Stochastic Modelling of Urban Structure

TL;DR

This paper introduces a stochastic modeling framework for urban structure that captures uncertainty and allows parameter estimation from structure alone, demonstrated through a London retail case study.

Contribution

It develops a novel stochastic differential equation approach for urban structure evolution and enables parameter estimation without flow data using Bayesian methods.

Findings

Structural variables modeled via potential functions

Parameters estimated from structure alone

Successful application to London retail system

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 (SDEs) to model the evolution. Secondly, 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 (MCMC) methods. We demonstrate our methodology with a case study on the London retail system.