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.

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?

No crowding With crowding

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)

Work with a new probabilistic programming library *(keanu)*.

Experiment with different amounts of observation data: how well can the probabilistic model find solutions that fit our 'real world' observations

Later:

Include all model parameters in probabilistic model, then work out their mean uncertainty (i.e. calibrate against data)

Other useful Baysean inference tasks, e.g. calculate maximum a posteriori probability (MAP) (should make for efficient sampling)

Data assimilation

1. Configure the model: only *input* is a list of random numbers

Every time the model needs a random number, chose the next in this list

Model is stochastic with respect to these numbers

2. Choose some random numbers and run the model to generate some hypothetical
*truth data*

Pretend that this represents a 'real' train station

3. Use the probabilistic model to find solutions that fit the observations

Can we estimate the original random numbers that were input into the model?

How many observations of the 'real' data do we need?

Observation Interval | Mean Range |
---|---|

0 (prior) | 254 |

1 | 91 |

5 | 130 |

10 | 136 |

50 | 116 |

Explain the relationship between observations and sample spread

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*

Move towards *data assimilation* (actually adjust the state of the
model while it is running in response to external data).

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

**Agent-Based Modelling of Smart Cities**

Start: October 2018

Fully-funded (fees and stipend) for four years

Available to UK/EU applicants

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