By Richard L. Cooley and Richard L. Naff
Introduction
Flow equation and boundary conditions
Types of solutions
Direct solution for head
Inverse solution for parameters
Solution using real data
Sources of error in ground-water data
Sources of error in head data
Sources of error in parameter data
Model construction
Trial and error methods
Formal optimization procedures
References cited
Additional reading
Review of probability and statistics
Basic concepts
Frequencies and distributions
Discrete random variables
Problem 2.2-1
Histograms
Continuous random variables
Problem 2.2-2
Properties of cumulative distribution functions
An example: the normal distribution
Expectation and the continuous random variable
The mean
Problem 2.3-l
Generalization and application of the expectation operator
The variance, standard deviation, and coefficient of variation
Problem 2.3-2
Jointly distributed random variables
Expectation of jointly distributed random variables
Independent random variables
Conditional probabilities
Problem 2.4-l
Variance of a column vector
Problem 2.4-2
Estimators of population parameters
Mean estimator
Problem 2.5-l
Variance estimator
Estimator of correlation coefficient
Summary
Problem 2.5-2
Transformation of random variables
Sum of independent normal random variables
The Chi-square distribution
The F distribution
Problem 2.6-l
Central limit theorem
Confidence limits
Problem 2.8-l
Hypothesis testing
Type I error
One-tailed test
Two-tailed test
Type II error
Summary of method
Problem 2.9-l
Tables of probability distributions
Appendices
Correlation of two linearly related random variables
Expected value of variance estimator
References cited
Additional reading
Regression solution of modeling problems
Introduction and background
Assumed model structure
Least-squares estimation
Inclusion of prior information
Problem 3.1-l
Regression when the model is linear
Derivation of solution
Solution algorithm
Problem 3.2-l
Singularity and conditioning
Regression when the model is nonlinear
Modified Gauss-Newton method
Problem 3.3-l
3.3.2 Non-linear regression when the model is numerical
Problem 3.3-2
Convergence and conditioning
Computation of and u and p
Regression including prior information
Model structure
Solution procedures
References cited
Additional reading
Numerical nonlinear regression solution of general steady-state ground-water flow problems
Assumed model and solution procedure
Problem specification
Matrix form of regression model
Nonlinear regression solution
Singularity and conditioning
Problem 4.2-l
Problem 4.2-2
Appendices
Integrated finite difference model
Computation of nodal sensitivities for the integrated finite difference model
Derivation of equation 4.2-l
Documentation of program for nonlinear regression solution of steady-state ground-water flow problems
References cited
Additional reading
Elementary analysis and use of the regression model
Assumed forms of model equations
Assumptions of regression modeling
Relationships between residuals and disturbances
Some statistical measures
The error variance
The correlation, Ry, between wY and wt
The variance-covariance matrix for b
The correlation, rij, between any two parameters bi and bj
Problem 5.4-l
Analysis of residuals
Distribution of residuals
Graphical procedures
Problem 5.5-l
Problem 5.5-2
Investigation of alternative parameter sets
Generalized W statistic
Joint confidence region for B2
Problem 5.6-l
Problem 5.6-2
Problem 5.6-3
Investigation of predictive reliability
The variance-covariance matrix for t
5.7.2 Confidence interval for fBi
5.7.3 Prediction interval for predicted observation Yjpred
Problem 5.7-l
Appendix
Documentation of program to compute vectors d and g of section 5.5.2
References cited
Additional reading
Some advanced topics
Advanced models
Regression when the dependent variable is implicit
Regression when the implicit-variable model is numerical
Modified Beale's measure of nonlinearity
Problem 6.2-l
Problem 6.2-2
Compatibility of prior and regression estimates of parameters
Problem 6.3-l
Appendix
Documentation of program to compute the modified Beale’s measure
References cited
Additional reading
Answers to exercises
| AccessibilityFOIAPrivacyPolicies and Notices | |
  |
|