A set of measured values with different coordinates in a sample space defines an infinite set of distance-weighted averages or kriged estimates. In contrast, a set of measured values with variable weights such as counts, densities, lengths, masses or volumes has but one count-, density-, length-, mass-, or volume-weighted average.

If all measured values in a set have identical weights, then the arithmetic mean is the central value of the set. Each central value (arithmetic mean or some weighted average) is a functionally dependent variable of a set of measured values of a random variable in a static stochastic system such as a volume of in-situ ore or a stockpile of crushed ore, or a dynamic stochastic system such as a wet mass of mill feed or concentrate.

We need not study more than a single page of Geostatistical Ore Reserve Estimation to find out why the requirement of functional independence and the concept of degrees of freedom are fundamental in classical statistics but violated and ignored in geostatistics. Here's all we need to know! Calculated values (arithmetic means and weighted averages) are functionally dependent values. Measured values are functionally independent values (but not necessarily spatially independent values). Degrees of freedom are awarded to measured values and not to calculated values. This is simpler stuff than dismissing degrees of freedom and making variances of kriged estimates vanish without a trace!