ترغب بنشر مسار تعليمي؟ اضغط هنا

A Multi-Resolution Model for Non-Gaussian Random Fields on a Sphere with Application to Ionospheric Electrostatic Potentials

72   0   0.0 ( 0 )
 نشر من قبل Minjie Fan
 تاريخ النشر 2017
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial models for non-Gaussian random fields on a sphere based on a multi-resolution analysis. Using a special wavelet frame, named spherical needlets, as building blocks, the proposed model is constructed in the form of a sparse random effects model. The spatial localization of needlets, together with carefully chosen random coefficients, ensure the model to be non-Gaussian and isotropic. The model can also be expanded to include a spatially varying variance profile. The special formulation of the model enables us to develop efficient estimation and prediction procedures, in which an adaptive MCMC algorithm is used. We investigate the accuracy of parameter estimation of the proposed model, and compare its predictive performance with that of two Gaussian models by extensive numerical experiments. Practical utility of the proposed model is demonstrated through an application of the methodology to a data set of high-latitude ionospheric electrostatic potentials, generated from the LFM-MIX model of the magnetosphere-ionosphere system.



قيم البحث

اقرأ أيضاً

We develop a new methodology for spatial regression of aggregated outputs on multi-resolution covariates. Such problems often occur with spatial data, for example in crop yield prediction, where the output is spatially-aggregated over an area and the covariates may be observed at multiple resolutions. Building upon previous work on aggregated output regression, we propose a regression framework to synthesise the effects of the covariates at different resolutions on the output and provide uncertainty estimation. We show that, for a crop yield prediction problem, our approach is more scalable, via variational inference, than existing multi-resolution regression models. We also show that our framework yields good predictive performance, compared to existing multi-resolution crop yield models, whilst being able to provide estimation of the underlying spatial effects.
Our problem is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics have been proposed in the neuroscience li terature for the analysis of fMRI data allowing for unknown delay in the hemodynamic response. However the null distribution of the maximum of this 3D random field of test statistics, and hence the threshold used to detect brain activation, was unsolved. To find a solution, we approximate the P-value by the expected Euler characteristic (EC) of the excursion set of the test statistic random field. Our main result is the required EC density, derived using the Gaussian Kinematic Formula.
273 - Xiongtao Dai 2021
The infinite-dimensional Hilbert sphere $S^infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Frechet mean as an intrinsic summary of the central tendency of data lying on $S^infty$. To break a path for sound statistical inference, we derive properties of the Frechet mean on $S^infty$ by establishing its existence and uniqueness as well as a root-$n$ central limit theorem (CLT) for the sample version, overcoming obstructions from infinite-dimensionality and lack of compactness on $S^infty$. Intrinsic CLTs for the estimated tangent vectors and covariance operator are also obtained. Asymptotic and bootstrap hypothesis tests for the Frechet mean based on projection and norm are then proposed and are shown to be consistent. The proposed two-sample tests are applied to make inference for daily taxi demand patterns over Manhattan modeled as densities, of which the square roots are analyzed on the Hilbert sphere. Numerical properties of the proposed hypothesis tests which utilize the spherical geometry are studied in the real data application and simulations, where we demonstrate that the tests based on the intrinsic geometry compare favorably to those based on an extrinsic or flat geometry.
The algorithms used for optimal management of ambulances require accurate description and prediction of the spatio-temporal evolution of emergency interventions. In the last years, several authors have proposed sophisticated statistical approaches to forecast the ambulance dispatches, typically modelling the events as a point pattern occurring on a planar region. Nevertheless, ambulance interventions can be more appropriately modelled as a realisation of a point process occurring along a network of lines, such as a road network. The constrained spatial domain raises specific challenges and unique methodological problems that cannot be ignored when developing a proper statistical model. Hence, this paper proposes a spatiotemporal model to analyse the ambulance interventions that occurred in the road network of Milan (Italy) from 2015 to 2017. We adopt a non-separable first-order intensity function with spatial and temporal terms. The temporal component is estimated semi-parametrically using a Poisson regression model, while the spatial dimension is estimated nonparametrically using a network kernel function. A set of weights is included in the spatial term to capture space-time interactions, inducing non-separability in the intensity function. A series of maps and graphical tests show that our approach successfully models the ambulance interventions and captures the space-time patterns.
This work is motivated by the Obepine French system for SARS-CoV-2 viral load monitoring in wastewater. The objective of this work is to identify, from time-series of noisy measurements, the underlying auto-regressive signals, in a context where the measurements present numerous missing data, censoring and outliers. We propose a method based on an auto-regressive model adapted to censored data with outliers. Inference and prediction are produced via a discretised smoother. This method is both validated on simulations and on real data from Obepine. The proposed method is used to denoise measurements from the quantification of the SARS-CoV-2 E gene in wastewater by RT-qPCR. The resulting smoothed signal shows a good correlation with other epidemiological indicators and an estimate of the whole system noise is produced.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا