Stochastic modelling of urban structure
File(s)
Published version
Author(s)
Ellam, Louis
Girolami, Mark
Pavliotis, Grigorios A
Wilson, Alan
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 Issued
2018-05-31
Date Acceptance
2018-04-11
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2018, 474 (2213), pp.1-20
ISSN
1364-5021
Publisher
Royal Society, The
Start Page
1
End Page
20
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
474
Issue
2213
Copyright Statement
© 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.
Creative Commons Attribution License http://creativecommons.org/licenses/
by/4.0/, which permits unrestricted use, provided the original author and
source are credited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Royal Academy Of Engineering
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://royalsocietypublishing.org/doi/10.1098/rspa.2017.0700
Grant Number
EP/L020564/1
EP/L024926/1
EP/P031587/1
EP/P020720/1
RCSRF1718/6/34
EP/J009636/1
EP/J016934/3
EP/R018413/1
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
urban modelling
urban structure
Bayesian inference
Bayesian statistics
Markov chain Monte Carlo
complexity
DYNAMICS
Bayesian inference
Bayesian statistics
Markov chain Monte Carlo
complexity
urban modelling
urban structure
stat.ME
stat.ME
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
20170700
Date Publish Online
2018-05-09