Completing the logarithmic scoring rule for assessing probability distributions

Lad, Frank; Sanfilippo, Giuseppe; Agró, Gianna

doi:10.1063/1.4759585

by Frank Lad, Giuseppe Sanfilippo, Gianna Agró

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 examineboth discrete and continuousforms 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

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Reference:

Frank Lad, Giuseppe Sanfilippo, Gianna Agró, "Completing the logarithmic scoring rule for assessing probability distributions", In AIP Conference Proceedings, AIP, vol. 1490, no. 1, pp. 13-30, 2012.

Bibtex Entry:

@ARTICLE{2012:1AIP,
  author = {Frank Lad and Giuseppe Sanfilippo and Gianna Agr\'{o}},
  title = {Completing the logarithmic scoring rule for assessing probability
	distributions},
  journal = {AIP Conference Proceedings},
  year = {2012},
  volume = {1490},
  pages = {13-30},
  number = {1},
  note = {ISBN: 978-0-7354-1102-9, ISSN 0094-243X},
  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 examineboth discrete and continuousforms
	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},
  doi = {10.1063/1.4759585},
  editor = {Julio Michael Stern and Marcelo De Souza Lauretto and Adriano Polpo
	and Marcio Alves Diniz},
  isbn = {978-0-7354-1102-9},
  issn = {0094-243X},
  keywords = {Probability},
  publisher = {AIP},
  scopus = {{2-s2.0-84870052585}},
  url = {http://link.aip.org/link/?APC/1490/13/1},
  wos = {{WOS:000310688900002}}
}