A-Level Further Maths · Further Statistics
Bayesian Statistics
What is it
Bayesian statistics uses Bayes' theorem to update the probability of a hypothesis as new evidence becomes available, combining prior knowledge with new data to produce an updated, 'posterior' probability.
Why it matters
Bayesian reasoning is the mathematical foundation behind spam filters, medical diagnosis systems, and machine learning classifiers — anywhere a system needs to update its beliefs incrementally as new evidence arrives.
Exam tip
Write out Bayes' theorem in full with clearly labelled events before substituting numbers — misassigning which probability is the prior, the likelihood, or the evidence is the most common conceptual error in Bayesian problems.
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