Summary
Updates probabilities for hypotheses using prior knowledge and observed data.
In depth
Posterior ∝ likelihood × prior. Gives probabilities of hypotheses and credible intervals. Useful for small samples and incorporating prior knowledge. Computation by MCMC.
Priors are explicit assumptions and can be tested for sensitivity. Posterior intervals have an intuitive meaning.
Key idea: Bayesian methods update belief as data accumulate.
Bayesian statistics treats probability as a degree of belief that is updated by data. Bayes' theorem combines a prior probability (what is believed beforehand) with the likelihood of the observed data to give a posterior probability: posterior is proportional to prior times likelihood.
Unlike frequentist p-values, Bayesian methods give direct statements, such as a 95 percent credible interval that contains the parameter with probability 0.95, and can naturally include prior knowledge and handle complex models. They underpin methods in phylogenetics (MrBayes, BEAST), population genetics and diagnostic testing.
Example: the chance a person who tests positive really has a disease depends on how common it is.
Common mistake: ignoring base rates, which Bayes' theorem corrects.
Frequently asked questions
What is Bayesian Statistics?
Updates probabilities for hypotheses using prior knowledge and observed data.
Which area of biology covers Bayesian Statistics, and how advanced is it?
Bayesian Statistics is one of the 51 topics in Lab Methods & Biostatistics. It is rated Advanced, so it suits learners who want specialist depth. Related topics in this area include Phylogenetic Statistics, P-Values and Multiple Testing, Sampling.
Can you give an example of Bayesian Statistics?
Bayesian phylogenetics estimates tree posterior probabilities.
What should I learn before Bayesian Statistics?
Work through the Beginner topics in Lab Methods & Biostatistics first, such as Scientific Method, Hypothesis, Variables, then return to Bayesian Statistics. Advanced topics assume the Intermediate vocabulary.
What topics are related to Bayesian Statistics?
The closest topics to Bayesian Statistics are Phylogenetic Statistics, P-Values and Multiple Testing, Sampling, Statistical Power. Comparing them side by side is a good way to see how the ideas connect.
How can I check that I understand Bayesian Statistics?
Read the summary and the in-depth section, then use the quick check on the interactive lesson for Bayesian Statistics. To practise the whole of Lab Methods & Biostatistics, use the Lab Methods & Biostatistics quiz.
How is Bayesian Statistics different from Phylogenetic Statistics?
Bayesian Statistics: Updates probabilities for hypotheses using prior knowledge and observed data. Phylogenetic Statistics: Bootstrap and posterior probabilities measure confidence in the branches of evolutionary trees. Read both side by side and note what each one explains.
What is a common mistake about Bayesian Statistics?
Ignoring base rates, which Bayes' theorem corrects.
How should I study Bayesian Statistics step by step?
First, read the summary and write the definition in your own words. Second, read the in-depth section and note any example. Third, compare it with Phylogenetic Statistics and explain the difference aloud. Finally, take the Lab Methods & Biostatistics quiz and come back to this page for any question you miss.