Estimating the spatial scale of herbicide and soil interactions by nested sampling, hierarchical analysis of variance and residual maximum likelihood

An unbalanced nested sampling design was used to investigate the spatial scale of soil and herbicide interactions at the field scale. A hierarchical analysis of variance based on residual maximum likelihood (REML) was used to analyse the data and provide a first estimate of the variogram. Soil samples were taken at 108 locations at a range of separating distances in a 9 ha field to explore small and medium scale spatial variation. Soil organic matter content, pH, particle size distribution, microbial biomass and the degradation and sorption of the herbicide, isoproturon, were determined for each soil sample. A large proportion of the spatial variation in isoproturon degradation and sorption occurred at sampling intervals less than 60 m, however, the sampling design did not resolve the variation present at scales greater than this. A sampling interval of 20-25 m should ensure that the main spatial structures are identified for isoproturon degradation rate and sorption without too great a loss of information in this field.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

A Functional Magnetic Resonance Imaging Predictor of Treatment Response to Venlafaxine in Generalized Anxiety Disorder

Background: Functional magnetic resonance imaging (fMRI) holds promise as a noninvasive means of identifying neural responses that can be used to predict treatment response before beginning a drug trial. Imaging paradigms employing facial expressions as presented stimuli have been shown to activate the amygdala and anterior cingulate cortex (ACC). Here, we sought to determine whether pretreatment amygdala and rostral ACC (rACC) reactivity to facial expressions could predict treatment outcomes in patients with generalized anxiety disorder (GAD).Methods: Fifteen subjects (12 female subjects) with GAD participated in an open-label venlafaxine treatment trial. Functional magnetic resonance imaging responses to facial expressions of emotion collected before subjects began treatment were compared with changes in anxiety following 8 weeks of venlafaxine administration. In addition, the magnitude of fMRI responses of subjects with GAD were compared with that of 15 control subjects (12 female subjects) who did not have GAD and did not receive venlafaxine treatment.Results The magnitude of treatment response was predicted by greater pretreatment reactivity to fearful faces in rACC and lesser reactivity in the amygdala. These individual differences in pretreatment rACC and amygdala reactivity within the GAD group were observed despite the fact that 1) the overall magnitude of pretreatment rACC and amygdala reactivity did not differ between subjects with GAD and control subjects and 2) there was no main effect of treatment on rACC-amygdala reactivity in the GAD group.Conclusions: These findings show that this pattern of rACC-amygdala responsivity could prove useful as a predictor of venlafaxine treatment response in patients with GAD.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Multidecadal modulation of El Nino-Southern Oscillation (ENSO) variance by Atlantic Ocean sea surface temperatures

Observations suggest a possible link between the Atlantic Multidecadal Oscillation (AMO) and El Nino Southern Oscillation (ENSO) variability, with the warm AMO phase being related to weaker ENSO variability. A coupled ocean-atmosphere model is used to investigate this relationship and to elucidate mechanisms responsible for it. Anomalous sea surface temperatures (SSTs) associated with the positive AMO lead to change in the basic state in the tropical Pacific Ocean. This basic state change is associated with a deepened thermocline and reduced vertical stratification of the equatorial Pacific ocean, which in turn leads to weakened ENSO variability. We suggest a role for an atmospheric bridge that rapidly conveys the influence of the Atlantic Ocean to the tropical Pacific. The results suggest a non-local mechanism for changes in ENSO statistics and imply that anomalous Atlantic ocean SSTs can modulate both mean climate and climate variability over the Pacific.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

Variance estimation with highly stratified sampling designs with unequal probabilities

It is common practice to design a survey with a large number of strata. However, in this case the usual techniques for variance estimation can be inaccurate. This paper proposes a variance estimator for estimators of totals. The method proposed can be implemented with standard statistical packages without any specific programming, as it involves simple techniques of estimation, such as regression fitting.

Variance estimation for systematic sampling from deliberately ordered populations

The systematic sampling (SYS) design (Madow and Madow, 1944) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982) and usual variance estimators (Yates and Grundy, 1953) are inadequate and can overestimate the variance significantly (Särndal et al., 1992). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.

Variance estimation with Chao's sampling scheme

We show that the Hájek (Ann. Math Statist. (1964) 1491) variance estimator can be used to estimate the variance of the Horvitz–Thompson estimator when the Chao sampling scheme (Chao, Biometrika 69 (1982) 653) is implemented. This estimator is simple and can be implemented with any statistical packages. We consider a numerical and an analytic method to show that this estimator can be used. A series of simulations supports our findings.