Relative Belief and Combining Evidence

The problem of combining the evidence in several Bayesian inference bases is considered. Evidence is measured in each inference base using the relative belief ratio which gives an unambiguous prescription of whether there is evidence in favour of or against each possible value of an unknown such as a parameter. While there are many possible ways to combine the evidence, the method of linear pooling stands out as it preserves a consensus while others may not. There are constraints on this application, however, if one requires a formal Bayesian justification. In some applications where these restrictions do not hold, the approach can be generalized by allowing for the methodology known as Jeffrey conditionalization.