Contrasting probabilistic scoring rules

• Scoring rules for probabilistic forecasts are contrasted.
• Guidance for scoring rule selection is given.
• The kinds of relative uncertainties preferred are highlighted.
• Implications to decision making are suggested.

There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion for preferring one proper scoring rule above another. This manuscript compares and contrasts some commonly used proper scoring rules and provides guidance on scoring rule selection. In particular, it is shown that the logarithmic scoring rule prefers erring with more uncertainty, the spherical scoring rule prefers erring with lower uncertainty, whereas the other scoring rules are indifferent to either option.