I wish to formulate a methodology that calculates the probability that
an event will occur based on historic data on when it has happened
before. For example, what is the probability that a person will be
murdered in London today given a complete set of data of the dates of
all previous murders in London. The methodology must take into account
the fact that historic data becomes less and less relavant (e.g. the
murder rate in 1950 is unlikely to have a significant impact on the
probability of being murdered today) and any methodology needs to be
justified. If you are weighting the data, what is the justification
for your weighting model? The method should also work for data where
the events of interest occur very infrequently and should provide
stable values that do not shift wildly when a new event occurs. The
'murder' scenario is just an example, please do not answer it
specifically, but rather please answer in the general case. Can it be
done using Bayesian inference?

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Request for Question Clarification by pafalafa-ga on 08 Aug 2005 10:34 PDT

This sort of thing is done all the time, especially for rare, but
significant, natural events.

I used to do flood management work, and there were numerous
methodologies for calculating the magnitude of a "ten year flood" or
the much rarer "hundred year flood".

Scientists try and work out the future likeliehood of an earthquake,
volcano or tsunami or asteroid strike occuring, based on what they
know of past events.

But there's no fixed methodology for these things.  Just a sort of
professional judgment that comes into play, followed by the criticisms
of your colleagues if they feel your judgment stinks!


Would it help to be pointed to some of the methods that are used in
situations like these?

Let me know.

pafalafa-ga

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Clarification of Question by subsonictom-ga on 09 Aug 2005 03:27 PDT

The key difference between my problem and natural events such as
asteroid impacts is that we can assume that asteroid impacts are
essentially random events. I am looking to model the probability of
events whose frequency changes with time due to external factors such
as political events.

My initial model finds the weighted average time between recorded
events (with weightings that decay in a Gaussian distribution as the
data becomes more and more historic). This weighted average is then
converted to an annualised occurrence rate. However, my weighting
curve is pretty arbitrary and i am looking for an alternate, more
rigorous, methodology. I hope that clarifies.

I am posting this as a comment since it is impossible to do a justice
to this complex question within a  $20 answer.

So this is just a free suggestion:

make a search on the 

SEARCH TERM: exponential average

you will get lot of investment links, like this

http://www.streetauthority.com/terms/simpleandexponentialmovingaverages.asp

but it is used elswhere as well. It gives less weight to the past as it
updates expected value based on recent events.

You still need stochastic model of the specific subject matter to get the
'right' time constant.

There is no 'universal' formula and stock market is a good example
of random walk which gets influenced by political as well natural events.

 General formula, even partly valid, would be worth more then $20,
 if it would exist.