design
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| ===== Literature ===== | ===== Literature ===== | ||
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| + | **//Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations//**\\ | ||
| + | **Cao, Jiguo and Huang, Jianhua Z. and Wu, Hulin**\\ | ||
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| + | Some quotes: | ||
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| + | > Classical optimal design criteria suffer from two major flaws when applied to nonlinear problems. First, they are based on linearizing the model around a point estimate of the unknown parameter and therefore depend on the uncertain value of that parameter. Second, classical design methods are unavailable in ill-posed estimation situations, where previous data lack the information needed to properly construct the design criteria... | ||
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| + | >The simulation-based approach allows one to start the model-based optimization of experiments at an early stage of the parameter estimation process, in situations where the classical design criteria are not available... | ||
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| + | Use the term "Experimental Map" to refer to a distribution of designs. | ||
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| + | <code> | ||
| + | @article{doi:10.1198/jcgs.2011.10021, | ||
| + | author = {Cao, Jiguo and Huang, Jianhua Z. and Wu, Hulin}, | ||
| + | title = {Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations}, | ||
| + | journal = {Journal of Computational and Graphical Statistics}, | ||
| + | volume = {21}, | ||
| + | number = {1}, | ||
| + | pages = {42-56}, | ||
| + | year = {2012}, | ||
| + | doi = {10.1198/jcgs.2011.10021}, | ||
| + | URL = {http://amstat.tandfonline.com/doi/abs/10.1198/jcgs.2011.10021}, | ||
| + | eprint = {http://amstat.tandfonline.com/doi/pdf/10.1198/jcgs.2011.10021} | ||
| + | } | ||
| + | </code> | ||
| + | |||
| + | ==== Further Reading ==== | ||
| + | |||
| + | === Optimal Design === | ||
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| + | **Han, C., and Chaloner, K. (2004), “Bayesian Experimental Design for Nonlinear Mixed-Effects Models With Application to HIV Dynamics,” Biometrics, 60, 25–33.** | ||
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| + | **Muller, P., Sanso, B., and De Iorio, M. (2004), “Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation,” Journal of the American Statistical Association, 99 (467), 788–798**. This is "Bayesian simulation-based ptimal design". | ||
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| + | === Differential Equations === | ||
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| + | **Liang, H., and Wu, H. (2008), “Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models,” Journal of the American Statistical Association, 103, 1570–1583.** | ||
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| + | **Ramsay, J. O., Hooker, G., Campbell, D., and Cao, J. (2007), “Parameter Estimation for Differential Equations: A Generalized Smoothing Approach” (with discussion), Journal of the Royal Statistical Society, Ser. B, 69, 741–796** | ||
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