GEOG3150 Semester 2

Lecture 9

Understanding Models through their Patterns:

Statistics, Visualisation and Complexity.

Dr Nick Malleson
Dr Alison Heppenstall

Click here for full screen

About these slides

These leture slides work in two dimensions; sometimes you have to press the 'down' arrow to find additional slides explaining a particular topic. You can press 'escape' to zoom out and see all the slides that are available.

The slides with voting windows on them wont work after the lecture, as we will have finished voting! You will just see a blank window.

Recap: ABM and Geography

Reasons to model:

Explanatory

Predictive

The reason for modelling will influence your decisions over the modelling environment

Different types of 'geography'

Grids

Continuous space

Social network?

GIS

Recap: ABM & GIS

Loose coupling

The GIS and the model do not interact directly

Tight coupling

The GIS and model are integrated

Loose coupling is more efficient and flexible, but it can make interacting with the model more difficult.

Recap: Simulation for Policy Modelling

Pedestrian modelling

Fluid dynamics / social forces

Magnetic model

Agent-based crowd models

Traffic modelling

Examples of spatially realistic models

Abstract models were surprisingly successful

Recap: Simulation for Policy Modelling

Steven J. Lansing and water management in Bali

Bali rice fields — Attribution: Nick Leonard (CC BY-NC-SA 2.0)

This Lecture: Understanding Models through their Patterns

About the patterns produced by models in their results:

methods that can be used to identify 'important' patterns in multi-dimensional space;

what these mean in terms of causality (i.e. how they have been caused by a model);

how patterns can be used to inform our understanding of real systems.

We're 'flipping' the classroom, so it is going to be much more interactive than normal

Preparation was to read:

Evans, A., A. Heppenstall and M. Birkin (2013) Understanding Simulation Results. In B. Edmonds and R. Meyer (eds) Simulating Social Complexity. Springer. [Available on the VLE: http://tinyurl.com/oq4bh64 ]

This is the hardest lecture, covering the most advanced topics. So don't worry if it takes some time to understand all the material.

So how is this 'flipped classroom' thing going to work?

1 - I ask a question, you think about it in silence

2 - We do a poll to see what everyone thinks

3 - You spend a few minutes discussing the results of the poll and try to persuade each other what the correct answer is.

4 - Poll again

5 - If lots of people still get the answer wrong I'll talk for a few minutes, otherwise we'll move on.

Question 1 - Causality and Emergence

The authors suggest that:

The concept of emergence is essentially a sign of our ignorance of the causal pathways within a system.

In other words, if we had massive brains we could run simulations in our heads and simply see how individual-level behaviours lead to emergent patterns (i.e. cause and effect).

Question 1 - Causality and Emergence

In a complex system, which direction does the path of causality flow:

1. From the individual to the aggregate

2. From the aggregate to the individual

3. In both directions

4. WTF?

Think about this in silence for a few minutes.

Vote at: http://www.polleverywhere.com/nickmalleson

There is no 'correct' answer to this, although it is probably 3 (both directions).

E.g. in a termite mound, ventilation ducts are built at specific locations as required, so the emergent phenomena (the mount itself) must have an imppact back onto the termites.

Similarly with the Romanesque Cauliflower, the structure has an impact on the growth of the cells in order for the perfect fractal shape to form (see http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html ).

Poll

Vote at: http://www.polleverywhere.com/nickmalleson

Discussion

In a complex system, which direction does the path of causality flow:

1. From the individual to the aggregate

2. From the aggregate to the individual

3. In both directions

4. WTF?

Discuss the answer with your neighbour(s) for a few minutes. Which is the right answer? Is there a right answer?

Some definitions: (by Nick) might help

Causality: the relationship between cause and effect

Causal pathway: the path taken from cause to effect.

E.g. in the festival model, the 'causal pathway' leads from the individual (agents) to the aggregate (crime patterns)

Remember the butterfly effect?

Poll again

Vote at: http://www.polleverywhere.com/nickmalleson

Question 2 - Recognising Patterns with Statistics

Data produced by models of complex systems can be voluminous, multi-dimensional and extremely complicated.

Capturing the movements of agents in a 3D system produces huge amounts (1 entry per agent per itetation) of 4D data (x, y, z, time).

This makes it very difficult to detect 'interesting' patterns

Fortunately there are methods that can be used to reduce the dimensionality of the data and aid pattern recognition

For example, clustering algorithms highlight areas with unusually high/low numbers of occurrences.

The chapter introduced a number of new and exciting methods to reduce the dimensionality in our data and to aid pattern recognition. In the lecture, we will focus on those that are mostly relevant to spatio-temporal data and that you are most likely to come across again. There are lots of interenet resources available if you would like to look up some of the other methods though.

Question 2 - Recognising Patterns with Statistics

Which of the following methods tells you about the overall amount of clustering in your data.

Nearest-Neighbour statistics (e.g. Nearest Neighbour Index, G, F, K)

Spatial auto-correlation statistics (e.g. Moran's I and Geary's C)

Local Indicators of Spatial Association (e.g. GI*, Geographical Analysis Machine)

Space-time scan statistics

Think about this in silence for a few minutes.

Vote at: http://www.polleverywhere.com/nickmalleson

Poll

Vote at: http://www.polleverywhere.com/nickmalleson

Discussion

Which of the following methods tells you about the overall amount of clustering in your data.

Nearest-Neighbour statistics (e.g. Nearest Neighbour Index, G, F, K)

Spatial auto-correlation statistics (e.g. Moran's I and Geary's C)

Local Indicators of Spatial Association (e.g. GI*, Geographical Analysis Machine)

Space-time scan statistics

Discuss the answer with your neighbour(s) for a few minutes. Which is the right answer? Is there a right answer?

Poll again

Vote at: http://www.polleverywhere.com/nickmalleson

Question 2 - Recognising Patterns with Statistics

Examples

Nearest-Neighbour Statistics

Compares average distances from one point to its nearest neighbour.

Tells you about overall clustering / dispersion in the data (NNI)

Can be extended to show clustering at different scales (G and F functions)

Spatial Autocorrelation

Everything is related to everything else, but near things are more related than distant things
- Waldo Tobler

Spatial autocorrelation:

a variable is correlated with itself through space

Positive: Nearby values are simlar to each other

Negative: Nearby values are different (unusual)

Common statistics: Moran's I, Geary's C, Ripley's K

Local Indicators of Spatial Association

AKA clustering statistics

Identify locations with a statistically significant high/low number of occurences

Examples: GI* (Getis and Ord), GAM (Stan Openshaw)

Space-Time Scan Statistics

Look for clusters of events in space and time.

Commonly applied to search for clusters of disease outbreak

Pass a cylinder over the events in space-time (3D)

Question 3 - Visualising Patterns

The tools that we have developed over some time ("2500 years"!) are poorly suited to exploring the detail associated with individual-level data.

Visualisation is a powerful means to understand these data as it aims to exploit the ease with which we (humans) recognise patterns.

Common techniques include:

Time series data

Choropleth maps

Rose diagrams

Space-time cube

Phase maps

Time Series Data

Example time series graph (crime rate agains time).

Choropleth maps

Example Choropleth map — Source: Malleson, N., 2010. *Agent-Based Modelling of Burglary*. PhD Thesis, School of Geography, University of Leeds, UK.

Rose diagrams

Rose diagrams

Space-time Cube

Phase Maps

Question 3 - Visualising Patterns

List some disadvantages associated with visualising data in order to find patterns and draw conclusions.

Think about this in silence for a few minutes.

Suggestions to: http://www.polleverywhere.com/nickmalleson

Poll

Vote at: http://www.polleverywhere.com/nickmalleson

Visualisation techniques attempt to exploit the ease with which humans recognise patterns. The main drawback with this approach is that it is vulnerable to human subjectivity. At best, we might identify patterns that we want to see, and at worst we might be incapable of recognising patterns that are outside the capabilities of our visual system and/or cultural experiences. As the authors note, we are better at perceiving some patterns than others.

Question 4 - Explanation, understanding and causality

Once patterns are recognised, "understanding" our models involves finding explanations highlighting the mechanisms within the models which give rise to these patterns
- (pg 13)

Key methods for developing understanding:

Types of relationship (correlation): linear, binomial, poisson

Experimentation: sensitivity testing, "what-if" scenarios

Causality: "find the lady problem" and "drop in the ocean problem"

Identifiability and Equifinality

Question 4 - Explanation, understanding and causality

Two GEOG3150 students work independently to create models of crime in a music festival. The causal mechanisms in the models are extremely different, and yet both models lead to the same result.

What best describes this phenomenon?

1. The "find the lady problem"

2. Equifinality

3. The "drop in the ocean problem"

4. Identifiability

Think about this in silence for a few minutes.

Vote at: http://www.polleverywhere.com/nickmalleson

Poll

Vote at: http://www.polleverywhere.com/nickmalleson

Discussion

The phenomena in which two very different models lead to the same result is know as:

1. The "find the lady problem"

2. Equifinality

3. The "drop in the ocean problem"

4. Identifiability

Discuss the answer with your neighbour(s) for a few minutes. Which is the right answer? Is there a right answer?

Vote at: http://www.polleverywhere.com/nickmalleson

Poll again

Vote at: http://www.polleverywhere.com/nickmalleson

Question 4 - Explanation

Identifiability

"a single model outcome may have more than one history of model parameters that leads to it"

i.e. one model, but lots of different parameter values can lead to the same results

Equifinality

"the model in the computer accurately reflects the system in the real world"

i.e. lots of different models could produce the same results.

The "find the lady problem"

The sheer number of interactions in a model make tracking causality extremely hard

The "drop in the ocean problem"

Often numbers are used to represent aggregated quantities (e.g. 2 children)

This makes it impossible to track a individual through the system

Sometimes this doesn't matter (e.g. drops of water in a lake), but sometimes it does (e.g. ??)

Summary

Causality and Emergence

Recognising Patterns with Statistics

Visualising Patterns

Explanation, understanding and causality

Rrevision & module roundup

http://www.geog.leeds.ac.uk/courses/level3/geog3150/lectures/revision/

GEOG3150 Semester 2

Lecture 9

Understanding Models through their Patterns:

Statistics, Visualisation and Complexity.

Dr Nick Malleson Dr Alison Heppenstall

About these slides

Recap: ABM and Geography

Recap: ABM & GIS

Recap: Simulation for Policy Modelling

Recap: Simulation for Policy Modelling

This Lecture: Understanding Models through their Patterns

So how is this 'flipped classroom' thing going to work?

Question 1 - Causality and Emergence

Question 1 - Causality and Emergence

Poll

Discussion

Poll again

Question 2 - Recognising Patterns with Statistics

Question 2 - Recognising Patterns with Statistics

Poll

Discussion

Poll again

Question 2 - Recognising Patterns with Statistics

Examples

Nearest-Neighbour Statistics

Spatial Autocorrelation

Local Indicators of Spatial Association

Space-Time Scan Statistics

Question 3 - Visualising Patterns

Time Series Data

Choropleth maps

Rose diagrams

Rose diagrams

Space-time Cube

Phase Maps

Question 3 - Visualising Patterns

Poll

Question 4 - Explanation, understanding and causality

Question 4 - Explanation, understanding and causality

Poll

Discussion

Poll again

Question 4 - Explanation

Summary

Next

Dr Nick Malleson
Dr Alison Heppenstall