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AuthorRue, Haavard (4)Genton, Marc G. (3)Riebler, Andrea (3)Jeong, Jaehong (2)Martins, Thiago G. (2)View MoreDepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (12)Statistics Program (9)Applied Mathematics and Computational Science Program (3)JournalThe Annals of Applied Statistics (6)Statistical Science (4)Bayesian Analysis (2)KAUST Grant NumberOSR-2015-CRG4-2640 (2)Publisher

Institute of Mathematical Statistics (12)

SubjectAxial symmetry (2)Angular measure (1)Bayesian inference (1)Bayesian theory (1)Bivariate extreme values (1)View MoreTypeArticle (12)Year (Issue Date)2019 (1)2018 (3)2017 (5)2016 (2)2014 (1)Item Availability
Open Access (12)

Now showing items 1-10 of 12

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On the Choice of Difference Sequence in a Unified Framework for Variance Estimation in Nonparametric Regression

Dai, Wenlin; Tong, Tiejun; Zhu, Lixing (Statistical Science, Institute of Mathematical Statistics, 2017-09-01) [Article]

Difference-based methods do not require estimating the mean function in nonparametric regression and are therefore popular in practice. In this paper, we propose a unified framework for variance estimation that combines the linear regression method with the higher-order difference estimators systematically. The unified framework has greatly enriched the existing literature on variance estimation that includes most existing estimators as special cases. More importantly, the unified framework has also provided a smart way to solve the challenging difference sequence selection problem that remains a long-standing controversial issue in nonparametric regression for several decades. Using both theory and simulations, we recommend to use the ordinary difference sequence in the unified framework, no matter if the sample size is small or if the signal-to-noise ratio is large. Finally, to cater for the demands of the application, we have developed a unified R package, named VarED, that integrates the existing difference-based estimators and the unified estimators in nonparametric regression and have made it freely available in the R statistical program http://cran.r-project.org/web/packages/.

Incorporating geostrophic wind information for improved space–time short-term wind speed forecasting

Zhu, Xinxin; Bowman, Kenneth P.; Genton, Marc G. (The Annals of Applied Statistics, Institute of Mathematical Statistics, 2014-09) [Article]

Accurate short-term wind speed forecasting is needed for the rapid development and efficient operation of wind energy resources. This is, however, a very challenging problem. Although on the large scale, the wind speed is related to atmospheric pressure, temperature, and other meteorological variables, no improvement in forecasting accuracy was found by incorporating air pressure and temperature directly into an advanced space-time statistical forecasting model, the trigonometric direction diurnal (TDD) model. This paper proposes to incorporate the geostrophic wind as a new predictor in the TDD model. The geostrophic wind captures the physical relationship between wind and pressure through the observed approximate balance between the pressure gradient force and the Coriolis acceleration due to the Earth’s rotation. Based on our numerical experiments with data from West Texas, our new method produces more accurate forecasts than does the TDD model using air pressure and temperature for 1to 6-hour-ahead forecasts based on three different evaluation criteria. Furthermore, forecasting errors can be further reduced by using moving average hourly wind speeds to fit the diurnal pattern. For example, our new method obtains between 13.9% and 22.4% overall mean absolute error reduction relative to persistence in 2-hour-ahead forecasts, and between 5.3% and 8.2% reduction relative to the best previous space-time methods in this setting.

You Just Keep on Pushing My Love over the Borderline: A Rejoinder

Simpson, Daniel; Rue, Haavard; Riebler, Andrea; Martins, Thiago G.; Sørbye, Sigrunn H. (Statistical Science, Institute of Mathematical Statistics, 2017-04-06) [Article]

The entire reason that we wrote this paper was to provide a concrete object around which to focus a broader discussion about prior choice and we are extremely grateful to the editorial team at Statistical Science for this opportunity. David Dunson (DD), Jim Hodges (JH), Christian Robert, Judith Rousseau (RR) and James Scott (JS) have taken this discussion in diverse and challenging directions and over the next few pages, we will try to respond to the main points they have raised.

Topological data analysis of single-trial electroencephalographic signals

Wang, Yuan; Ombao, Hernando; Chung, Moo K. (The Annals of Applied Statistics, Institute of Mathematical Statistics, 2018-09-11) [Article]

Epilepsy is a neurological disorder marked by sudden recurrent episodes of sensory disturbance, loss of consciousness, or convulsions, associated with abnormal electrical activity in the brain. Statistical analysis of neuro-physiological recordings, such as electroencephalography (EEG), facilitates the understanding of epileptic seizures. Standard statistical methods typically analyze amplitude and frequency information in EEG signals. In the current study, we propose a topological data analysis (TDA) framework to analyze single-trial EEG signals. The framework denoises signals with a weighted Fourier series (WFS), and tests for differences between the topological features—persistence landscapes (PLs) of denoised signals through resampling in the frequency domain. Simulation studies show that the test is robust for topologically similar signals while bearing sensitivity to topological tearing in signals. In an application to single-trial epileptic EEG signals, EEG signals in the diagnosed seizure origin and its symmetric site are found to have similar PLs before and during a seizure attack, in contrast to signals at other sites showing significant statistical difference in the PLs of the two phases.

Reducing storage of global wind ensembles with stochastic generators

Jeong, Jaehong; Castruccio, Stefano; Crippa, Paola; Genton, Marc G. (The Annals of Applied Statistics, Institute of Mathematical Statistics, 2018-03-09) [Article]

Wind has the potential to make a significant contribution to future energy resources. Locating the sources of this renewable energy on a global scale is however extremely challenging, given the difficulty to store very large data sets generated by modern computer models. We propose a statistical model that aims at reproducing the data-generating mechanism of an ensemble of runs via a Stochastic Generator (SG) of global annual wind data. We introduce an evolutionary spectrum approach with spatially varying parameters based on large-scale geographical descriptors such as altitude to better account for different regimes across the Earth’s orography. We consider a multi-step conditional likelihood approach to estimate the parameters that explicitly accounts for nonstationary features while also balancing memory storage and distributed computation. We apply the proposed model to more than 18 million points of yearly global wind speed. The proposed SG requires orders of magnitude less storage for generating surrogate ensemble members from wind than does creating additional wind fields from the climate model, even if an effective lossy data compression algorithm is applied to the simulation output.

Time-varying extreme value dependence with application to leading European stock markets

Castro, Daniela; de Carvalho, Miguel; Wadsworth, Jennifer (The Annals of Applied Statistics, Institute of Mathematical Statistics, 2018-03-09) [Article]

Extremal dependence between international stock markets is of particular interest in today’s global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, or other suitable covariate. Working within a framework of asymptotic dependence, we introduce a regression model for the angular density of a bivariate extreme value distribution that allows us to assess how extremal dependence evolves over a covariate. We apply the proposed model to assess the dynamics governing extremal dependence of some leading European stock markets over the last three decades, and find evidence of an increase in extremal dependence over recent years.

Intuitive Joint Priors for Variance Parameters

Fuglstad, Geir-Arne; Hem, Ingeborg Gullikstad; Knight, Alexander; Rue, Haavard; Riebler, Andrea (Bayesian Analysis, Institute of Mathematical Statistics, 2019-10-30) [Article]

Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a tree structure to the individual model components. For each split in the tree, an analyst may be ignorant or have a sound intuition on how to attribute variance to the branches. In the former case a Dirichlet prior is appropriate to use, while in the latter case a penalised complexity (PC) prior provides robust shrinkage. A bottom-up combination of the conditional priors results in a proper joint prior. We suggest default values for the hyperparameters and offer intuitive statements for eliciting the hyperparameters based on expert knowledge. The prior framework is applicable for R packages for Bayesian inference such as INLA and RStan.
Three simulation studies show that, in terms of the application-specific measures of interest, PC priors improve inference over Dirichlet priors when used to penalise different levels of complexity in splits. However, when expressing ignorance in a split, Dirichlet priors perform equally well and are preferred for their simplicity. We find that assigning current state-of-the-art default priors for each variance parameter individually is less transparent and does not perform better than using the proposed joint priors. We demonstrate practical use of the new framework by analysing spatial heterogeneity in neonatal mortality in Kenya in 2010–2014 based on complex survey data.

Spherical Process Models for Global Spatial Statistics

Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G. (Statistical Science, Institute of Mathematical Statistics, 2017-11-28) [Article]

Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.

Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales

Yuan, Yuan; Bachl, Fabian E.; Lindgren, Finn; Borchers, David L.; Illian, Janine B.; Buckland, Stephen T.; Rue, Haavard; Gerrodette, Tim (The Annals of Applied Statistics, Institute of Mathematical Statistics, 2017-12-28) [Article]

Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consistent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.

A stochastic space-time model for intermittent precipitation occurrences

Sun, Ying; Stein, Michael L. (The Annals of Applied Statistics, Institute of Mathematical Statistics, 2016-01-28) [Article]

Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time t random field (tRF) model for 15-minute precipitation occurrences. This model is constructed through a space-time Gaussian random field (GRF) with random scaling varying along time or space and time. It can be viewed as a generalization of the purely spatial tRF, and has a hierarchical representation that allows for Bayesian interpretation. Developing appropriate tools for evaluating precipitation models is a crucial part of the model-building process, and we focus on evaluating whether models can produce the observed conditional dry and rain probabilities given that some set of neighboring sites all have rain or all have no rain. These conditional probabilities show that the proposed space-time model has noticeable improvements in some characteristics of joint rainfall occurrences for the data we have considered.

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