On the Equilibrium Properties of Spatial Models

Joint modeling of spatially oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This article develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a vegetation index data set with spatially dependent observations numbering in the millions.

Framework of modern sustainable urban spatial development model based on smart cities is studied in this paper. With the continuous development and launch of high-resolution satellites, satellite images have covered multiple chromatograms such as multispectral, panchromatic, and hyperspectral. Hence, using the state-of-the-art models to construct the efficient model will be the essential way of promoting the development. Firstly, this research work analyzes the remote sensing as the service for the analysis of data collection. In the process of data update, it is necessary to then pay attention to the full use of existing information, therefore the decision tree is used for further analysis. Secondly, urban model is designed to assist in constructing the smart cities. Through the test on the construct and service, the performance is studied in the experiment with the test on different scenarios.

The spatial equilibrium approach to urban systems has been criticized for lack of geographic details and realism. Agent-based urban simulation takes a bottom-up approach as an alternative perspective on urban modeling. The architecture of many urban simulation frameworks, though built upon geographical features, does not necessarily provide a structural understanding of urban systems. Structural understanding of urban systems requires taking into account all geographic, social, economic components, and their interrelationships in a unified framework. Urban spatial structure models integrate two major components: socio-economic behavior and landscape. Incorporating urban spatial structure, therefore, provides simulation of an urban system with solid behavioral foundation and socio-economic intuition. From a public policy perspective, explicit urban spatial structure can help to identify more general policy implications out of simulation results, for example, on land use, transportation, housing, and other aspects of urban life. In this chapter, necessary components of agent-based urban simulations are discussed, with an agent-based modeling (ABM) simulation on transportation cost and congestion effects developed to illustrate the role that urban spatial structure models can play in urban simulations.

In this paper, we present new statistical methodology for the analysis of repeated measures of spatially correlated growth data. Our motivating application, a 10 year study of height growth in a plantation of even‐aged white spruce, presents several challenges for statistical analysis. Here, the growth measurements arise from an asymmetric distribution, with heavy tails, and thus standard longitudinal regression models based on a Gaussian error structure are not appropriate. We seek more flexibility for modeling both skewness and fat tails, and achieve this within the class of skew‐elliptical distributions. Within this framework, robust space–time regression models are formulated using random effect growth curves, with coefficients arising from an underlying multivariate spatial process. Computational difficulties arise when data are collected at a large number of locations, and we consider two approaches for spatial modeling in the large data context. Both approaches are compared within the context of our application, and inference is conducted in a Bayesian framework, with implementation based on hybrid Monte Carlo. Copyright © 2010 John Wiley & Sons, Ltd.

Landowner characteristics influence his/her willingness to change landuse practices to provide more or less environmental benefits. However, most studies of agricultural/environmental polices identify landowners as homogenous. And, the primary cause of failure of many environmental and other polices is the lack of knowledge on how humans may respond to polices based on changes in their behavior (Stern, 1993). From socioeconomic theory and empirical research, landowners can be identified as individuals who make agricultural landuse decisions independently based on their objectives. Identifying possible classes of landowners, assessing how each would potentially respond to policy alternatives, and the resulting pattern of land uses in a watershed or a riparian corridor would be very useful to policy makers as they evaluated alternatives. Agricultural landscapes are important producers of ecosystem services. The mix of ecosystem services and commodity outputs of an agricultural landscape depends on the spatial pattern of land uses emerging from individual land use decisions. However, many empirical studies show that the production of ecosystem services from agricultural landscapes is declining. This is consistent with research conducted over the last few decades showing there is a narrow range of social circumstances under which landowners are willing to make investments in the present to achieve public benefits in the future through investing in natural capital resulting in public goods which are frequently produced as ecosystem services. In this study an agent-based model within a watershed planning context is used to analyze the tradeoffs involved in producing a number of ecosystem services and agricultural commodities given price and policy scenarios while assuming three different types of agents in terms of their goals. The agents represent landowners who have been divided into a number of different groups based on their goals and the size of their farm operations. The multi-agent-based model is developed using a heuristic search and optimization technique called genetic algorithm (GA) (Holland), which belongs to a broader class of evolutionary algorithms. GAs exhibit three properties (1) they start with a population of solution, (2) they explore the solution space through recombination and mutation and (3) they evaluate individual solutions based on their appropriate fitness value(s), for example given profit maximizing agents this would be gross margin. A GA is a heuristic stochastic search and optimization method, which works by mimicking the evolutionary principles and chromosomal processing in natural genetics. The three economic agents that are modeled are based on variations in their objective functions and constraints. This study will help in identifying the tradeoffs associated with various agents in the provision of ecosystem services and agricultural commodities. The agent model developed here will help policy and decision maker identify the various agents within the watershed and assess various policy options based on that information. The study will also help to understand the interaction and feedback between the agents and their environment associated with various policy initiatives. The results of the study indicate that the agent model correctly predicts the actual landuse landcover map by 75 percent. Key words: Multifunctional agriculture, Agent based modeling, Genetic Algorithm.

One of the more interesting developments in urban and regional modelling in recent years has been the analysis of the bifurcation properties of a wide variety of models. Just as Jay Forrester’s (1969) attempts to explicitly focus on urban dynamics provided the impetus for those within the modelling discipline to move away from purely static analysis, the innovative work of Thorn, Zeeman and others has brought the notion of bifurcation behaviour to the notice of those currently engaged in urban modelling. In this paper we outline how we have attempted to analyse the bifurcation properties of a well-known set of spatial interaction and activity models, both in their equilibrium and disequilibrium formulations. In addition, we give a number of illustrations of numerical simulations performed for both a 729-zone hypothetical system and also a 30 x 900 Leeds system where we explicitly focus on the problem of modelling urban spatial structure. (A much fuller set of results can be found in Clarke and Wilson, 1984).

This article addresses a model coupling based approach (i.e reusing and combining spatial models) for modeling and simulating complex systems. Our research is conducted by a land use program of Metouia city (Tunisia) for which administration would study (by simulations) different planning scenarios to identify strategies of industrial development. These simulations should take into account demographic, socio-economic and environmental factors. Many urban models are available but they do not integrate these three aspects. This limitation could be solved by a model coupling based approach. In this paper, from an analysis of models and approaches presented in the literature, we identify key points, needs and the basis of an approach to couple models. Then, we introduce an original approach, based on agent paradigm, in which space is the coupling factor to interconnect heterogeneous models (mathematical models, stochastic models, individual based models, and so on). The pertinence of this coupling approach is also raised by the correlation to observe the impact of models on each other.

Timing Equilibria in an Urban Model with Congestion

Urban growth modeling is essential for effective urban planning, yet conventional techniques often lack spatial precision and rely heavily on manual image processing. This study proposes a semi-automated methodology using Spatial Markov Chains (SMC) to enhance urban growth projection by incorporating a novel image pre-processing technique. This approach combines automated image treatment with SMC modeling to estimate not only the probability of urban expansion but also its spatial placement, addressing a critical gap in urban growth forecasting methods. Using Landsat 7 and 8 satellite imagery, six Mexican cities–Acapulco, Puebla, Querétaro, Tampico, Tijuana, and Toluca–were selected as case studies. Data from 2003 were used to project urban expansion for 2017 and 2031, with four performance metrics–Kappa index, Jaccard index, Shannon’s entropy, and fractal dimension–applied to evaluate model accuracy. Results indicate that this approach produces reliable projections with a spatial accuracy exceeding 85%, as validated by metrics such as the Kappa index (0.75–0.81) and the Jaccard index (0.68–0.92). These results highlight the method’s capability to outperform traditional models in terms of precision and spatial detail, making it a robust tool for urban planning. The findings demonstrate the potential of semi-automated SMC methods to improve the precision of urban growth models, offering a valuable resource for policymakers and urban planners seeking to manage sustainable development effectively.

Abstract. In recent years, 3D virtual indoor/outdoor urban modelling becomes a key spatial information framework for many civil and engineering applications such as evacuation planning, emergency and facility management. For accomplishing such sophisticate decision tasks, there is a large demands for building multi-scale and multi-sourced 3D urban models. Currently, Building Information Model (BIM) and Geographical Information Systems (GIS) are broadly used as the modelling sources. However, data sharing and exchanging information between two modelling domains is still a huge challenge; while the syntactic or semantic approaches do not fully provide exchanging of rich semantic and geometric information of BIM into GIS or vice-versa. This paper proposes a novel approach for integrating BIM and GIS using semantic web technologies and Resources Description Framework (RDF) graphs. The novelty of the proposed solution comes from the benefits of integrating BIM and GIS technologies into one unified model, so-called Integrated Geospatial Information Model (IGIM). The proposed approach consists of three main modules: BIM-RDF and GIS-RDF graphs construction, integrating of two RDF graphs, and query of information through IGIM-RDF graph using SPARQL. The IGIM generates queries from both the BIM and GIS RDF graphs resulting a semantically integrated model with entities representing both BIM classes and GIS feature objects with respect to the target-client application. The linkage between BIM-RDF and GIS-RDF is achieved through SPARQL endpoints and defined by a query using set of datasets and entity classes with complementary properties, relationships and geometries. To validate the proposed approach and its performance, a case study was also tested using IGIM system design.

How and in what manner has the social been instrumental in formulating planning policies, and does Hong Kong ascribe to any social concept that facilitates its current spatial planning framework? The legacy of the social in planning originally came to fruition within the Chicago School of Social Sciences during the early 1920s. Since then, the understanding of the social and how planning responds to the social has been wide and varied. This paper examines the social’s application in spatial notions in addition to its context within Hong Kong. At its core this argument outlines the consequences of a social notion within planning and the spatial modes of recourse. Issues of scaling are brought into question when addressing planning as well as economic focus, in both the local as well as regional governance levels, which further emphasises the dynamic proxies of social and spatial factors for territorial planning. Having neither of these, the argument then highlights the realities of economic asymmetries in the disempowerment of a local populous through land speculation and housing shortages.

Spatial frameworks are a class of spatial mental model that code locations of objects relative to the body axes. Spatial frameworks predict accessibility of spatial relations from memory primarily on the basis of the relative asymmetry of the body axes, such that highly asymmetric axes lead to faster retrieval of information. The present research examined how bodily asymmetries affect retrieval. Experiment 1 contrasted two theoretical accounts. The Salience Account proposes that relative degrees of asymmetry render axes differentially salient, and hence differentially foregrounded in one's mental model. The Direction Decision Account proposes that an explicit decision process is necessary to access specific locations along body axes. The ease of the decision process presumably depends on the degree of asymmetry that exists to discriminate poles along a body axis. The spatial framework pattern of accessibility was observed both when subjects identified specific directions of objects and when subjects identified just the axis to which objects were associated, supporting the Salience Account. Experiment 2 investigated whether lateralization affects accessibility from spatial frameworks. Performance of highly lateralized individuals did not differ from that of weakly lateralized individuals.

Urban modeling is being reshaped by advances in artificial intelligence (AI) and data-rich sensing. This review assembles an integrated evidence base connecting spatial dynamic modeling (SDM), planning support systems (PSSs), urban analytics, and governance concerns. We analyze 1290 publications (2000–2025) using a reproducible pipeline that combines structured literature retrieval with retrieval-augmented generation (RAG) for semantic screening and evidence extraction. Bibliometric mapping and a rigorous coding framework structure the synthesis. The results reveal three linked trajectories. First, SDM has progressed from rule-based simulation toward learned spatial representations using deep and multimodal learning. Second, PSS has evolved from static analytical tools to interactive and participatory environments that embed AI for scenario exploration and stakeholder engagement. Third, governance themes such as transparency, fairness, and accountability have gained importance but remain unevenly implemented in modeling workflows. Building on these findings, we advance AI-aligned SDM, which integrates explainability, uncertainty reporting, documentation, and participation into model design to strengthen institutional accountability and evidence-based planning. A forward research agenda emphasizes methodological fusion between simulation and learning, institutional design for continuous model stewardship, and epistemic pluralism connecting local knowledge with AI to advance equitable and transparent urban governance.

Assessing cellular automata model behaviour using a sensitivity analysis approach

Financial institutions, government-sponsored enterprises, and asset-backed security investors are often exposed to delinquency and prepayment risk from large numbers of loans. Examples include mortgages, credit cards, and auto, student, and business loans. Because of the size of the pools, the measurement of these exposures is computationally expensive. This paper develops and tests efficient numerical methods for the analysis of large pools of loans as well as asset-backed securities backed by such pools. For a broad class of statistical and machine learning models of loan-level risk in discrete time, we prove a law of large numbers and a central limit theorem for the pool-level risk. The asymptotics are then used to construct computationally efficient approximations for a large pool. The approximations aggregate the full loan-level dynamics, making it possible to take advantage of the detailed loan-level data often available in practice. We furthermore prove a convergence rate for the approximation and a uniform integrability result. The latter allows the approximation to be applied to a wide class of pool-level risk statistics. To demonstrate the effectiveness of our approach, we implement it on a data set of over 25 million mortgages. The results show the accuracy and speed of the approximation in comparison to brute-force simulation of a pool, for a variety of pools with different risk profiles. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2947 . This paper was accepted by Noah Gans, stochastic models.