Journal ArticleDOI
Simultaneous confidence and prediction intervals for nonlinear regression models with application to a groundwater flow model
TLDR
In this paper, the authors presented methods for computing three types of simultaneous confidence and prediction intervals (exact, likelihood ratio, and linearized) on output from nonlinear regression models with normally distributed residuals.Abstract:
Methods are presented for computing three types of simultaneous confidence and prediction intervals (exact, likelihood ratio, and linearized) on output from nonlinear regression models with normally distributed residuals. The confidence intervals can be placed on individual regression parameters or on the true regression function at any number of points in the domain of the independent variables, and the prediction intervals can be placed on any number of future observations. The confidence intervals are analogous to simultaneous Scheffe intervals for linear models and the prediction intervals are analogous to the prediction intervals of Hahn (1972). All three types of intervals can be computed efficiently by using the same straightforward Lagrangian optimization scheme. The prediction intervals can be treated in the same computational framework as the confidence intervals by including the random errors as pseudoparameters in the Lagrangian scheme. The methods are applied to a hypothetical groundwater model for flow to a well penetrating a leaky aquifer. Three different data sets are used to demonstrate the effect of sampling strategies on the intervals. For all three data sets, the linearized confidence intervals are inferior to the exact and likelihood ratio intervals, with the latter two being very similar; however, all three types of prediction intervals yielded similar results. The third data set (time drawdown data at only a single observation well) points out many of the problems that can arise from extreme nonlinear behavior of the regression model.read more
Citations
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MonographDOI
Estimating groundwater recharge
TL;DR: In this article, a critical evaluation of the theory and assumptions that underlie methods for estimating rates of groundwater recharge is provided, with detailed explanations of the methods provided - allowing readers to apply many of the techniques themselves without needing to consult additional references.
Journal ArticleDOI
Inverse problem in hydrogeology
TL;DR: It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data, proper accounting of uncertainty, etc.
Proceedings ArticleDOI
Methods and Guidelines for Effective Model Calibration
TL;DR: This document summarizes current capabilities, research and operational priorities, and plans for further studies that were established at the 2015 USGS workshop on quantitative hazard assessments of earthquake-triggered landsliding and liquefaction in the Central American region.
Journal ArticleDOI
Inverse Models: A Necessary Next Step in Ground‐Water Modeling
Eileen P. Poeter,Mary C. Hill +1 more
TL;DR: Inverse models using nonlinear least-squares regression provide capabilities that help modelers take full advantage of the insight available from ground-water models as discussed by the authors, but lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use.
Journal ArticleDOI
Review of strategies for handling geological uncertainty in groundwater flow and transport modeling
Jens Christian Refsgaard,Steen Christensen,Torben O. Sonnenborg,Dorte Seifert,Anker Lajer Højberg,Lars Troldborg +5 more
TL;DR: General challenge in model averaging with respect to choosing mutually exclusive and collectively exhaustive choice models, as well as to assign weights when models are used beyond their calibration base, are discussed.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
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TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
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Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
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