Applied Geospatial Bayesian Modeling in the Big Data Era: Challenges and Solutions

Abstract

Two important trends in applied statistics are an increased usage of geospatial models and an increased usage of big data. Naturally, there has been overlap as analysts utilize the techniques associated with each. With geospatial methods such as kriging, the computation required becomes intensive quickly, even with datasets that would not be considered huge in other contexts. In this work we describe a solution to the computational problem of estimating Bayesian kriging models with big data, Bootstrap Random Spatial Sampling (BRSS), and first provide an analytical argument that BRSS produces consistent estimates from the Bayesian spatial model. Second, with a medium-sized dataset on fracking in West Virginia, we show that bootstrap sample effects from a full-information Bayesian model are reduced with more bootstrap samples and more observations per sample as in standard bootstrapping. Third, we offer a realistic illustration of the method by analyzing campaign donors in California with a large geocoded dataset. With this solution, scholars will not be constrained in their ability to apply theoretically relevant geospatial Bayesian models when the size of the data produces computational intractability.

Where Are We Going with Statistical Computing? From Mathematical Statistics to Collaborative Data Science

“…This line of research connects biological intelligence with AI, and efforts are thus being made to optimize Bayesian estimation processes (which are typically computationally expensive) to improve or extend AI capabilities. The bidirectional influence applies here too, as AI research, such as into convolutional neural networks (CNN), is helping scientists in many areas of research, from neuroscientists attempting to better understand the brain and test neurocognitive theories (see [23] for a recent example linking deep learning with psychological manifestations such as hallucinations), to political scientists uncovering election fraud (see [24] for a clever application of CNN to reveal systematic voting fraud in the 1988 Mexican presidential election), and social scientists with new applications of methods such as Bayesian kriging for geospatial modeling (see [25] for a computational exploration of Bayesian kriging in the big data era, published in this Special Issue of Mathematics).…”

The Usability of Big Data in Statistical Studies of the Population in the Conditions of War

“…ґрунтується на даних з усіх видів джерел, де реалізовано різноманітні сучасні технології, -GPS, датчиків розташування, соціальних мереж, мобільних пристроїв, супутникових зображень [30]. У контексті цього питання варто згадати позицію J. Byers та J. Gill, що наразі у прикладній статистиці існує тенденція до збільшення використання двох важливих інструментів: геопросторових моделей і великих даних [31]. З огляду на зазначене варто підкреслити, що загалом геопросторовий аналіз є цінним інструментом для розуміння складних взаємозв'язків між характеристиками населення та просторовим контекстом, у якому вони мають місце.…”