Imperial College London

Professor Grigorios A. Pavliotis

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Ellam:2018:10.1098/rspa.2017.0700,
author = {Ellam, L and Girolami, M and Pavliotis, GA and Wilson, A},
doi = {10.1098/rspa.2017.0700},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
pages = {1--20},
title = {Stochastic modelling of urban structure},
url = {http://dx.doi.org/10.1098/rspa.2017.0700},
volume = {474},
year = {2018}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - 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.
AU - Ellam,L
AU - Girolami,M
AU - Pavliotis,GA
AU - Wilson,A
DO - 10.1098/rspa.2017.0700
EP - 20
PY - 2018///
SN - 1364-5021
SP - 1
TI - Stochastic modelling of urban structure
T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR - http://dx.doi.org/10.1098/rspa.2017.0700
UR - https://royalsocietypublishing.org/doi/10.1098/rspa.2017.0700
UR - http://hdl.handle.net/10044/1/59019
VL - 474
ER -