Page 15 - Modern Spatiotemporal Geostatistics
P. 15
xiv Modern Spatiotemporal Geostatistics
Correlation analysis and Spatiotemporal geometry 61
Permissibility criteria and Spatiotemporal geometry 64
Effect of Spatiotemporal geometry on mapping 66
Some Final Thoughts 69
CHAPTER 3: Physical Knowledge 71
From the General to the Specific 71
The General Knowledge Base 73
A mathematical formulation of the general knowledge base 74
General knowledge in terms of statistical moments 75
General knowledge in terms of physical laws 76
Some other forms of general knowledge 81
The Specificatory Knowledge Base 82
Specificatory knowledge in terms of hard data 84
Specificatory knowledge in terms of soft data 85
Summa Theologica 87
CHAPTER 4: The Epistemic Paradigm 89
Acquisition and Processing of Physical Knowledge 89
Epistemic Geostatistics and the BME Analysis 90
Prior stage 92
Meta-prior stage 94
Integration or posterior stage 95
Conditional Probability of a Spatiotemporal Map and its
Relation to the Probability of Conditionals 98
Material and strict map conditionals 98
Other map conditionals 100
The BME Net 101
CHAPTER 5: Mathematical Formulation of the
BME Method 103
A Pragmatic Framework of the Mapping Problem 103
The Prior Stage 104
Map information measures in light of general knowledge 104
General knowledge-based map pdf 106
General knowledge in the form of random field statistics
(including multiple-point statistics) 107
General knowledge in the form of physical laws 109
Possible modifications and generalizations of the prior stage 118
The Meta-Prior Stage 119
The Integration or Posterior Stage 120
The Structure of the Modern Spatiotemporal Geostatistics Paradigm . 122
The Two Legs on Which the BME Equations Stand 123
CHAPTER 6: Analytical Expressions of the Posterior
Operator 125