40: Competing models

My immediately preceding blog post, ‘Truth is what we agree about’, provides a framework for thinking about competing models in the social sciences. There are competing models in physics, but not in relation to most of the ‘core’ – which is ‘agreed’. Most, probably all, of the social sciences are not as mature and so if we have competition, it is not surprising. However, it seems to me that we can make some progress by recognising that our systems of interest are typically highly complex and it is very difficult to isolate ideal and simple systems of interest (as physicists do) to develop the theory – even the building bricks. Much of the interest rests in the complexity. So that means that we have to make approximations in our model building. We can then distinguish two categories of competing models: those that are developed through the ‘approximations’ being done differently; and those that are paradigmatically different. Bear in mind also that models are representations of theories and so the first class – different ways of approximating – may well have the same underlying theory; whereas the second will have different theoretical underpinnings in at least some respects.

I can illustrate these ideas from my own experience. Much of my work has been concerned with spatial interaction: flows across space – for example, journey to work, to shop, to school, to health services, telecoms’ flows of all kinds. Flows decrease with ‘distance’ – measured as some kind of generalised cost – and increase with the attractiveness of the destination. There was even an early study that showed that marriage partners were much more likely to find each other if they lived or worked ‘nearer’ to each other – something that might be different now in times of greater mobility. Not surprisingly, these flows were first modelled on a Newtonian gravity model analogy. The models didn’t quite work and my own contribution was to shift from a Newtonian analogy to a Boltzmann one – a statistical averaging procedure. In this case, there is a methodological shift, but as in physics, whatever there is in underlying theory is the same: the physics of particles is broadly the same in Newton or Boltzmann. The difference is because Newton can deal with small numbers of particles, Boltzmann with very large numbers – but answering different questions. The same applies in spatial interaction: it is the large number methodology that works.

These models are consistent with an interpretation that people behave according to how they perceive ‘distance’ and ‘attractiveness’. Economists then argue that people behave so as to maximise utility functions. In this case the two can be linked by making the economists’ utility functions those that appear in the spatial interaction model. This is easily done – provided that it is recognised that the average behaviour is such that it does not arise from the maximisation of a particular utility function. So the economists have to assume imperfect information and/or, a variety of utility functions. They do this in most instances by assuming a distribution of such functions which, perhaps not surprisingly, is closely related to an entropy function. The point of this story is that apparently competing models can be wholly reconciled even though in some cases the practitioners on one side or other firmly locate themselves in silos that proclaim the rightness of their methods.

The same kind of system can be represented in an agent-based model – an ABM. In this case, the model functions with individuals who then behave according to rules. At first sight, this may seem fundamentally different but in practice, these rules are probabilities that can be derived from the coarser grain models. Indeed, this points us in a direction that shows how quite a range of models can be integrated. At the root of all the models I am using as an illustration, are conditional probabilities – a probability that an individual will make a particular trip from an origin to a destination. These probabilities can then be manipulated in different ways at different scales.

An argument is beginning to emerge that most of the differences involve judgements about such things as scale – of spatial units, sectors or temporal units – or methodology. The obvious example of the latter is the divide between statisticians and mathematicians, particularly as demonstrated by econometrics and mathematical economics. But, recall, we all work with probabilities, implicitly or explicitly.

There is perhaps one more dimension that we need to characterise differences in the social sciences when we are trying to categorise possibly competing approaches. That is when the task in hand is to ‘solve’ a real-world problem, or to meet a challenge. This determines some key variables at the outset: work on housing would need housing in some way as a variable and the corresponding data. This in turn illustrates a key aspect of the social scientists approach: the choice of variables to include in a model. We know that our systems are complex and the elements – the variables in the model – are highly interdependent. Typically, we can only handle a fraction of them, and when these choices are made in different ways for different purposes, it appears that we have competing models.  Back to approximations again.

Much food for thought. The concluding conjecture is that most of the differences between apparently competing models come from either different ways of making approximations, or  through different methodological (rather than theoretical) approaches. Below the surface, there are degrees of commonality that we should train ourselves to look for; and we should be purposeful!

Alan Wilson

May 2016

36: Block chains and urban analytics

I argued in an earlier piece that game-changing advances in urban analytics may well depend on technological change. One such possibility is the introduction of block chain software. a block is a set of accounts at a node. This is part of a network of many nodes many of which – in some cases all? – are connected. Transactions are recorded in the appropriate nodal accounts with varying degrees of openness. It is this openness that guarantees veracity and verifiability. This technology is considered to be a game changer in the financial world – with potential job losses because a block chain system excludes the ‘middlemen’ who normally record the transactions. Illustrations of the concept on the internet almost all rely on the bitcoin technology as the key example.

The ideas of ‘accounts at nodes’ and ‘transactions between nodes’ resonate very strongly with the core elements of urban analytics and models – the location of activities and spatial interaction. In the bitcoin case, the nodes are presumably account holders but it is no stretch of the imagination to imagine the nodes as being associated with spatial addresses. There must also be a connection to the ‘big data’ agenda and the ‘internet of things’. Much of the newly available real time data is transactional and one can imagine it being transmitted to blocks and used to update data bases on a continuous basis. This would have a very obvious role in applied retail modelling for example.

If this proved to be a mechanism for handling urban and regional data, and because a block chain is not owned by anyone, this could be a parallel internet for our research community.

This is a shorter than usual blog piece because to develop the idea, I need to do a lot more work!! The core concepts are complicated and not easy to follow. I have watched two You Tube videos – an excellent one from the Kahn Academy. I recommend these but what I would really like is someone to take on the challenge of (a) really understanding block chains and (b) thinking through possible urban analytics applications!

Alan Wilson

April  2016

35 Big data and high-speed analytics

My first experience of big data and high-speed analytics was at CERN and the Rutherford Lab over 50 years ago. I was in the Rutherford Lab part of a large distributed team working on a CERN bubble chamber experiment. There was a proton-proton collision every second or so which, for the charged particles, produced curved tracks in the chamber which were photographed from three different angles. The data from these tracks was recorded in something called the Hough-Powell device (after its inventors) in real time. This data was then turned into geometry; this geometry was then passed to my program. I was at the end of the chain and my job was to take the geometry, work out for this collision which of a number of possible events it actually was – the so-called kinematics analysis. This was done by chi-squared testing which seemed remarkably effective. The statistics of many events could then be computed, hopefully leading to the discovery of new (and anticipated) particles – in our case the Ω. In principle, the whole process for each event, through to identification, could be done in real time – though in practice, my part was done off-line. It was in the early days of big computers, in our case, the IBM 7094. I suspect now it will be all done in real time. Interestingly, in a diary I kept at the time, I recorded my immediate boss, John Burren, as remarking that ‘we could do this for the economy you know’!

So if we could do it then for quite a complicated problem, why don’t we do it now? Even well-known and well-developed models – transport and retail for example – typically take weeks or even months to calibrate, usually from a data set that refers to a point in time. We are progressing to a position at which, for these models, we could have the data base continually updated from data flowing from censors. (There is an intermediate processing point of course: to convert the sensor data to what is needed for model calibration.) This should be a feasible research challenge. What would have to be done? I guess the first step would be to establish data protocols so by the time the real data reached the model – the analytics platform, it was in some standard form. The concept of a platform is critical here. This would enable the user to select the analytical toolkit needed for a particular application. This could incorporate a whole spectrum from maps and other visualisation to the most sophisticated models – static and dynamic.

There are two possible guiding principles for the development of this kind of system: what is needed for the advance of the science, and what is needed for urban planning and policy development. In either case, we would start from an analysis of ‘need’ and thus evaluate what is available from the big data shopping list for a particular set of purposes – probably quite a small subset. There is a lesson in this alone: to think what we need data for rather than taking the items on the shopping list and asking what we can use them for.

Where do we start? The data requirements of various analytics procedures are pretty well known. There will be additions – for example incorporating new kinds of interaction from the Internet-of-Things world. This will be further developed in the upcoming blog piece on block chains.

So why don’t we do all this now? Essentially because the starting point – the first demo – is a big team job, and no funding council has been able to tackle something on this scale. There lies a major challenge. As I once titled a newspaper article: ‘A CERN for the social sciences’?

Alan Wilson

March 2016

27: Beware of optimisation

The idea of ‘optimisation’ is basic to lots of things we do and to how we think. When driving from A to B, what is the optimum route? When we learn calculus for the first time, we quickly come to grips with the maximisation and minimisation of functions. This is professionalised within operational research. If you own a transport business, you have to plan a daily schedule of collections and deliveries. Continue reading “27: Beware of optimisation”

23: Missing Data

All the talk of ‘big data’ sometimes carries the implication that we must now surely have all the data that we need. However, frequently, crucial data is ‘missing’. This can then be seen as inhibiting research: ‘can’t work on that because there’s no data’! For important research, I want to make the case that missing data can often be estimated with reasonable results. This then links to the ‘statistics vs mathematical models’ issue: purist statisticians really do need the data – or at least a good sample; if there is a good model, then there is a better chance of getting good estimates of missing data. Continue reading “23: Missing Data”

19: Territories and flows

Territories are defined by boundaries at scales ranging from countries and indeed alliances of countries) to neighbourhoods via regions and cities. These may be government or administrative boundaries, some formal, some less so; or they may be socially defined as in gang territories in cities. Much data relates to territories; some policies are defined by them – catchment areas of schools or health facilities for example. It is at this point that we start to see difficulties. Continue reading “19: Territories and flows”

17: Equations with names: the importance of Lotka and Volterra (and Tolstoy?)

The most famous equations with names – in one case by universal association – seem to come from physics: Newton’s Law of Gravity – the gravitational force between two objects is proportional to their masses and inversely proportional to the distance between them; Maxwell’s equations for electromagnetic fields; the Navier-Stokes’ equation in fluid dynamics; and E = mc2, Einstein’s equation which converts mass into energy. Continue reading “17: Equations with names: the importance of Lotka and Volterra (and Tolstoy?)”

16: New maths needed

In the modern era, mathematical and computer models of cities have been in development for around sixty years – not surprisingly, mirroring the growth of computing power. Much has been achieved. We are pretty good at modelling the flows of people in cities for a variety of purposes and loading these trips on to transport networks; we are pretty good at estimating some activity totals at locations such as retail revenue or demand for housing. Much of this has been stitched together into comprehensive models, embracing demography and input-output economics. Continue reading “16: New maths needed”

14: Learning from history

I was recruited to a post that was the start of my urban modelling career in the Autumn of 1964 by Christopher Foster (now Sir Christopher) to work on the cost-benefit analysis of major transport projects. My job was to do the computing and mathematics and at the same time to learn some economics. Of course, the project needed good transport models and at the time, all the experience was in the United States. Christopher had worked with Michael Beesley (LSE) on the pioneering cost-benefit analysis of the Victoria Line. To move forward on modelling, in 1965, Christopher, Michael and I embarked on a tour of the US. Continue reading “14: Learning from history”

7: Following Fashion

Much research follows the current fashion. This leads me to develop an argument around two questions. How does ‘fashion’ come about? How should we respond to it? I begin by reflecting on my personal experience.

My research career began in transport modelling (cf. ‘Serendipity’ entry) in the 1960s and was driven forward from an academic perspective by my work on entropy maximising and from a policy perspective by working in a group of economists on cost-benefit analysis. Both modelling and cost-benefit analysis were the height of fashion at the time. Continue reading “7: Following Fashion”

3: Lowry and his legacy

A brief history

The ‘science of cities’ has a long history. The city was the market for von Thunen’s analysis of agriculture in the late 18th Century. There were many largely qualitative explorations in the first half of the 20th Century. However, cities are complex systems and the major opportunities for scientific development came with the beginnings of computer power in the 1950s. This coincided with major investment in highways in the United States and computer models were developed to predict both current transport patterns and the impacts of new highways. Plans could be evaluated and the formal methods of what became cost-benefit analysis were developed around that time. However, it was always recognised that transport and land use were interdependent and that a more comprehensive model was needed. There were several attempts to build such models but the one that stands out is I. S. (Jack) Lowry’s model of Pittsburgh which was published in 1964. This was elegant and (deceptively) simple – represented in just 12 algebraic equations and inequalities. Many contemporary models are richer in detail and have many more equations but most are Lowry-like in that they have a recognisably similar core structure.[1] Continue reading “3: Lowry and his legacy”

1: Systems Thinking

When I was studying physics, I was introduced to the idea of ‘system of interest’: defining at the outset that ‘thing’ you were immediately interested in learning about. There are three ideas to be developed from this starting point. First, it is important simply to list all the components of the system, what Graham Chapman called ‘entitation’; secondly, to simplify as far as possible by excluding all possible extraneous elements from this list; and thirdly, taking us beyond what the physicists were thinking at the time, to recognise the idea of a ‘system’ as made up of related elements, and so it was as important to understand these relationships as it was to enumerate the components. all three ideas are important. Identifying the components will also lead us into counting them; simplification is the application of Occam’s Razor to the problem; and the relationships take us into the realms of interdependence. Around the time that I was learning about the physicists’ ideas of a ‘system’, something more general, ‘systems theory’ was in the air though I didn’t become aware of it until much later. Continue reading “1: Systems Thinking”