Monday, 16 January 2012

Introducing probablistic models

Recently I have been revisiting some mathematics. Often maths becomes very complex very quickly so here I enjoy keeping it simple.

Probabilistic models consist of 3 parts
1. A model that produces a random variable(s) X
2. A model that creates probabilities for the random variables
3. The sum of frequencies must add up to 1

If we take the example of flipping a coin: The coin has 2 faces and these correspond to the random variable X. The values of X can be give a value such as X=1 for heads and X=2 for tails. The model would be the probability of X=1 is 0.5 and the probability of X=2 is 0.5 and the sum of these probabilities sum to 1. Then you have a coin that may not be completely round or evenly balanced meaning it may behave differently to the model.

There are other types of models for example the number of people in a queue can be modeled with Poison. Mr Poison was a lawyer that studied the lengths of queues Research on the "Probability of Judgments in Criminal and Civil Matters" and build a model around this. This is a very interesting model when modeling the length of queues, It's also very useful when converting an Event loss table to a Year loss table. Here the problem is to sample the number of events that happen in a year given a mean and a standard deviation

Catastrophe probabilistic models can also be broken down into these 3 components.
1. A modeling that combines the Hazard, Vulnerability and Exposure to produce the random variable ground up loss
2. A model that assigns a frequency for each event
3. An event catalogue where the sum of frequencies adds up to the total length of time the catalogue is constructed for

A catastrophe model is more elaborate than the coin example and comprises of the Hazard (the earthquake or the windstorm), the vulnerability (how fragile it is) and en exposure (what buildings are at risk)