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Stochastic modelling of urban Structure

Ellam, L; Girolami, M; Pavliotis, GA; Wilson, A; (2018) Stochastic modelling of urban Structure. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 474 (2213) , Article 20170700. 10.1098/rspa.2017.0700. Green open access

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Abstract

The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban structure to formally account for uncertainty arising from less predictable events. Standard practice has been to calibrate the spatial interaction models independently and to explore the dynamics through simulation. We present two significant results that will be transformative for both elements. First, we represent the structural variables through a single potential function and develop stochastic differential equations to model the evolution. Second, we show that the parameters of the spatial interaction model can be estimated from the structure alone, independently of flow data, using the Bayesian inferential framework. The posterior distribution is doubly intractable and poses significant computational challenges that we overcome using Markov chain Monte Carlo methods. We demonstrate our methodology with a case study on the London, UK, retail system.

Type: Article
Title: Stochastic modelling of urban Structure
Open access status: An open access version is available from UCL Discovery
DOI: 10.1098/rspa.2017.0700
Publisher version: https://doi.org/10.1098/rspa.2017.0700
Language: English
Additional information: © 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Keywords: Urban modelling, urban structure, Bayesian inference, Bayesian statistics, Markov chain Monte Carlo, complexity
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Centre for Advanced Spatial Analysis
URI: https://discovery.ucl.ac.uk/id/eprint/10055004
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