Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time

The challenge for genetic epidemiologists: how to analyze large numbers of SNPs in relation to complex diseases

Genetic epidemiologists have taken the challenge to identify genetic polymorphisms involved in the development of diseases. Many have collected data on large numbers of genetic markers but are not familiar with available methods to assess their association with complex diseases. Statistical methods have been developed for analyzing the relation between large numbers of genetic and environmental predictors to disease or disease-related variables in genetic association studies. In this commentary we discuss logistic regression analysis, neural networks, including the parameter decreasing method (PDM) and genetic programming optimized neural networks (GPNN) and several non-parametric methods, which include the set association approach, combinatorial partitioning method (CPM), restricted partitioning method (RPM), multifactor dimensionality reduction (MDR) method and the random forests approach. The relative strengths and weaknesses of these methods are highlighted. Logistic regression and neural networks can handle only a limited number of predictor variables, depending on the number of observations in the dataset. Therefore, they are less useful than the non-parametric methods to approach association studies with large numbers of predictor variables. GPNN on the other hand may be a useful approach to select and model important predictors, but its performance to select the important effects in the presence of large numbers of predictors needs to be examined. Both the set association approach and random forests approach are able to handle a large number of predictors and are useful in reducing these predictors to a subset of predictors with an important contribution to disease. The combinatorial methods give more insight in combination patterns for sets of genetic and/or environmental predictor variables that may be related to the outcome variable. As the non-parametric methods have different strengths and weaknesses we conclude that to approach genetic association studies using the case-control design, the application of a combination of several methods, including the set association approach, MDR and the random forests approach, will likely be a useful strategy to find the important genes and interaction patterns involved in complex diseases

Active learning and optimal climate policy

This paper develops a climate-economy model with uncertainty, irreversibility, and active learning. Whereas previous papers assume learning from one observation per period, or experiment with control variables to gain additional information, this paper considers active learning from investment in monitoring, specifically in improved observations of the global mean temperature. We find that the decision maker invests a significant amount of money in climate research, far more than the current level, in order to increase the rate of learning about climate change. This helps the decision maker make improved decisions. The level of uncertainty decreases more rapidly in the active learning model than in the passive learning model with only temperature observations. As the uncertainty about climate change is smaller, active learning reduces the optimal carbon tax. The greater the risk, the larger is the effect of learning. The method proposed here is applicable to any dynamic control problem where the quality of monitoring is a choice variable, for instance, the precision at which we observe GDP, unemployment, or the quality of education

Do serum biomarkers really measure breast cancer?

Background Because screening mammography for breast cancer is less effective for premenopausal women, we investigated the feasibility of a diagnostic blood test using serum proteins. Methods This study used a set of 98 serum proteins and chose diagnostically relevant subsets via various feature-selection techniques. Because of significant noise in the data set, we applied iterated Bayesian model averaging to account for model selection uncertainty and to improve generalization performance. We assessed generalization performance using leave-one-out cross-validation (LOOCV) and receiver operating characteristic (ROC) curve analysis. Results The classifiers were able to distinguish normal tissue from breast cancer with a classification performance of AUC = 0.82 ± 0.04 with the proteins MIF, MMP-9, and MPO. The classifiers distinguished normal tissue from benign lesions similarly at AUC = 0.80 ± 0.05. However, the serum proteins of benign and malignant lesions were indistinguishable (AUC = 0.55 ± 0.06). The classification tasks of normal vs. cancer and normal vs. benign selected the same top feature: MIF, which suggests that the biomarkers indicated inflammatory response rather than cancer. Conclusion Overall, the selected serum proteins showed moderate ability for detecting lesions. However, they are probably more indicative of secondary effects such as inflammation rather than specific for malignancy.United States. Dept. of Defense. Breast Cancer Research Program (Grant No. W81XWH-05-1-0292)National Institutes of Health (U.S.) (R01 CA-112437-01)National Institutes of Health (U.S.) (NIH CA 84955