Bayesian analysis for nonlinear regression model under skewed errors,with application in growth curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew‐t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.     

Direct Observation of Li‐Ion Transport in Electrodes under Nonequilibrium Conditions Using Neutron Depth Profiling

One of the key challenges of Li‐ion electrodes is enhancement of (dis)charge rates. This is severely hindered by the absence of a technique that allows direct and nondestructive observation of lithium ions in operating batteries. Direct observation of the Li‐ion concentration profiles using operando neutron depth profiling reveals that the rate‐limiting step is depended not only on the electrode morphology but also on the cycling rate itself. In the LiFePO₄ electrodes phase nucleation limits the charge transport at the lowest cycling rates, whereas electronic conductivity is rate limiting at intermediate rates, and only at the highest rates ionic transport through the electrode is rate limiting. These novel insights into electrode kinetics are imperative for the improvement of Li‐ion batteries and show the large value of in situ NDP in Li‐ion battery research and development.     

Predicting fine‐scale distributions of peripheral aquatic species in headwater streams

Headwater species and peripheral populations that occupy habitat at the edge of a species range may hold an increased conservation value to managers due to their potential to maximize intraspecies diversity and species' adaptive capabilities in the context of rapid environmental change. The southern Appalachian Mountains are the southern extent of the geographic range of native Salvelinus fontinalis and naturalized Oncorhynchus mykiss and Salmo trutta in eastern North America. We predicted distributions of these peripheral, headwater wild trout populations at a fine scale to serve as a planning and management tool for resource managers to maximize resistance and resilience of these populations in the face of anthropogenic stressors. We developed correlative logistic regression models to predict occurrence of brook trout, rainbow trout, and brown trout for every interconfluence stream reach in the study area. A stream network was generated to capture a more consistent representation of headwater streams. Each of the final models had four significant metrics in common: stream order, fragmentation, precipitation, and land cover. Strahler stream order was found to be the most influential variable in two of the three final models and the second most influential variable in the other model. Greater than 70% presence accuracy was achieved for all three models. The underrepresentation of headwater streams in commonly used hydrography datasets is an important consideration that warrants close examination when forecasting headwater species distributions and range estimates. Additionally, it appears that a relative watershed position metric (e.g., stream order) is an important surrogate variable (even when elevation is included) for biotic interactions across the landscape in areas where headwater species distributions are influenced by topographical gradients.     

Determination of Sample Sizes for Demonstrating Efficacy of Radiation Countermeasures

Summary .  In response to the ever increasing threat of radiological and nuclear terrorism, active development of nontoxic new drugs and other countermeasures to protect against and/or mitigate adverse health effects of radiation is ongoing. Although the classical LD₅₀ study used for many decades as a first step in preclinical toxicity testing of new drugs has been largely replaced by experiments that use fewer animals, the need to evaluate the radioprotective efficacy of new drugs necessitates the conduct of traditional LD₅₀ comparative studies ( FDA, 2002 ,  Federal Register   67, 37988–37998). There is, however, no readily available method to determine the number of animals needed for establishing efficacy in these comparative potency studies. This article presents a sample-size formula based on Student's  t  for comparative potency testing. It is motivated by the U.S. Food and Drug Administration's (FDA's) requirements for robust efficacy data in the testing of response modifiers in total body irradiation experiments where human studies are not ethical or feasible. Monte Carlo simulation demonstrated the formula's performance for Student's  t , Wald, and likelihood ratio tests in both logistic and probit models. Importantly, the results showed clear potential for justifying the use of substantially fewer animals than are customarily used in these studies. The present article may thus initiate a dialogue among researchers who use animals for radioprotection survival studies, institutional animal care and use committees, and drug regulatory bodies to reach a consensus on the number of animals needed to achieve statistically robust results for demonstrating efficacy of radioprotective drugs.     

Quantifying change in distributions: a new departure index that detects,measures and describes change in distributions from population structures,size-classes and other ordered data

Many statistics are available to compare distributions. Some are limited to nominal data while others, such as skew, Kullback-Leibler, Kolmogorov-Smirnov and the Gini coefficient, are useful for providing information about ordered distributions. While many of these tests are useful for determining properties of data in histograms, there has not been a test until now that allows for the detection of differences between distributions, describes the difference and is sensitive to the location of the departures. Such a test could be critical for comparing pre-and post-event distributions, such as a change in the distribution of biomass due to fire, for example, or for comparing data from different locations, such as soil size distributions, and even for evaluating economic disparity or examining differences in age demographics. We present a new statistic, a departure index, which allows a test distribution to be compared with any reference distribution. The resulting index contains information about the location, magnitude and direction of departure from the reference distribution to the test distribution. The departure index in turn provides a standardized response range that allows for a comparison of results from different analyses. A case study of actual fire data demonstrates the sensitivity and range of the test.     

Glacial and interglacial refugia within a long-term rainforest refugium: The Wet Tropics Bioregion of NE Queensland, Australia

An artificial neural network is used to classify environments, including climate, terrain and soil variables, according to their suitability for fifteen structural/environmental forest classes in the Wet Tropics Bioregion of north-east Queensland. We map the environments characteristic of these forest classes in four climate regimes (the present and three past climate scenarios), quantify the changes in area of these environments in response to past regional changes in climate and identify areas that would have been environmentally suitable for rainforests at last glacial maximum (glacial refugia). We also identify areas that would have been suitable for upland and highland rainforest classes during the warmest parts of the interglacial (interglacial refugia) and map locations that consistently remain favourable to specific forest classes despite large changes in climate.In the climate of the last glacial maximum (LGM), rainforest environments are predicted in three relatively distinct refugia in the northern, central and southern Wet Tropics. Only three percent of the total area contains lowland, Mesophyll Vine Forest and the majority of the area of the rainforest refugia supports upland rainforest classes. In the cool, wet climate of the Pleistocene/Holocene transition (PHT), rainforest environments expand to form a more or less continuous block from the northern limits of the region to the Walter Hill Range, except for discontinuous patches extending through the Seaview and Paluma Ranges in the south. During the Holocene climatic optimum (HCO), rainforest environments become more fragmented, especially in the south. Lowland rainforest environments are very extensive in this climate while upland rainforest classes are restricted to what we term “interglacial refugia”.Estimated distributions and stable locations (consistently predicted in all four climate scenarios) for the various rainforest environment classes are our main, novel contribution. Each forest environment responds individualistically to climate change. Our results confirm the highly dynamic nature of the Wet Tropics landscape and present a much more detailed picture of landscape change since the late Pleistocene than previously has been available. This mapping exercise should be useful in the future for analyses of present-day biogeographic patterns. We argue that empirical modelling approaches have an important role in palaeoecology and global change research that is complementary to the developing mechanistic methods.     

Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework

Species abundance distributions (SADs) follow one of ecology's oldest and most universal laws – every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science.     

Disease mapping and spatial regression with count data

In this paper, we provide critical reviews of methods suggested for the analysis of aggregate count data in the context of disease mapping and spatial regression. We introduce a new method for picking prior distributions, and propose a number of refinements of previously used models. We also consider ecological bias, mutual standardization, and choice of both spatial model and prior specification. We analyze male lip cancer incidence data collected in Scotland over the period 1975-1980, and outline a number of problems with previous analyses of these data. In disease mapping studies, hierarchical models can provide robust estimation of area-level risk parameters, though care is required in the choice of covariate model, and it is important to assess the sensitivity of estimates to the spatial model chosen, and to the prior specifications on the variance parameters. Spatial ecological regression is a far more hazardous enterprise for two reasons. First, there is always the possibility of ecological bias, and this can only be alleviated by the inclusion of individual-level data. For the Scottish data, we show that the previously used mean model has limited interpretation from an individual perspective. Second, when residual spatial dependence is modeled, and if the exposure has spatial structure, then estimates of exposure association parameters will change when compared with those obtained from the independence across space model, and the data alone cannot choose the form and extent of spatial correlation that is appropriate.