These slides and abstract: https://urban-analytics.github.io/dust/presentations.html

We need to better understand urban flows:

Crime – how many possible victims?

Pollution – who is being exposed? Where are the hotspots?

Economy – can we attract more people to our city centre?

Health - can we encourage more active travel?

Understanding *and predicting* short-term urban flows

Uncertainty abounds

Inputs (measurement noise)

Parameter values

Model structure

Nonlinear models predict near future well, but diverge over time.

Used in meteorology and hydrology to constrain models closer to reality.

Try to improve estimates of the true system state by combining:

Noisy, real-world observations

Model estimates of the system state

Should be more accurate than data / observations in isolation.

Create new methods for dynamically assimilating data into agent-based models.

Developing methods that can be used to better understand uncertainty in individual-level models of cities

Example: Crowds in a train station

We want a real-time model to forecast short-term crowding

How much data do we need?

Counts of people entering?

Counts at various points in the concourse (e.g. cameras)

Full traces of all individuals?

Crowding emerges from random choices of exit and maximum walking speed

Very simple, not designed to be a competitive crowd model

Markovian model

Produces output from a set of inputs (the ‘state vector’) without any other information.

Parameters are fixed

E.g. an agent's max speed and it's chosen destination

This is easier for the DA algorithm

Later work will include the parameters in the state vector and get the DA algorithm to find suitable values

Use probability theory to express all forms of uncertainty

Synonymous with Bayesian modelling

*Probabilistic Programming:* "a general framework for expressing probabilistic models as computer programs" (Ghahramani, 2015)

By expressing the model probabilistically (i.e. with variables represented as
*probability distributions*), we can explore the impacts of uncertainty and
(importantly) begin to assimilate data.

(hopefully)

1. Run StationSim to generate pseudo-truth data

2. Data assimilation framework

Run the model for *N* iterations up to time *t* (i.e. 'now')

Construct a Bayesian network to represent the state vector

This gives the a prior estimate of the current state

Observe some 'current' pseudo-truth data and use the probabilistic model (with MCMC) to a produce posterior estimate of the state vector

Forecasts from this point should be more accurate.

"By the time of the work- shop the paper will report initial experiments"

**Malleson, 2019 **

Technically difficult, probabilistic programming is still relatively new

Difficult to test and debug

Positions of agents could be latent (unobserved) in the probabilistic model

Can then include additional observed variables, such as crowd density, and use these to generate a posterior over the latent ones

In other words: very elegant way to include different data (hopefully!)

Results!!

Get it working with all agents

Experiment with different types of observations, e.g.

Cameras that count the passers-by in a single place

Full traces of all agents

*Basically: how much do we need to find solutions that fit the observations*

Overall aim: data assimilation for agent-based models

We want to be able to simulate cities, assimilating real time 'smart city' data as they emerge to reduce uncertainty (and prevent divergence).

Current goal: use a new probabilistic programming library to:

Experiment with the amount of data needed to simulate a system

Perform Bayesian inference on an ABM

Implement data assimilation

These slides and abstract: https://urban-analytics.github.io/dust/presentations.html