On Generalized Cross Validation for Stable Parameter Selection in Disease Models
نویسندگان
چکیده
In this paper we study advantages and limitations of the Generalized Cross Validation (GCV) approach for selecting a regularization parameter in the case of a partially stochastic linear irregular operator equation. The research has been motivated by an inverse problem in epidemiology, where the goal was to reconstruct a time dependent treatment recovery rate for Plasmodium falciparum, the most dangerous form of malaria. Initial numerical simulations gave rise to a theoretical analysis of the expected value of the GCV function and the efficiency of the GCV method for different noise levels. It was shown that, as opposed to L-curve, the GCV does not necessarily generate a systematic error in the value of the regularization parameter for Tikhonov’s stabilizing algorithm.
منابع مشابه
Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation
In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...
متن کاملEfficient Tuning Parameter Selection by Cross-Validated Score in High Dimensional Models
As DNA microarray data contain relatively small sample size compared to the number of genes, high dimensional models are often employed. In high dimensional models, the selection of tuning parameter (or, penalty parameter) is often one of the crucial parts of the modeling. Cross-validation is one of the most common methods for the tuning parameter selection, which selects a parameter value with...
متن کاملShrinkage Tuning Parameter Selection in Precision Matrices Estimation
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This paper tries to fill this gap by focusing on the problem of shrinkage parameter selection when estimating sparse precision matrices using the penalized likelih...
متن کاملGeneralized Nonparametric Mixed-Effect Models: Computation and Smoothing Parameter Selection
Generalized linear mixed-effect models are widely used for the analysis of correlated nonGaussian data such as those found in longitudinal studies. In this article, we consider extensions with nonparametric fixed effects and parametric random effects. The estimation is through the penalized likelihood method, and our focus is on the efficient computation and the effective smoothing parameter se...
متن کاملModelling and smoothing parameter estimation with multiple quadratic penalties
Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single penalty case the analyst has several well founded techniques to choose from. However, many modelling problems suggest a formulat...
متن کامل