  A common concern with Bayesian methodology in scientific contexts is that
inferences can be heavily influenced by subjective biases. As presented here,
there are two types of bias for some quantity of interest: bias against and
bias in favor. Based upon the principle of evidence, it is shown how to measure
and control these biases for both hypothesis assessment and estimation
problems. Optimality results are established for the principle of evidence as
the basis of the approach to these problems. A close relationship is
established between measuring bias in Bayesian inferences and frequentist
properties that hold for any proper prior. This leads to a possible resolution
to an apparent conflict between these approaches to statistical reasoning.
Frequentism is seen as establishing a figure of merit for a statistical study,
while Bayesianism plays the key role in determining inferences based upon
statistical evidence.
