Bayesian Nonstationary Spatial Modeling for Very Large Datasets

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large spatial domains. Statistical analyses of such datasets provide two main challenges: First, traditional spatial-statistical techniques are often unable to handle large numbers of observations in a computationally feasible way. Second, for large and heterogeneous spatial domains, it is often not appropriate to assume that a process of interest is stationary over the entire domain. We address the first challenge by using a model combining a low-rank component, which allows for flexible modeling of medium-to-long-range dependence via a set of spatial basis functions, with a tapered remainder component, which allows for modeling of local dependence using a compactly supported covariance function. Addressing the second challenge, we propose two extensions to this model that result in increased flexibility: First, the model is parameterized based on a nonstationary Matern covariance, where the parameters vary smoothly across space. Second, in our fully Bayesian model, all components and parameters are considered random, including the number, locations, and shapes of the basis functions used in the low-rank component. Using simulated data and a real-world dataset of high-resolution soil measurements, we show that both extensions can result in substantial improvements over the current state-of-the-art.Comment: 16 pages, 2 color figure

2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Spatial--temporal mesoscale modeling of rainfall intensity using gage and radar data

Gridded estimated rainfall intensity values at very high spatial and temporal resolution levels are needed as main inputs for weather prediction models to obtain accurate precipitation forecasts, and to verify the performance of precipitation forecast models. These gridded rainfall fields are also the main driver for hydrological models that forecast flash floods, and they are essential for disaster prediction associated with heavy rain. Rainfall information can be obtained from rain gages that provide relatively accurate estimates of the actual rainfall values at point-referenced locations, but they do not characterize well enough the spatial and temporal structure of the rainfall fields. Doppler radar data offer better spatial and temporal coverage, but Doppler radar measures effective radar reflectivity ($Ze$) rather than rainfall rate ($R$). Thus, rainfall estimates from radar data suffer from various uncertainties due to their measuring principle and the conversion from $Ze$ to $R$. We introduce a framework to combine radar reflectivity and gage data, by writing the different sources of rainfall information in terms of an underlying unobservable spatial temporal process with the true rainfall values. We use spatial logistic regression to model the probability of rain for both sources of data in terms of the latent true rainfall process. We characterize the different sources of bias and error in the gage and radar data and we estimate the true rainfall intensity with its posterior predictive distribution, conditioning on the observed data.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS166 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spatial modeling of extreme snow depth

The spatial modeling of extreme snow is important for adequate risk management in Alpine and high altitude countries. A natural approach to such modeling is through the theory of max-stable processes, an infinite-dimensional extension of multivariate extreme value theory. In this paper we describe the application of such processes in modeling the spatial dependence of extreme snow depth in Switzerland, based on data for the winters 1966--2008 at 101 stations. The models we propose rely on a climate transformation that allows us to account for the presence of climate regions and for directional effects, resulting from synoptic weather patterns. Estimation is performed through pairwise likelihood inference and the models are compared using penalized likelihood criteria. The max-stable models provide a much better fit to the joint behavior of the extremes than do independence or full dependence models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS464 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Do political instability, terrorism, and corruption have deterring effects on tourism development even in the presence of UNESCO heritage? A cross-country panel estimate

This article evaluates the effects of political instability, terrorism, and corruption on tourism development, particularly UNESCO-listed heritage destinations. Using a fixed-effects panel data analysis for 139 countries over the period 1999-2009, the result reveals that a one-unit increase in political instability decreases tourist arrivals and tourism revenue between 24 and 31 and 30 and 36, respectively. Furthermore, in the presence of heritage, terrorism has negative effects on tourism demand even though its effect is lower than that of political instability. However, the study shows that an increase in corruption index would not have an adverse influence on tourist arrival numbers, particularly for those countries that have historical and natural heritage. Perhaps, many experienced travelers have expectations that they would require paying bribes to corrupt authorities for travel visa or permits to some tourist destinations in order to make things accessible. Moderation effect results indicate that political instability reduces tourism demand even in UNESCO-listed heritage destinations © 2013 Cognizant Comm. Corp

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

The Second Competition on Spatial Statistics for Large Datasets

In the last few decades, the size of spatial and spatio-temporal datasets in many research areas has rapidly increased with the development of data collection technologies. As a result, classical statistical methods in spatial statistics are facing computational challenges. For example, the kriging predictor in geostatistics becomes prohibitive on traditional hardware architectures for large datasets as it requires high computing power and memory footprint when dealing with large dense matrix operations. Over the years, various approximation methods have been proposed to address such computational issues, however, the community lacks a holistic process to assess their approximation efficiency. To provide a fair assessment, in 2021, we organized the first competition on spatial statistics for large datasets, generated by our {\em ExaGeoStat} software, and asked participants to report the results of estimation and prediction. Thanks to its widely acknowledged success and at the request of many participants, we organized the second competition in 2022 focusing on predictions for more complex spatial and spatio-temporal processes, including univariate nonstationary spatial processes, univariate stationary space-time processes, and bivariate stationary spatial processes. In this paper, we describe in detail the data generation procedure and make the valuable datasets publicly available for a wider adoption. Then, we review the submitted methods from fourteen teams worldwide, analyze the competition outcomes, and assess the performance of each team