A model based framework for air quality indices and population risk evaluation, with an application to the analysis of Scottish air quality data

The paper is devoted to the development of a statistical framework for air quality assessment at the country level and for the evaluation of the ambient population exposure and risk with respect to airborne pollutants. The framework is based on a multivariate space–time model and on aggregated indices defined at different levels of aggregation in space and time. The indices are evaluated, uncertainty included, by considering both the model outputs and the information on the population spatial distribution. The framework is applied to the analysis of air quality data for Scotland for 2009 referring to European and Scottish air quality legislation

Capturing Multivariate Spatial Dependence: Model, Estimate and then Predict

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction between these two dependencies that is the focus of Genton and Kleiber's paper under discussion. We see the problem of ensuring that any multivariate spatial covariance matrix is nonnegative definite as important, but we also see it as a means to an end. That "end" is solving the scientific problem of predicting a multivariate field. [arXiv:1507.08017].Comment: Published at http://dx.doi.org/10.1214/15-STS517 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial datasets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article is submitted to the Practice section of the journal with the aim of developing massively scalable Bayesian approaches that can rapidly deliver Bayesian inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (e.g., a standard desktop or laptop) using easily available statistical software packages without requiring message-parsing interfaces or parallel programming paradigms. Key insights are offered regarding assumptions and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table

Graphics for uncertainty

Graphical methods such as colour shading and animation, which are widely available, can be very effective in communicating uncertainty. In particular, the idea of a ‘density strip’ provides a conceptually simple representation of a distribution and this is explored in a variety of settings, including a comparison of means, regression and models for contingency tables. Animation is also a very useful device for exploring uncertainty and this is explored particularly in the context of flexible models, expressed in curves and surfaces whose structure is of particular interest. Animation can further provide a helpful mechanism for exploring data in several dimensions. This is explored in the simple but very important setting of spatiotemporal data

Calculation of the effect of random superfluid density on the temperature dependence of the penetration depth

Microscopic variations in composition or structure can lead to nanoscale inhomogeneity in superconducting properties such as the magnetic penetration depth, but measurements of these properties are usually made on longer length scales. We solve a generalized London equation with a non-uniform penetration depth, lambda(r), obtaining an approximate solution for the disorder-averaged Meissner effect. We find that the effective penetration depth is different from the average penetration depth and is sensitive to the details of the disorder. These results indicate the need for caution when interpreting measurements of the penetration depth and its temperature dependence in systems which may be inhomogeneous

Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

Private Outsourced Kriging Interpolation

Kriging is a spatial interpolation algorithm which provides the best unbiased linear prediction of an observed phenomena by taking a weighted average of samples within a neighbourhood. It is widely used in areas such as geo-statistics where, for example, it may be used to predict the quality of mineral deposits in a location based on previous sample measurements. Kriging has been identified as a good candidate process to be outsourced to a cloud service provider, though outsourcing presents an issue since measurements and predictions may be highly sensitive. We present a method for the private outsourcing of Kriging interpolation using a tailored modification of the Kriging algorithm in combination with homomorphic encryption, allowing crucial information relating to measurement values to be hidden from the cloud service provider

Spatial vegetation patterns and neighborhood competition among woody plants in an East African savanna

The majority of research on savanna vegetation dynamics has focused on the coexistence of woody and herbaceous vegetation. Interactions among woody plants in savannas are relatively poorly understood. We present data from a 10-year longitudinal study of spatially explicit growth patterns of woody vegetation in an East African savanna following exclusion of large herbivores and in the absence of fire. We examined plant spatial patterns and quantified the degree of competition among woody individuals. Woody plants in this semi-arid savanna exhibit strongly clumped spatial distributions at scales of 1 - 5 m. However, analysis of woody plant growth rates relative to their conspecific and heterospecific neighbors revealed evidence for strong competitive interactions at neighborhood scales of up to 5 m for most woody plant species. Thus, woody plants were aggregated in clumps despite significantly decreased growth rates in close proximity to neighbors, indicating that the spatial distribution of woody plants in this region depends on dispersal and establishment processes rather than on competitive, density-dependent mortality. However, our documentation of suppressive effects of woody plants on neighbors also suggests a potentially important role for tree-tree competition in controlling vegetation structure and indicates that the balanced-competition hypothesis may contribute to well-known patterns in maximum tree cover across rainfall gradients in Africa

A procedure for the change point problem in parametric models based on phi-divergence test-statistics

This paper studies the change point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on general divergence measures for testing the hypothesis of the existence of a change. For comparing the accuracy of the new test-statistic a simulation study is performed for the special case of a univariate discrete model. Finally, the procedure proposed in this paper is illustrated through a classical change-point example

Entropy: The Markov Ordering Approach

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the {\em Markov order}). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally "most random" distributions.Comment: 50 pages, 4 figures, Postprint version. More detailed discussion of the various entropy additivity properties and separation of variables for independent subsystems in MaxEnt problem is added in Section 4.2. Bibliography is extende