Completing the logarithmic scoring rule for assessing probability distributions

Research output: Chapter in Book/Report/Conference proceedingChapter

16 Citations (Scopus)

Abstract

We propose and motivate an expanded version of the logarithmic score for forecasting distributions, termed the Total Log score. It incorporates the usual logarithmic score, which is recognised as incomplete and has been mistakenly associated with the likelihood principle. The expectation of the Total Log score equals the Negentropy plus the Negextropy of the distribution. We examine both discrete and continuous forms of the scoring rule, and we discuss issues of scaling for scoring assessments. The analysis suggests the dual tracking of the quadratic score along with the usual log score when assessing the qualities of probability distributions. An application to the sequential scoring of forecast distributions for the daily rate of stock returns displays the usefulness of the proposal.
Original languageEnglish
Title of host publicationXI BRAZILIAN MEETING ON BAYESIAN STATISTICS: EBEB 2012
Pages13-30
Number of pages18
Publication statusPublished - 2012

Publication series

NameAIP Conference Proceeedings

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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