Quantitative Analysis and Modeling of Earth and Environmental Data: Space-Time and Spacetime Data Considerations

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Quantitative Analysis and Modeling of Earth and Environmental Data: Space-Time and Spacetime Data Considerations
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Contents
Preface
Chapter 1: Chronotopologic data analysis
	1. From topos to chronotopos
		1.1. Scientific paradigms
		1.2. Interplay of science and mathematics
		1.3. Natural attributes
		1.4. Kinds of scientific data analysis
			1.4.1. Geostatistics and time-series statistics
			1.4.2. S-TDA and STDA
		1.5. The unifying chronotopologic data analysis notion
			1.5.1. CTDA conditions
			1.5.2. Generic CTDA notions
			1.5.3. Fourfold CTDA objectives
	2. Chronotopologic variability, dependency and uncertainty
		2.1. Conceptual chronotopology
		2.2. Quantitative chronotopology
			2.2.1. Revisiting Tobler's law
		2.3. Concerning real-world uncertainty and its probabilistic description
			2.3.1. Multifaceted notion
			2.3.2. The limited notion of practical certainty
			2.3.3. Sources of uncertainty
			2.3.4. Consequences of uncertainty
			2.3.5. Quantification of uncertainty
	3. Theory and evidence
		3.1. The value of theory
		3.2. Against convenient slogans
		3.3. Evidence unavailability
		3.4. Synergy
	4. Chronotopologic estimation and mapping
		4.1. Threefold conditions
		4.2. Confidence and accuracy
		4.3. Interpretation
	5. A review of CTDA techniques
		5.1. Classification
		5.2. Computer technology
	6. Chronotopologic visualization technology
		6.1. The emergence of visual thinking
	7. The range of CTDA applications
	8. Public domain software libraries
	9. Practice exercises
Chapter 2: Chronotopology theory
	1. Introduction
	2. Basic chronotopologic notions
		2.1. Space and time
		2.2. Chronotopologic domains
		2.3. Equipping the domain with quantitative tools
		2.4. Worldtube, worldsequence and worldlines
		2.5. Assigning physical meaning to points, worldlines, and worldtubes
	3. Chronotopologic metric modeling
		3.1. Bi-metric modeling: S-TDA
		3.2. Uni-metric modeling: STDA
		3.3. Accessibility indicators
	4. Metric effects on chronotopologic attribute interpolation
	5. Practice exercises
Chapter 3: CTDA methodology
	1. Methodologic chain
		1.1. Study attributes
		1.2. Chronotopologic domain
		1.3. Relevant body of knowledge
		1.4. Attribute modeling
			1.4.1. From Altamira paintings to quantum physics
			1.4.2. Interpretation
			1.4.3. Content-free vs. content-driven modeling
			1.4.4. A modeling process
		1.5. Visualization means
	2. About knowledge
		2.1. General and specificatory
			2.1.1. KB interplay
			2.1.2. KB symbolization
			2.1.3. Measurement vs. observation
			2.1.4. S-KB structural features
			2.1.5. Emerging skepticism
		2.2. Data collection issues
			2.2.1. Techniques
			2.2.2. Selection criteria
		2.3. Data quality issues
			2.3.1. Error as negative information
			2.3.2. Seven key requirements
		2.4. Theoretical evaluation of empirical evidence
			2.4.1. Warnings and fallacies
			2.4.2. Probabilistic thinking
			2.4.3. Misleading evidence
	3. Big data: Why learn, if you can look it up?
		3.1. The new analytics
		3.2. The DIA epistemology
			3.2.1. The symbiosis of science and analytics
		3.3. Concerns with DIA
			3.3.1. BD threshold
		3.4. The unbearable naivety of BD-crunchers
			3.4.1. Not BD alone
	4. Attribute data scales
		4.1. Property-oriented classification
		4.2. Attribute-oriented classification
	5. Emergence of chronotopology-dependent statistics
		5.1. The CS inadequacy
		5.2. Blending chronotopology with uncertainty assessment
	6. More on chronotopologic visualization
		6.1. The epistemic value of visualization
		6.2. Producer and viewer
		6.3. Epistemic conditions on visualization
	7. Practice exercises
Chapter 4: Chrono-geographic statistics
	1. Introduction
	2. CGS of data point information
		2.1. Fundamental domain distinction
		2.2. Descriptive measures
		2.3. Point distribution center
			2.3.1. Separate space-time center measures
			2.3.2. Time-averaged CGMC
			2.3.3. Composite spacetime center measure
		2.4. Point dispersion
			2.4.1. Separate space-time dispersion measures
			2.4.2. Time-averaged CGSD
			2.4.3. Composite spacetime dispersion measure
		2.5. Normalized point distribution diffusion
			2.5.1. Separate space-time relative dispersion measures
			2.5.2. Time-averaged CGRD
			2.5.3. Composite spacetime relative dispersion measure
	3. CGS of chrono-geographic attribute values
		3.1. Assessing attribute correlation
			3.1.1. Spacetime global correlation measure
			3.1.2. Space-time global correlation measures
			3.1.3. Spacetime local correlation measure
			3.1.4. Space-time local correlation measure
		3.2. Assessing attribute decorrelation
			3.2.1. Spacetime global decorrelation measure
			3.2.2. Space-time global decorrelation measure
			3.2.3. Spacetime local decorrelation measure
			3.2.4. Space-time local decorrelation measure
		3.3. Practical issues
			3.3.1. Connectivity weights
			3.3.2. CGMI vs. CGGI
			3.3.3. Global vs. local indexes
		3.4. Assessing diversity
			3.4.1. Conjunction or Simpson index
			3.4.2. Equivalence index
			3.4.3. Implication index
			3.4.4. Comparative analysis of the diversity indices
			3.4.5. Computational diversity issues
		3.5. Distributional segregation
	4. Chrono-geographic clustering and hotspot (coldspot) analysis
		4.1. Nearest neighbor (NN) point techniques
			4.1.1. Theoretical mean nearest neighbor distance computation
			4.1.2. Numerical CGNN scale
			4.1.3. Other CGNN measures
		4.2. The issue of statistically significant attribute hotspots (coldspots)
		4.3. Concluding remarks
	5. Practice exercises
Chapter 5: Classical geostatistics
	1. Historical introduction
		1.1. Spatial geostatistics: Basic postulates
		1.2. Spatiotemporal geostatistics: Methodological notions
	2. Random field theory
		2.1. Intuitive setting: The four theses
			2.1.1. Links between physics and geometry
			2.1.2. Separate space-time and composite spacetime
			2.1.3. Basic operational rules
		2.2. Mathematical setting
			2.2.1. S/TRF characterization
			2.2.2. S/TRF classifications
		2.3. Chronotopologic statistics
			2.3.1. General operator
			2.3.2. One-, two-, and three-point chronotopologic statistics
			2.3.3. Modeling assumptions
			2.3.4. Model permissibility
	3. Covariography and variography
		3.1. Data selection and preprocessing
			3.1.1. Covariography and variography prerequisites
		3.2. Empirical covariance and variogram computations
			3.2.1. Computational techniques
		3.3. Covariance and variogram modeling
			3.3.1. Variogram visualization
			3.3.2. 1st class: Separable variability models
			3.3.3. 2nd Class: Nonseparable or composite variability models
			3.3.4. Metric-dependent variogram models
			3.3.5. Case-dependent variogram models
		3.4. Variogram features and their interpretation
			3.4.1. Variogram shape-Real-world attribute correspondence
			3.4.2. Nugget
			3.4.3. Correlation (or dependence) range vector
			3.4.4. Sill
			3.4.5. Behavior at the origin
			3.4.6. Directional anisostationarity
			3.4.7. Periodicity or cyclicity
			3.4.8. Behavior at large space-time lags
		3.5. Variography guidelines, tips, and rules of thumb
	4. Chronotopologic block data analysis
		4.1. Basic concepts
		4.2. Scale issues
	5. Practice exercises
Chapter 6: Modern geostatistics
	1. Toward a theory-driven CTDA
		Threefold requirement
		1.1. Bayesian maximum entropy theory
		1.2. Spatiotemporal random field modeling
			1.2.1. Chronotopologic point sets
			1.2.2. Physical and digital worlds: A synthetic reality perspective
	2. Knowledge bases revisited
		Forms of knowledge and knowing
		2.1. Core or general KB and the science-based BME
			2.1.1. G-KB semantics
			2.1.2. Science-based BME
			2.1.3. Operational G-formalism
			2.1.4. Practical issues
			2.1.5. Empirical algebraic equation models
			2.1.6. Differential equation models
		2.2. Specificatory KB
			2.2.1. Hard and soft datasets
			2.2.2. The protean structure of knowledge
	3. Integrating lawful and dataful statistics
		3.1. The epistemic paradigm: Cassandra and Pollyanna
			3.1.1. Main BME stages
		3.2. Analytical expressions of the BME stages
			3.2.1. A fusion of the empiricical and rational perspectives
			3.2.2. Logical and epistemic distinctions
			3.2.3. Analytical derivations
			3.2.4. More practical issues
		3.3. BME assets
			3.3.1. The value of core knowledge
			3.3.2. The value of soft data
			3.3.3. Auxiliary information
			3.3.4. Stochastic logic in CTDA
	4. Rethinking chronotopologic dependence
		4.1. Problems with tradition
		4.2. Chronotopologic sysketogram and contingogram functions
			4.2.1. The λ-ratio
			4.2.2. Interpretation
			4.2.3. Properties
			4.2.4. Links to factoras and copulas
			4.2.5. Important special cases
		4.3. Construction techniques
			4.3.1. The direct technique
			4.3.2. Analytical and visual comparisons
			4.3.3. Sysketogram- and contingogram-based covariance models
	5. Applications
		5.1. Synthetic experiment
			5.1.1. Synthetic dataset
			5.1.2. Computational issues and simulation results
			5.1.3. Fitting and accuracy performance
		5.2. The sea surface salinity case study
			5.2.1. The SSS domain and the study motivation
			5.2.2. The SSS dataset and its statistical description
			5.2.3. Ordinary covariance- and contingogram-derived covariance
	6. Practice exercises
Chapter 7: Chronotopologic interpolation
	1. Introduction
		1.1. Chronotopologic estimation types
		1.2. Linear CTI
		1.3. Classifications of CTI techniques
		1.4. Mapping technology
			1.4.1. The merging of two worlds
	2. Deterministic chronotopologic interpolation techniques
		2.1. The inverse chronotopologic metric interpolation technique
			2.1.1. Pros and cons
		2.2. The generalized ICTM technique
			2.2.1. Power selection
			2.2.2. Interpolation neighborhood
			2.2.3. Pros and cons
		2.3. The chronotopologic natural neighbor interpolation technique
			2.3.1. Pros and cons
		2.4. Concluding remarks
	3. Statistical chronotopologic interpolation techniques
		3.1. The chronotopologic sample mean technique
			3.1.1. Pros and cons
		3.2. The chronotopologic regression interpolation techniques
			3.2.1. Linear case
			3.2.2. Pros and cons
		3.3. Concluding remarks
	4. Practice exercises
Chapter 8: Chronotopologic krigology
	1. The emergence of geostatistical Kriging
		1.1. Kriging logic
		1.2. Technical characteristics
		1.3. Generic linear Kriging interpolator
		1.4. The Kriging decalogue
		1.5. Kriging neighborhood
		1.6. A review of Kriging techniques
		1.7. Kriging implementation
		1.8. Kriging visualization
	2. 1st Kriging classification
		2.1. Space-time ordinary kriging (STOK)
			2.1.1. STOK equations
			2.1.2. Analytical STOK solutions
			2.1.3. STOK interpretation
			2.1.4. STOK implementation-A case study
			2.1.5. Effect of data noise
		2.2. Space-time simple kriging (STSK)
			2.2.1. STSK equations
			2.2.2. STSK interpretation
			2.2.3. More practical issues
			2.2.4. Violation of Tobler's law
		2.3. Space-time Indicator Kriging (STIK)
			2.3.1. STIK equations
			2.3.2. Pros and cons
	3. Second Kriging classification: point, chronoblock and functional
		3.1. Chronoblock Kriging (CBK)
			3.1.1. CBOK equations
		3.2. Space-time functional Kriging (STFK)
	4. Mapping accuracy indicators and cross-validation tests
		4.1. Mapping accuracy indicators
		4.2. Cross validation
			4.2.1. ``Leave-one-out´´ and other strategies
			4.2.2. Cross-validation guidelines
			4.2.3. Pros and cons
	5. Applied krigology: benefits and concerns
		5.1. Benefits of Kriging interpolation
		5.2. Concerns with Kriging interpolation
	6. Practice exercises
Chapter 9: Chronotopologic BME estimation
	1. Epistemic underpinnings
	2. Mathematical developments
		2.1. BME chronotopologic estimation methodology
			2.1.1. Prior stage: Core knowledge processing
			2.1.2. Metaprior or preposterior stage: Evidential support
			2.1.3. Posterior stage: Total knowledge processing
			2.1.4. Knowledge synthesis
			2.1.5. Posterior probability interpretation
			2.1.6. Self-reference issues
		2.2. The chronotopologic BME estimation equations
			2.2.1. Formalization of the BME estimation
			2.2.2. The BME types of estimators
			2.2.3. The BME estimation uncertainty
			2.2.4. Generalization power
			2.2.5. A BME estimation outline
	3. An overview of real world BME case studies
		3.1. A study of climate-HFRS associations
			3.1.1. The HFRS dataset
			3.1.2. Methodology and result
		3.2. A class-dependent study of chronotopologic HFRS distributions
			3.2.1. The HFRS dataset
			3.2.2. HFRS modeling and methodology
			3.2.3. Dataset classification and processing
			3.2.4. Chronotopologic correlation of HFRS incidence
			3.2.5. Accuracy performance of CD-BME mapping
			3.2.6. Chronotopologic mapping of the HFRS incidence
			3.2.7. Mean HFRS patch distances
		3.3. The sea surface salinity case study
			3.3.1. SSS maps and their interpretation
			3.3.2. SSS mapping performance of the cX(ψ) and cX models
			3.3.3. Comparative SSS mapping accuracy
	4. Practice exercises
Chapter 10: Studying physical laws
	1. The important role of physical PDE in CTDA
		1.1. Stochastic partial differential equations
		1.2. A BME perspective
	2. BME solution of a physical law
		2.1. Deriving the PDF of the SPDE
		2.2. SPDE-derived chronotopologic statistics
		2.3. Assimilating specificatory knowledge (S-KB)
		2.4. Updating the physical SPDF in light of S-KB
		2.5. Accuracy comparison of the standard stochastic solution vs. the BME stochastic solution
	3. BME solution of an epidemic law
	4. Comparing core and specificatory probabilities
		4.1. Generalization and realism
		4.2. The S-KB effect on solution uncertainty
	5. Practice exercises
Chapter 11: CTDA by dimensionality reduction
	1. The motivation
	2. The space-time projection (STP) method
		2.1. Introduction
			2.1.1. The machine learning link
			2.1.2. The threefold notion
		2.2. Dimensionality reduction transformation
			2.2.1. Linear DRT
			2.2.2. Space-time statistics reduction
		2.3. Multiplier determination
			2.3.1. Analytical -expressions
			2.3.2. Differential -expressions
		2.4. Coordinate calculation
		2.5. Projected covariance and variogram models
		2.6. Attribute interpolation and mapping
			2.6.1. STP vs. STOK
	3. Noteworthy STP features
	4. Practice exercises
Chapter 12: DIA models
	1. Introduction
		1.1. Data constraints
		1.2. Big data
	2. Machine learning
	3. Linear regression techniques
		3.1. Multiple linear regression
			3.1.1. Simple linear regression
			3.1.2. Land-use regression
		3.2. Geographically weighted regression
	4. Artificial neural network
		4.1. Human brain as a neural network
		4.2. From the BNN to the ANN
		4.3. ANN structure
			4.3.1. Activation or transfer functions
			4.3.2. Nodes
			4.3.3. Output values
			4.3.4. Pros and cons of ANN
		4.4. ANN modeling in practice
	5. Practice exercises
Chapter 13: Syntheses of CTDA techniques with DIA models
	1. A broad synthesis perspective
		1.1. BME-ML integration
	2. A synthesis of the STP and BME techniques
		2.1. HFRS in Heilongjiang Province (China)
		2.2. Datasets and modeling assumptions
		2.3. Step-by-step STP-BME
		2.4. Comparative analysis
	3. A synthesis of the STP-BME technique with the LUR and ANN models
		3.1. The environmental Jing-Jin-Ji study
		3.2. Datasets and step-by-step synthesis
	4. A synthesis of the BME technique with the MLR and GWR models
		4.1. Public health concerns in China
		4.2. Intersections of data
		4.3. Integration of techniques
		4.4. Covariance modeling
		4.5. BME assessment and mapping
	5. Epilogue
	6. Practice exercises
References
Index
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