Generalized Sobol sensitivity indices for dependent variables: numerical methods

The hierarchically orthogonal functional decomposition of any measurable function η of a random vector X=(X₁,?…?, X_p) consists in decomposing η(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when X₁,?…?, X_p are assumed to be dependent, this decomposition is unique if the components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y=η(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y due to each dependent input in X [Chastaing G, Gamboa F, Prieur C. Generalized Hoeffding–Sobol decomposition for dependent variables – application to sensitivity analysis. Electron J Statist. 2012;6:2420–2448]. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sensitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem.     

A New Test for Short Memory in Long Memory Time Series

This article considers short memory characteristics in a long memory process. We derive new asymptotic results for the sample autocorrelation difference ratios. We used these results to develop a new portmanteau test that determines if short memory parameters are statistically significant. In simulations, the new test can detect short memory components more often than the Ljung-Box test when these short memory components are in fact within a long memory process. Interestingly, our test finds short memory autocorrelations in U.S. inflation rate data, whereas the Ljung-Box test fails to find these autocorrelations. Modeling these short memory autocorrelations of the inflation rate data leads to improved model accuracy and more precise prediction.     

Variable selection in partial linear regression with functional covariate

The problem of variable selection is considered in high-dimensional partial linear regression under some model allowing for possibly functional variable. The procedure studied is that of nonconcave-penalized least squares. It is shown the existence of a √n/s_n-consistent estimator for the vector of p_n linear parameters in the model, even when p_n tends to ∞ as the sample size n increases (s_n denotes the number of influential variables). An oracle property is also obtained for the variable selection method, and the nonparametric rate of convergence is stated for the estimator of the nonlinear functional component of the model. Finally, a simulation study illustrates the finite sample size performance of our procedure.     

Evaluation of program success for programs with multiple trials in binary outcomes

A late‐stage clinical development program typically contains multiple trials. Conventionally, the program's success or failure may not be known until the completion of all trials. Nowadays, interim analyses are often used to allow evaluation for early success and/or futility for each individual study by calculating conditional power, predictive power and other indexes. It presents a good opportunity for us to estimate the probability of program success (POPS) for the entire clinical development earlier. The sponsor may abandon the program early if the estimated POPS is very low and therefore permit resource savings and reallocation to other products. We provide a method to calculate probability of success (POS) at an individual study level and also POPS for clinical programs with multiple trials in binary outcomes. Methods for calculating variation and confidence measures of POS and POPS and timing for interim analysis will be discussed and evaluated through simulations. We also illustrate our approaches on historical data retrospectively from a completed clinical program for depression. Copyright © 2015 John Wiley & Sons, Ltd.     

Understanding preferences for tree attributes: the relative effects of socio-economic and local environmental factors

Urban plant biodiversity is influenced by both the physical environment and attitudes and preferences of urban residents for specific plant types. Urban residents are assumed to be disconnected from their immediate environment, and cultural and societal factors have been emphasized over environmental factors in studies of landscaping choices. However, we postulate that local climatic and environmental factors can also affect preferences for plant attributes. Therefore, spatial and temporal patterns in urban tree biodiversity may be driven not only by the direct effect of environmental variables on plant function, but also by the effect of environmental variables on attitudes toward trees and associated choices about which types of trees to plant. Here, we tested the relative effects of socio-economic and local environmental factors on preferences toward tree attributes in five counties in southern California in and surrounding Los Angeles, based on 1,029 household surveys. We found that local environmental factors have as strong an effect on preferences for tree attributes as socio-economic factors. Specifically, people located in hotter climates (average maximum temperature 25.1 °C) were more likely to value shade trees than those located in cooler regions (23.1 °C). Additionally, people located in desert areas were less likely to consider trees to be important in their city compared with people located in naturally forested areas. Overall, our research demonstrates the inherent connections between local environmental factors and perceptions of nature, even in large modern cities. Accounting for these factors can contribute to the growing interest in understanding patterns of urban biodiversity.     

Identity Development in a Transracial Environment: Racial/Ethnic Minority Adoptees in Minnesota

It has been argued that transracially adopted children have increased risk of problems related to self-esteem and ethnic identity development. We evaluated this hypothesis across four groups of transracial adoptees: Asian (n = 427), Latino (n = 28), Black (n = 6), mixed/other (n = 20), and same-race White adoptees (n = 126) from 357 adoptive families. No mean differences were found in adoptees’ ratings of affect about adoption or of curiosity about birth parents. Some differences were found in general identity development and adjustment. There were notable differences in communication about race/ethnicity across groups and between parent and child report.     

Regression Methods for Combining Multiple Classifiers

As no single classification method outperforms other classification methods under all circumstances, decision-makers may solve a classification problem using several classification methods and examine their performance for classification purposes in the learning set. Based on this performance, better classification methods might be adopted and poor methods might be avoided. However, which single classification method is the best to predict the classification of new observations is still not clear, especially when some methods offer similar classification performance in the learning set. In this article we present various regression and classical methods, which combine several classification methods to predict the classification of new observations. The quality of the combined classifiers is examined on some real data. Nonparametric regression is the best method of combining classifiers.     

When Costs Are Unequal and Unknown: A Subtree Grafting Approach for Unbalanced Data Classification*

In binary classifications, a decision tree learned from unbalanced data typically creates an important challenge related to the high misclassification rate of the minority class. Assigning different misclassification costs can address this problem, though usually at the cost of accuracy for the majority class. This effect can be particularly hazardous if the costs cannot be specified precisely. When the costs are unknown or difficult to determine, decision makers may prefer a classifier with more balanced accuracy for both classes rather than a standard or cost‐sensitively learned one. In the context of learning trees, this research therefore proposes a new tree induction approach called subtree grafting (STG). On the basis of a real bank data set and several other data sets, we test the proposed STG method and find that our proposed approach provides a successful compromise between standard and cost‐sensitive trees.