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.

Recent changes in solar outputs and the global mean surface temperature. III. Analysis of contributions to global mean air surface temperature rise

A multivariate fit to the variation in global mean surface air temperature anomaly over the past half century is presented. The fit procedure allows for the effect of response time on the waveform, amplitude and lag of each radiative forcing input, and each is allowed to have its own time constant. It is shown that the contribution of solar variability to the temperature trend since 1987 is small and downward; the best estimate is -1.3% and the 2sigma confidence level sets the uncertainty range of -0.7 to -1.9%. The result is the same if one quantifies the solar variation using galactic cosmic ray fluxes (for which the analysis can be extended back to 1953) or the most accurate total solar irradiance data composite. The rise in the global mean air surface temperatures is predominantly associated with a linear increase that represents the combined effects of changes in anthropogenic well-mixed greenhouse gases and aerosols, although, in recent decades, there is also a considerable contribution by a relative lack of major volcanic eruptions. The best estimate is that the anthropogenic factors contribute 75% of the rise since 1987, with an uncertainty range (set by the 2sigma confidence level using an AR(1) noise model) of 49–160%; thus, the uncertainty is large, but we can state that at least half of the temperature trend comes from the linear term and that this term could explain the entire rise. The results are consistent with the intergovernmental panel on climate change (IPCC) estimates of the changes in radiative forcing (given for 1961–1995) and are here combined with those estimates to find the response times, equilibrium climate sensitivities and pertinent heat capacities (i.e. the depth into the oceans to which a given radiative forcing variation penetrates) of the quasi-periodic (decadal-scale) input forcing variations. As shown by previous studies, the decadal-scale variations do not penetrate as deeply into the oceans as the longer term drifts and have shorter response times. Hence, conclusions about the response to century-scale forcing changes (and hence the associated equilibrium climate sensitivity and the temperature rise commitment) cannot be made from studies of the response to shorter period forcing changes.

Effects of beverage alcohol taxes and prices on drinking: a meta-analysis of 1003 estimates from 112 studies

Aims: We conducted a systematic review of studies examining relationships between measures of beverage alcohol tax or price levels and alcohol sales or self-reported drinking. A total of 112 studies of alcohol tax or price effects were found, containing 1003 estimates of the tax/price–consumption relationship. Design: Studies included analyses of alternative outcome measures, varying subgroups of the population, several statistical models, and using different units of analysis. Multiple estimates were coded from each study, along with numerous study characteristics. Using reported estimates, standard errors, t-ratios, sample sizes and other statistics, we calculated the partial correlation for the relationship between alcohol price or tax and sales or drinking measures for each major model or subgroup reported within each study. Random-effects models were used to combine studies for inverse variance weighted overall estimates of the magnitude and significance of the relationship between alcohol tax/price and drinking. Findings: Simple means of reported elasticities are -0.46 for beer, -0.69 for wine and -0.80 for spirits. Meta-analytical results document the highly significant relationships (P < 0.001) between alcohol tax or price measures and indices of sales or consumption of alcohol (aggregate-level r = -0.17 for beer, -0.30 for wine, -0.29 for spirits and -0.44 for total alcohol). Price/tax also affects heavy drinking significantly (mean reported elasticity = -0.28, individual-level r = -0.01, P < 0.01), but the magnitude of effect is smaller than effects on overall drinking. Conclusions: A large literature establishes that beverage alcohol prices and taxes are related inversely to drinking. Effects are large compared to other prevention policies and programs. Public policies that raise prices of alcohol are an effective means to reduce drinking.

Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.

Comparative analysis of performance and stability among composite cross populations, variety mixtures and pure lines of winter wheat in organic and conventional cropping systems

This study investigated the effects of increased genetic diversity in winter wheat (Triticum aestivum L.), either from hybridization across genotypes or from physical mixing of lines, on grain yield, grain quality, and yield stability in different cropping environments. Sets of pure lines (no diversity), chosen for high yielding ability or high quality, were compared with line mixtures (intermediate level of diversity), and lines crossed with each other in composite cross populations (CCPn, high diversity). Additional populations containing male sterility genes (CCPms) to increase outcrossing rates were also tested. Grain yield, grain protein content, and protein yield were measured at four sites (two organically-managed and two conventionally-managed) over three years, using seed harvested locally in each preceding year. CCPn and mixtures out-yielded the mean of the parents by 2.4% and 3.6%, respectively. These yield differences were consistent across genetic backgrounds but partly inconsistent across cropping environments and years. Yield stability measured by environmental variance was higher in CCPn and CCPms than the mean of the parents. An index of yield reliability tended to be higher in CCPn, CCPms and mixtures than the mean of the parents. Lin and Binns’ superiority values of yield and protein yield were consistently and significantly lower (i.e. better) in the CCPs than in the mean of the parents, but not different between CCPs and mixtures. However, CCPs showed greater early ground cover and plant height than mixtures. When compared with the (locally non-predictable) best-yielding pure line, CCPs and mixtures exhibited lower mean yield and somewhat lower yield reliability but comparable superiority values. Thus, establishing CCPs from smaller sets of high-performing parent lines might optimize their yielding ability. On the whole, the results demonstrate that using increased within-crop genetic diversity can produce wheat crops with improved yield stability and good yield reliability across variable and unpredictable cropping environments.