32
IRUS TotalDownloads
Altmetric
Stochastic modelling of urban structure
File | Description | Size | Format | |
---|---|---|---|---|
![]() | Published version | 970.35 kB | Adobe PDF | View/Open |
Title: | Stochastic modelling of urban structure |
Authors: | 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. |
Issue Date: | 31-May-2018 |
Date of Acceptance: | 11-Apr-2018 |
URI: | http://hdl.handle.net/10044/1/59019 |
DOI: | 10.1098/rspa.2017.0700 |
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. |
Sponsor/Funder: | 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) |
Funder's 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 |
Keywords: | 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 |
Online Publication Date: | 2018-05-09 |
Appears in Collections: | Mathematics Statistics Applied Mathematics and Mathematical Physics Faculty of Natural Sciences |