Modelling with Probability

Modelling with Probability

Using Probability Models

Definition and Purpose

  • 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.

How to Build Probability Models

  • 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.

Common Probability Models

  • 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.

Applications in Real-life Contexts

  • 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.

Evaluating Probability Models

  • 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.