Stochastic modelling of urban structure

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Title: Stochastic modelling of urban structure
Author(s): Ellam, L
Girolami, M
Pavliotis, GA
Wilson, A
Item Type: Journal Article
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.
Date of Acceptance: 11-Apr-2018
URI: http://hdl.handle.net/10044/1/59019
DOI: https://dx.doi.org/10.1098/rspa.2017.0700
ISSN: 1364-5021
Publisher: Royal Society, The
Journal / Book Title: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Copyright Statement: © 2018 The Author(s) Published by the Royal Society. All rights reserved.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L020564/1
EP/L024926/1
EP/P031587/1
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published online
Online Publication Date: 2018-05-09
2018-05-09
2018-05-09
Appears in Collections:Mathematics
Statistics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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