1,300 research outputs found
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
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
Phase I–II trial design for biologic agents using conditional auto‐regressive models for toxicity and efficacy
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147824/1/rssc12314_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147824/2/rssc12314.pd
Real-time information processing of environmental sensor network data using Bayesian Gaussian processes
In this article, we consider the problem faced by a sensor network operator who must infer, in real time, the value of some environmental parameter that is being monitored at discrete points in space and time by a sensor network. We describe a powerful and generic approach built upon an efficient multi-output Gaussian process that facilitates this information acquisition and processing. Our algorithm allows effective inference even with minimal domain knowledge, and we further introduce a formulation of Bayesian Monte Carlo to permit the principled management of the hyperparameters introduced by our flexible models. We demonstrate how our methods can be applied in cases where the data is delayed, intermittently missing, censored, and/or correlated. We validate our approach using data collected from three networks of weather sensors and show that it yields better inference performance than both conventional independent Gaussian processes and the Kalman filter. Finally, we show that our formalism efficiently reuses previous computations by following an online update procedure as new data sequentially arrives, and that this results in a four-fold increase in computational speed in the largest cases considered
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
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
Predictive Inference for Big, Spatial, Non‐Gaussian Data: MODIS Cloud Data and its Change‐of‐Support
Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling
Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises
- …