Illuminating Statistical Analysis Using Scenarios and Simulations

FBayesian Statistics

Bayesian statistics provides a special method for calculating probability estimates and learning about unknown population statistics. To explore its workings, let's use the framework introduced in Chapter 1. This time we will use a statistical scenario involving medical diagnosis rather than courts of law. Table F.1 shows the various possible conditions and outcomes of a diagnostic test for a fictional disease, Krobze.

Table F.1 Scenario structure.

Bayesian inference can be used to estimate conditional (if…then…) probabilities like:

1. If you test negative, then what is the probability that you really don't have Krobze?
2. If you test positive, then what is the probability that you really do have Krobze?

The first involves the test negative column: we need to calculate the probability of a true negative divided by the sum of the probabilities of true and false negatives. The second involves the test positive column: we need to calculate the probability of a true positive divided by the sum of the probabilities of true and false positives.

In order to calculate these, we need to know the probability of having the disease in general—that is, how common Krobze is in the population. We also need to know how reliable the diagnostic test is. Listed below is this required information, which is then used to fill in Table F.2.

Table F.2 Probabilities after a single ...