Bayesian vs frequentist statistics: afraid of losing the reference?

Abstract

While on his first hospital duty, a second-year cardiology resident receives a message in his pager about a patient who has just been admitted to the emergency room with chest pain. Specifically, he is asked to discard that the pain is of coronary origin. The resident questions the patient on his symptoms, examines his risk factors, and analyzes the electrocardiogram (ECG). With the ECG data, the qualitative information of pain provided by the patient, together with his past medical history, the presence of coronary pain is eventually discarded. The patient’s past medical history reads «the symptoms described by the patient, the presence of hypertension as the only risk factor, and the lack of specific changes on the ECG suggest that the chances of coronary pain are extremely low». Intuitively, the resident considers that the chances the pain is due to coronary artery disease (CAD) with the data available (qualitative data of pain, risk factors, ECG) is lower than, let’s say, 5%. In other words, the resident instinctively concludes that: p(CAD |qualitative data, risk factors, ECG) < .05, that is, the probability of having CAD according to all the abovementioned information (qualitative data, risk factors, and ECG) is < 5%. However, before the patient...