Bayesian Probability

Bayesian Probability

Bayesian probability is the likeliness of something based on our hypothesis. In other words, it’s a measure of how strong our belief is that something is going to happen

Bayesian vs. frequentist statistics

• Frequentist probability is based on data and testing a hypothesis
• Bayesian probability is based on strength of belief of hypothesis and not data

Prior Probability Distribution - The probabilities of events whose knowledge is known to us a priori or that which we know beforehand

• Prior information before incorporating measurements are called priors
• Updated information after incorporating measurements is called posterior
• Bayesian statistics takes past information into account
• The more information we get, the closer our probabilities move to 1

$$\text{posterior}=\frac{\text{likelihood}\times \text{prior}}{\text{normalization}}$$

• Likelihood is, as the name says, an estimate of the likeliness of something.