Probability

Probability is a branch of mathematics that handles the questions of how certain we are about a quantity or how likely some event is to happen. Probability is a framework for reasoning about randomness and making predictions from data, which is never truly complete or noise-free.

Fig. 20 An approach to estimate π using a random, probability-driven approach.

The use of probability is very important in the areas of data science and machine learning. For example, probabilistic objects can describe the distribution of some data or handle the propagation of uncertainty in models. In fact, this is the basis for Bayesian modelling, which has become an exciting area of scientific application in recent years. The use of generative models inherently involves probability, as these generate new data based on some probabilistic description of the data that has been observed previously.

In this section, we will look briefly at some of the mathematics of probability distributions, which will be the foundation for later work involving Bayesian modelling and generative AI.