Related papers: Spatial Statistics
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
The characteristics and determinants of health and disease are often organised in space, reflecting our spatially extended nature. Understanding the influence of such factors requires models capable of capturing spatial relations. Though a…
The first law of geography is a cornerstone of spatial analysis, emphasizing that nearby and related locations tend to be more similar, however, defining what constitutes "near" and "related" remains challenging, as different phenomena…
This manuscript unites causal inference and spatial statistics, presenting novel insights for causal inference in spatial data analysis, and drawing from tools in spatial statistics to estimate causal effects. We introduce spatial causal…
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…
Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…
We introduce a model for spatial statistics which can account explicitly for interactions among more than two field components at a time. The theoretical aspects of the model are dealt with: cumulant and moment generating functions, spatial…
Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
In software maintenance work, software architects and programmers need to identify modules that require modification or deletion. Whilst user requests and bug reports are utilised for this purpose, evaluating the execution status of modules…
Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We…
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…