Visualization in spatial modeling

This chapter deals with issues arising from a central theme in contemporary computer modeling - visualization. We first tie visualization to varieties of modeling along the continuum from iconic to symbolic and then focus on the notion that our models are so intrinsically complex that there are many different types of visualization that might be developed in their understanding and implementation. This focuses the debate on the very way of 'doing science' in that patterns and processes of any complexity can be better understood through visualizing the data, the simulations, and the outcomes that such models generate. As we have grown more sensitive to the problem of complexity in all systems, we are more aware that the twin goals of parsimony and verifiability which have dominated scientific theory since the 'Enlightenment' are up for grabs: good theories and models must 'look right' despite what our statistics and causal logics tell us. Visualization is the cutting edge of this new way of thinking about science but its styles vary enormously with context. Here we define three varieties: visualization of complicated systems to make things simple or at least explicable, which is the role of pedagogy; visualization to explore unanticipated outcomes and to refine processes that interact in unanticipated ways; and visualization to enable end users with no prior understanding of the science but a deep understanding of the problem to engage in using models for prediction, prescription, and control. We illustrate these themes with a model of an agricultural market which is the basis of modern urban economics - the von Thünen model of land rent and density; a model of urban development based on interacting spatial and temporal processes of land development - the DUEM model; and a pedestrian model of human movement at the fine scale where control of such movements to meet standards of public safety is intrinsically part of the model about which the controllers know intimately. © Springer-Verlag Berlin Heidelberg 2006

Statistical Modeling of Spatial Extremes

The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent progress in the statistical modeling of spatial extremes, starting with sketches of the necessary elements of extreme value statistics and geostatistics. The main types of statistical models thus far proposed, based on latent variables, on copulas and on spatial max-stable processes, are described and then are compared by application to a data set on rainfall in Switzerland. Whereas latent variable modeling allows a better fit to marginal distributions, it fits the joint distributions of extremes poorly, so appropriately-chosen copula or max-stable models seem essential for successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Channels of Synthesis Forty Years On: Integrated Analysis of Spatial Economic Systems

Isard’s vision of integrated modeling that was laid out in the 1960s book Methods of Regional Science provided a road map for the development of more sophisticated analysis of spatial economic systems. Some forty years later, we look back at this vision and trace developments in a sample of three areas – demographic-econometric integrated modeling, spatial interaction modeling, and environmental-economic modeling. Attention will be focused on methodological advances and their motivation by new developments in theory as well as innovations in the applications of these models to address new policy challenges. Underlying the discussion will be an evaluation of the way in which spatial issues have been addressed, ranging from concerns with regionalization to issues of spillovers and spatial correlation.Spatial economic system, Integrated analysis,

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

Spatial Memory for Context Reasoning in Object Detection

Modeling instance-level context and object-object relationships is extremely challenging. It requires reasoning about bounding boxes of different classes, locations \etc. Above all, instance-level spatial reasoning inherently requires modeling conditional distributions on previous detections. Unfortunately, our current object detection systems do not have any {\bf memory} to remember what to condition on! The state-of-the-art object detectors still detect all object in parallel followed by non-maximal suppression (NMS). While memory has been used for tasks such as captioning, they mostly use image-level memory cells without capturing the spatial layout. On the other hand, modeling object-object relationships requires {\bf spatial} reasoning -- not only do we need a memory to store the spatial layout, but also a effective reasoning module to extract spatial patterns. This paper presents a conceptually simple yet powerful solution -- Spatial Memory Network (SMN), to model the instance-level context efficiently and effectively. Our spatial memory essentially assembles object instances back into a pseudo "image" representation that is easy to be fed into another ConvNet for object-object context reasoning. This leads to a new sequential reasoning architecture where image and memory are processed in parallel to obtain detections which update the memory again. We show our SMN direction is promising as it provides 2.2\% improvement over baseline Faster RCNN on the COCO dataset so far.Comment: Draft submitted to ICCV 201

Modeling Spatial Sustainability: Spatial Welfare Economics versus Ecological Footprint

A spatial welfare framework for the analysis of the spatial dimensions of sustainability is developed. It incorporates agglomeration effects, interregional trade, negative environmental externalities and various land use categories. The model is used to compare rankings of spatial configurations according to evaluations based on social welfare and ecological footprint indicators. Five spatial configurations are considered for this purpose. The exercise is operationalized with the help of a two-region model of the economy that is in line with the ‘new economic geography’. Various (counter) examples show that the footprint method is not consistent with an approach aimed at maximum social welfare.Agglomeration effects, Trade advantages, Negative externalities, Population density, Spatial configuration, Transport

Geographical and temporal weighted regression (GTWR)

Both space and time are fundamental in human activities as well as in various physical processes. Spatiotemporal analysis and modeling has long been a major concern of geographical information science (GIScience), environmental science, hydrology, epidemiology, and other research areas. Although the importance of incorporating the temporal dimension into spatial analysis and modeling has been well recognized, challenges still exist given the complexity of spatiotemporal models. Of particular interest in this article is the spatiotemporal modeling of local nonstationary processes. Specifically, an extension of geographically weighted regression (GWR), geographical and temporal weighted regression (GTWR), is developed in order to account for local effects in both space and time. An efficient model calibration approach is proposed for this statistical technique. Using a 19-year set of house price data in London from 1980 to 1998, empirical results from the application of GTWR to hedonic house price modeling demonstrate the effectiveness of the proposed method and its superiority to the traditional GWR approach, highlighting the importance of temporally explicit spatial modeling

Generative Image Modeling Using Spatial LSTMs

Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a number of problems but only recently have found their way into generative image models. We here introduce a recurrent image model based on multi-dimensional long short-term memory units which are particularly suited for image modeling due to their spatial structure. Our model scales to images of arbitrary size and its likelihood is computationally tractable. We find that it outperforms the state of the art in quantitative comparisons on several image datasets and produces promising results when used for texture synthesis and inpainting