Full Bayesian analysis is an alternative statistical paradigm, as opposed to traditionally used methods, usually called frequentist statistics. Bayesian analysis is controversial because it requires assuming a prior distribution, which can be arbitrarily chosen; thus there is a subjective element, which is considered to be a major weakness. However, this could also be considered a strength since it provides a formal way of incorporating prior knowledge. Since it is flexible and permits repeated looks at evolving data, Bayesian analysis is particularly well suited to the evaluation of new medical technology. Bayesian analysis can refer to a range of things: from a simple, noncontroversial formula for inverting probabilities to an alternative approach to the philosophy of science. Its advantages include: (1) providing direct probability statements--which are what most people wrongly assume they are getting from conventional statistics; (2) formally incorporating previous information in statistical inference of a data set, a natural approach which we follow in everyday reasoning; and (3) flexible, adaptive research designs allowing multiple looks at accumulating study data. Its primary disadvantage is the element of subjectivity which some think is not scientific. We discuss and compare frequentist and Bayesian approaches and provide three examples of Bayesian analysis: (1) EKG interpretation, (2) a coin-tossing experiment, and (3) assessing the thromboembolic risk of a new mechanical heart valve.