# Stochastic Modelling of Urban Structure

arXiv: https://arxiv.org/abs/1805.03567 · HTML: https://mlsanity.com/paper/1805.03567/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2018.

## Built on by (most cited first, 4 of 4)

- [Neural parameter calibration for large-scale multi-agent models](https://mlsanity.com/paper/2209.13565/) (2022)
- [Inferring networks from time series: a neural approach](https://mlsanity.com/paper/2303.18059/) (2023)
- [Generating Origin-Destination Matrices in Neural Spatial Interaction Models](https://mlsanity.com/paper/2410.07352/) (2024)
- [A variational Bayesian spatial interaction model for estimating revenue and demand at business facilities](https://mlsanity.com/paper/2108.02594/) (2021)

## Abstract (arXiv)

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.