A Rejoinder

Extract

Whiteley's comment presents a ‘full’ Bayesian argument for the identification of councillors. A Bayesian analysis is a procedure by which an individual can make coherent judgements between hypotheses in terms of conceptual gambles. It is important to recognize that the coherence is between the individual's prior and posterior beliefs when presented with evidence and is not to be interpreted as the agreement between the decision and the correct decision. There is in the argument no appeal to the probability of a correct decision as a relative frequency concept. In many circumstances the correct decision may be undecidable so that a frequentist approach would be inapplicable anyway. Two Bayesians who disagree on their prior beliefs concerning a finite number of hypotheses will disagree on their posterior beliefs when presented with the same data provided that no hypothesis is declared impossible by the data.