Non-Linear Estimation is a handbook for the practical statistician or modeller interested in fitting and interpreting non-linear models with the aid of a computer. A major theme of the book is the use of 'stable parameter systems'; these provide rapid convergence of optimization algorithms, more reliable dispersion matrices and confidence regions for parameters, and easier comparison of rival models. The book provides insights into why some models are difficult to fit, how to combine fits over different data sets, how to improve data collection to reduce prediction variance, and how to program…mehr
Non-Linear Estimation is a handbook for the practical statistician or modeller interested in fitting and interpreting non-linear models with the aid of a computer. A major theme of the book is the use of 'stable parameter systems'; these provide rapid convergence of optimization algorithms, more reliable dispersion matrices and confidence regions for parameters, and easier comparison of rival models. The book provides insights into why some models are difficult to fit, how to combine fits over different data sets, how to improve data collection to reduce prediction variance, and how to program particular models to handle a full range of data sets. The book combines an algebraic, a geometric and a computational approach, and is illustrated with practical examples. A final chapter shows how this approach is implemented in the author's Maximum Likelihood Program, MLP.
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Inhaltsangabe
1 Models, Parameters, and Estimation.- 1.1. The Models To Be Considered.- 1.2. Maximum Likelihood Estimation.- 2 Transformations of Parameters.- 2.1. What Are Parameters?.- 2.2. A Priori Stable Parameters.- 2.3. A Posteriori Stable Parameters.- 2.4. Theoretical Justification for Stable Parameters Using Deviance Residuals.- 2.5. Similarity of Models.- 3 Inference and Stable Transformations.- 3.1. Existence and Uniqueness of Solutions.- 3.2. Inferences on Functions of Parameters.- 3.3. Effective Replication, Influential Observations, and Design.- 4 The Geometry of Nonlinear Inference.- 4.1. The Role of Graphical Representations.- 4.2. Data Plots in (x?y)Space.- 4.3. Data Plots in (y?y)Space.- 4.4. Plots in Parameter Space.- 5 Computing Methods for Nonlinear Modeling.- 5.1. Computer Programs, Libraries, and Packages.- 5.2. Requirements for Fitting Nonlinear Models.- 5.3. Algorithms for Nonlinear Inference.- 5.4. Separable Linear Parameters.- 5.5. Confidence Intervals for Parameters and Functions.- 6 Practical Applications of Nonlinear Modeling.- 6.1. Some Questions To Be Asked in any Practical Application.- 6.2 Curve Fitting to Regular Observations in Time.- 6.3. Fitting Data to Models Defined by Differential Equations.- 7 A Program for Fitting Nonlinear Models, MLP.- 7.1. Structure of MLP.- 7.2. Curve Fitting y = f(x, ?)+ ?.- 7.3. Fitting Frequency Distributions.- 7.4. Standard Biological Models Requiring Maximum Likelihood Estimation.- 7.5. General User-Defined Models in MLP.- Appendix Glossary of Unfamiliar Terms Used in This Work.- References.- Author Index.
1 Models, Parameters, and Estimation.- 1.1. The Models To Be Considered.- 1.2. Maximum Likelihood Estimation.- 2 Transformations of Parameters.- 2.1. What Are Parameters?.- 2.2. A Priori Stable Parameters.- 2.3. A Posteriori Stable Parameters.- 2.4. Theoretical Justification for Stable Parameters Using Deviance Residuals.- 2.5. Similarity of Models.- 3 Inference and Stable Transformations.- 3.1. Existence and Uniqueness of Solutions.- 3.2. Inferences on Functions of Parameters.- 3.3. Effective Replication, Influential Observations, and Design.- 4 The Geometry of Nonlinear Inference.- 4.1. The Role of Graphical Representations.- 4.2. Data Plots in (x?y)Space.- 4.3. Data Plots in (y?y)Space.- 4.4. Plots in Parameter Space.- 5 Computing Methods for Nonlinear Modeling.- 5.1. Computer Programs, Libraries, and Packages.- 5.2. Requirements for Fitting Nonlinear Models.- 5.3. Algorithms for Nonlinear Inference.- 5.4. Separable Linear Parameters.- 5.5. Confidence Intervals for Parameters and Functions.- 6 Practical Applications of Nonlinear Modeling.- 6.1. Some Questions To Be Asked in any Practical Application.- 6.2 Curve Fitting to Regular Observations in Time.- 6.3. Fitting Data to Models Defined by Differential Equations.- 7 A Program for Fitting Nonlinear Models, MLP.- 7.1. Structure of MLP.- 7.2. Curve Fitting y = f(x, ?)+ ?.- 7.3. Fitting Frequency Distributions.- 7.4. Standard Biological Models Requiring Maximum Likelihood Estimation.- 7.5. General User-Defined Models in MLP.- Appendix Glossary of Unfamiliar Terms Used in This Work.- References.- Author Index.
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