Introduction

Bayesian statistics is a mathematical approach that uses probability to express uncertainty about events, parameters, or hypotheses.

Unlike ‘frequentist’ statistics, which treats parameters as fixed but unknown constants, Bayesian statistics treats parameters as random variables with probability distributions.

This allows us to:

• Update our beliefs as new evidence becomes available;
• Incorporate prior knowledge into our statistical analyses;
• Make probabilistic statements about parameters of interest; and
• Handle small sample sizes more effectively.

Video

https://www.youtube.com/watch?v=9TDjifpGj-k

Bayes' Theorem

Central to Bayesian statistics is ‘Bayes' Theorem’, which describes how to update the probability of a hypothesis given new evidence.

The theorem is expressed as:

$$ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} $$

Where:

• P(A|B) is the ‘posterior’ probability - the probability of A given B has occurred (A IF B);
• P(B|A) is the likelihood - the probability of B given A (B IF A);
• P(A) is the prior probability of A; and