  A simple, intuitive approach to the assessment of probabilistic inferences is
introduced. The Shannon information metrics are translated to the probability
domain. The translation shows that the negative logarithmic score and the
geometric mean are equivalent measures of the accuracy of a probabilistic
inference. Thus there is both a quantitative reduction in perplexity, which is
the inverse of the geometric mean of the probabilities, as good inference
algorithms reduce the uncertainty and a qualitative reduction due to the
increased clarity between the original set of probabilistic forecasts and their
central tendency, the geometric mean. Further insight is provided by showing
that the R\'enyi and Tsallis entropy functions translated to the probability
domain are both the weighted generalized mean of the distribution. The
generalized mean of probabilistic forecasts forms a spectrum of performance
metrics referred to as a Risk Profile. The arithmetic mean is used to measure
the decisiveness, while the -2/3 mean is used to measure the robustness.
