Terminology

There are a lot of terms that are borrowed from economics, mathematics and philosophy that may not be familiar to architects. This section will briefly explain them.

Forecasting

In a general sense fore casting is predicting the future, so any prediction about what will happen after now counts as a forecast. In a more strict statistical sense, a forecast is a projection of the known data’s trend into a future unknown area. It is also possible to back-cast to see if a model based on current data agrees with historical data.

The law of large numbers

If I flip a coin three times there is a reasonably good chance that I’ll get three heads. As the objective probability that I’ll get a head on any particular flip is 50% then the observed probability differs from the objective probability. If I flipped that coin a thousand times, I’d probably get almost exactly 500 heads (within 5 or so), and the error margin would probably be about the same by the time I’d got to a million.

This is useful when trying to take a statistical sample of a population as any given individual probably differs from the mean a bit, but over a large number of samples the average will be pretty representative of the population. This is also known as regression to the mean.

AJAX

AJAX is a conglomeration of a few web technologies that make it relatively easy to have dynamic sections of web content that can do things like checking that an email address is well formed, or fetching some content without needing to refresh the whole page. It is short for asynchronous JavaScript and XML.

PHP

PHP is a server side scripting language. This means that all the computation is done on the server, and then a web page is generated and sent to the user. It allows websites to be built that refer to databases, or that respond to the user.

Pay off function

A pay off function describes what the expected pay off or utility will be given a certain set of inputs. The interesting thing about them for this study is not the value of the pay off, but the shape of the curve. If it is steep in the critical region, then a small deviation in one’s calibration can result in a radically different payoff.

Priors

When one makes a prediction it is based on certain propositions. These propositions tend to come from prior experience. For example “I predict that it will rain tomorrow” is based on the prior that it rained today, that in my experience a tomorrow always follows a today, etc.

Probability densities can be assigned to a prior, and these can be combined through various methods (see Monte Carlo) to give an overall probability density function for the whole prediction

a priori

Latin, basically meaning known before. It is used to describe the knowledge one has before embarking on some sort of task.

a posteriori

Latin, basically meaning known afterwards. It is used to describe the knowledge one has when looking back on some sort of task.

Monte Carlo

Other than being a principality with a lot of casinos, Monte Carlo lends its name to a class of stochastic modelling where the inputs have probability density functions. This means that if a series of dartboards were divided up into unequally sized slices, then the function (which might be something simple like a+b+c+d =?) is fed by the values that a blindfolded dart thrower would generate.

The output of a Monte Carlo analysis is a probability density function that describes the likelihood of any of those outcomes happening. The interesting thing about this kind of analysis is that it doesn’t produce an answer, but an assessment of the probability of a range of events.

Probability density

If a dice is rolled or a coin is flipped, then all the possible outcomes are equal. If a complicated hedge fund is invested in then the different outcomes that are possible have differing probabilities. The probability density is essentially the shape that these probabilities make when plotted on a graph.

Search Space

If a number of variables are fed to a function, then the output of that function can be used as another value on a graph. This seems quite abstract, so imagine the function being the amount I enjoy my coffee, and the variable being the amount of sugar put in. I like no sugar at all most, but a lot of sugar is quite fun, with a dip around one sugar.

The same can be done with 2 variables, which makes a 3d surface, which is where the term ‘landscape’ comes from. It can be extended into n dimensional landscapes, but they get a bit hard to visualise.

Benchmark

The term benchmark originates from the chiselled horizontal marks that surveyors made, into which an angle-iron could be placed to bracket (“bench”) a levelling rod, thus ensuring that the levelling rod can be repositioned in exactly the same place in the future.(Wikipedia).

In our case, a benchmark is a value that we can compare something to. This value may change over time, but it is usually well accepted by the group that uses it. i.e. the benchmark height for an NBA basketball player might well be 2m, and then all other players can be considered tall if taller than this, or short if shorter.

 

Rational

In this situation we are using the word ‘rational’ in the economics context, rather than the way it is used in general parlance. In economics and probability theory, to be rational simply requires one to have an internally consistent world view, and to have constant desires and beliefs. For example, if I intend an end, then it is rational for me to intend the means to that end. If I intended to go to town, it would be irrational for me not to intend to get the bus, unless I believed that I could get to town by another means, like walking or cycling. See the introduction of Irrationality (Sutherland, 1992) for an elegant expansion of this. The more common use of the word ‘rational’ is its use to describe some thought or action that would be that which was the ‘best’ or most ‘sensible’ given a set of criteria. It is hard to completely define this as it is not strict utility maximisation from a naïve perspective, as utility might be assigned to actions that provide intangible benefits.