Bayesian Inference

Bayesian inference is a statistical method which gives a framework to update probabilities of a hypothesis based on evidence or additional data. This method is rooted in the principle of Bayesian probability, a theory that describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

How Bayesian Inference works

At the heart of Bayesian inference is Bayes' theorem, which is used to update a prior belief once new data or information is obtained. The theorem combines the prior probability and the likelihood of the data under the hypothesis (known as the "likelihood function") to produce a "posterior probability".

Bayesian inference works in four steps.

1. It begins with establishing a prior probability; known information or belief about the event before new data is observed
2. New data or evidence is collected.
3. Applying Bayes' theorem to update the existing prior probability based on the new evidence. The prior probability, the likelihood function for the observed data and the total probability of the data (marginal likelihood) are used in the theorem to calculate the posterior probability.
4. Finally, the posterior probability becomes the new prior, or “updated belief”, ready for further evidence to be collected and the process to be repeated.

Through this self-learning mechanism, Bayesian inference enables continuous learning and improvement, adapting its predictions as new data is added, thus making it particularly useful in machine learning algorithms and predictive modeling.