Bayesian statistics refers to an approach to statistical inference characterized by two key ideas: (a) all unknown quantities, including parameters, are treated as random variables with probability distributions used to describe the state of knowledge about the values of these unknowns, and (b) statistical inferences about the unknown quantities based on observed data are derived using Bayes' theorem. Qualitatively, the Bayesian approach to inference begins with a probability distribution describing the state of knowledge about unknown quantities (usually parameters) before collecting data, and then uses observed data to update this distribution. In this article the basic elements of a Bayesian analysis are reviewed (model specification, calculation of the posterior distribution, model checking and sensitivity analysis). Additional sections address the choice of prior distribution, and the application of Bayesian methods.