Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 474, Issue 2213, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2017.0700
Keywords
urban modelling; urban structure; Bayesian inference; Bayesian statistics; Markov chain Monte Carlo; complexity
Categories
Funding
- EPSRC [EP/P020720/1, EP/J016934/3, EP/K034154/1, EP/R018413/1, EP/P031587, EP/L020564, EP/L024926, EP/L025159, EP/M023583/1, EP/N510129/1]
- EPSRC Established Career Fellowship
- Alan Turing Institute - Lloyd's Register Foundation Programme on Data-Centric Engineering
- Royal Academy of Engineering Research Chair in Data Centric Engineering
- EPSRC [EP/J009636/1, EP/K034154/1, EP/J016934/1, EP/P020720/1, EP/M023583/1, EP/L024926/1, EP/L020564/1, EP/J016934/3, EP/P031587/1, EP/R018413/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/M023583/1, EP/J016934/3, EP/P020720/1, EP/J016934/1, EP/K034154/1, EP/R018413/1] Funding Source: researchfish
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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.
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