Books on the topic 'Spatial point patterns'

The climate system consists of interactions between physical, biological, chemical, and human processes across a wide range of spatial and temporal scales. Characterizing the behavior of components of this system is crucial for scientists and decision makers. There is substantial uncertainty associated with observations of this system as well as our understanding of various system components and their interaction. Thus, inference and prediction in climate science should accommodate uncertainty in order to facilitate the decision-making process. Statistical science is designed to provide the tools to perform inference and prediction in the presence of uncertainty. In particular, the field of spatial statistics considers inference and prediction for uncertain processes that exhibit dependence in space and/or time. Traditionally, this is done descriptively through the characterization of the first two moments of the process, one expressing the mean structure and one accounting for dependence through covariability.Historically, there are three primary areas of methodological development in spatial statistics: geostatistics, which considers processes that vary continuously over space; areal or lattice processes, which considers processes that are defined on a countable discrete domain (e.g., political units); and, spatial point patterns (or point processes), which consider the locations of events in space to be a random process. All of these methods have been used in the climate sciences, but the most prominent has been the geostatistical methodology. This methodology was simultaneously discovered in geology and in meteorology and provides a way to do optimal prediction (interpolation) in space and can facilitate parameter inference for spatial data. These methods rely strongly on Gaussian process theory, which is increasingly of interest in machine learning. These methods are common in the spatial statistics literature, but much development is still being done in the area to accommodate more complex processes and “big data” applications. Newer approaches are based on restricting models to neighbor-based representations or reformulating the random spatial process in terms of a basis expansion. There are many computational and flexibility advantages to these approaches, depending on the specific implementation. Complexity is also increasingly being accommodated through the use of the hierarchical modeling paradigm, which provides a probabilistically consistent way to decompose the data, process, and parameters corresponding to the spatial or spatio-temporal process.Perhaps the biggest challenge in modern applications of spatial and spatio-temporal statistics is to develop methods that are flexible yet can account for the complex dependencies between and across processes, account for uncertainty in all aspects of the problem, and still be computationally tractable. These are daunting challenges, yet it is a very active area of research, and new solutions are constantly being developed. New methods are also being rapidly developed in the machine learning community, and these methods are increasingly more applicable to dependent processes. The interaction and cross-fertilization between the machine learning and spatial statistics community is growing, which will likely lead to a new generation of spatial statistical methods that are applicable to climate science.

The research problem undertaken in the study is the occurrence of dispersed and concentrated built-up (in particular residential) area patterns caused by suburbanisation processes in a large urban agglomeration, on the example of the Warsaw metropolitan area. The research concerned the period after 1989, when the political and economic transformation in Poland began. The historical and contemporary socio-economic conditions of suburbanization and urban sprawl are described, which have the features of a spontaneous, chaotic dispersion, quite different than in Western countries. It is partly to blame for faulty spatial planning. The succession of urban development into rural areas is subordinated to the factors of the construction market. In the empirical part of the analysis, topographic data on all buildings in the urban agglomeration and databases on land use derived from satellite images were used to investigate settlement changes. A multidimensional study was carried out relating to various spatial scales, types of spatial relations and territorial units. Measures of spatial concentration of point patterns as well as landscape metrics were used for this purpose. The indicators used were subject to critical methodological evaluation afterwards. The study was performed in several temporal cross-sections. The locations of new development in agricultural, forest and wasteland areas have been identified. Finally, recommendations for the implementation of appropriate spatial policy and improvement of the spatial order in the Warsaw agglomeration were formulated

This chapter analyzes the main topics and questions about offender mobility and crime location choice in terms of individual motivations, resources, constraints, and decisions. It begins with a brief overview of the four main frameworks that have been used to theorize offender mobility and crime location choice. This is followed by a characterization of general human mobility as a series of cyclical movements between a limited set of anchor points, and a review of two research initiatives that collected detailed spatial and temporal information on offender mobility. The subsequent section addresses the extent to which offenders plan and prepare their crimes. The chapter also discusses two core elements in crime pattern theory, namely the facilities that attract offenders and offenses (crime generators and attractors) and awareness space. The final section discusses the spatial unit of analysis in offender mobility and location choice.