A Bayesian statistician approaches statistical inference using Bayesian probability, which represents a degree of belief or certainty. Bayesian statistics incorporates prior knowledge or beliefs about parameters and updates them based on observed data using Bayes’ theorem. This leads to the calculation of posterior probabilities, which express the probability of hypotheses given the data. Bayesian methods are particularly useful when dealing with small sample sizes or when incorporating existing knowledge into statistical analysis.

For example imagine a scenario where a pharmaceutical company wants to test the effectiveness of a new drug. A Bayesian statistician would start with prior beliefs about the drug’s effectiveness based on existing knowledge or previous studies. As new data from clinical trials becomes available, these prior beliefs are updated using Bayes’ theorem to calculate the posterior probability of the drug being effective. The Bayesian approach allows for the incorporation of prior knowledge into the analysis, making it especially useful when dealing with limited data.