Nonlinear Estimation

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. Language: English