Modelling with Probability

Using Probability Models

Probability models provide simplified representations of real-world phenomena.
They can help to derive predictions and make decisions based on uncertainty.
The models offer ways to quantify and visualise the likelihood of various possible outcomes.

Identify the random variable – the variable outcome that is subject to uncertainty.
Decide on the possible outcomes and establish their probabilities. Represent these in the model.
Ensure that the sum of all possible outcomes equals 1, as this reflects absolute certainty that one of the stated outcomes will happen.

The Uniform distribution, where each possible outcome has an equal chance of occurring.
The Normal distribution, characterised by its bell-shaped curve. The likelihood of outcomes decreases as you move away from the mean.
The Binomial distribution, applied when there are multiple trials but each with only two possible outcomes.
The Poisson distribution, used when the interest lies in the number of events that occur within a fixed interval of time or space.

Probability models are used widely across various fields that handle uncertainty, such as Statistics, Finance, Engineering, and Ecology.
In finance, risk models use probabilities to predict potential losses.
Weather forecasts use probability to predict outcomes like rainfall or sunshine.

Models should be tested against real-world data to assess their accuracy.
There are formal statistical tests for this, like chi-squared tests and goodness of fit tests.
Discrepancies between the model’s predictions and actual outcomes can highlight areas where the model needs to be refined.

Probability models rely on assumptions which might not perfectly reflect reality.
They may not account for exceptional events, which fall outside of normal probability parameters.
A model is only as good as the quality and completeness of the data it is based upon. Misleading or incomplete data will affect the model’s accuracy and reliability.
Over-reliance on models can be dangerous, they should be used as tools to support decision making, not to replace judgement.