Sampling and Statistics Explained

In the early 1990s, I advised JMG 's Editor that geostatistics violates the requirement of functional independence and ignores the concept of degrees of freedom. IAMG 's Councilors, JMG 's Editor, and his Associate and Assistant Editors, have yet to explain why the distance-weighted average lost its variance before it was reborn as a kriged estimate. I have explained that one-to-one correspondence between variances and central values (arithmetic means and all sorts of weighted averages) is inviolable in classical statistics. I have asked IAMG's Councilors, JMG's Editor, and his Associate and Assistant Editors to explain why one-to-one correspondence is irrelevant in geostatistics. The silence of the geostatistocrats is deeply disturbing.

The rise of kriging covariances and the fall of kriging variances implies that the requirement of functional independence should not be ignored. Armstrong and Champigny's caution against oversmoothing suggests that this requirement may be violated a little but not a lot. Geostatistics is all about rigging the rules of mathematical statistics with impunity. Geostatistics ought to return to its roots but its practitioners assume, krige, smooth, and apply a mind-boggling hodgepodge of kriging methods.

What would happen if each distance-weighted average did have its own variance, if verifying spatial dependence did precede interpolating by kriging, if sampling variograms did show where orderliness in sample spaces dissipates into randomness, and if confidence limits for contents and grades of ore reserves were measures for risk? Matheronian madness and all of the kriging games would vanish! That's all!

A synopsis of Tools and Techniques is downloadable while I'm working on Sampling and Statistics Explained, Towards commonsensical sampling practices and scientically sound statistical methods. The objective is to describe and implement in Excel spreadsheet templates a wide range of tools and techniques applicable in sampling and statistics. It's a work in progress!

List of Contents
Preface
Chapter 1 Introduction
Chapter 2 Sampling theory
Figure 2.5 Different population variances and same mean
Figure 2.6 Different means and same population variance
Figure 2.7 Population variance and sample variance
Table 2.1 Event space and dot sum count for three dice
Table 2.2 Relative and cumulative percentages for gold particles
Table 2.3 Bernouilli and Poisson distributions
Table 2.7.1 Test for bias (SURNs)
Table 2.7.2 Test for homogeneity of variances
Table 2.7.3 Test for spatial dependence
Table 2.8.1 Test for bias (SNRNs)
Table 2.8.2 Test for homogeneity of variances
Table 2.8.3 Test for spatial dependence
Table 2.10.1 Test for spatial dependence
Table 2.10.2 Confidence limits for block grades

Chapter 3 Statistical methods
Chapter 4 Sampling practice