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.

Lad, F., Sanfilippo, G., Agro', G. (2012). Completing the logarithmic scoring rule for assessing probability distributions. In Julio Michael Stern and Marcelo De Souza Lauretto and Adriano Polpo and Marcio Alves Diniz (a cura di), XI BRAZILIAN MEETING ON BAYESIAN STATISTICS: EBEB 2012 (pp. 13-30). AIP - Springer [10.1063/1.4759585].

Completing the logarithmic scoring rule for assessing probability distributions

SANFILIPPO, Giuseppe;AGRO', Gianna
2012-01-01

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.
Settore MAT/06 - Probabilita' E Statistica Matematica
Settore SECS-S/01 - Statistica
http://link.aip.org/link/?APC/1490/13/1
Lad, F., Sanfilippo, G., Agro', G. (2012). Completing the logarithmic scoring rule for assessing probability distributions. In Julio Michael Stern and Marcelo De Souza Lauretto and Adriano Polpo and Marcio Alves Diniz (a cura di), XI BRAZILIAN MEETING ON BAYESIAN STATISTICS: EBEB 2012 (pp. 13-30). AIP - Springer [10.1063/1.4759585].
File in questo prodotto:
File Dimensione Formato  
APC000013.pdf

Solo gestori archvio

Descrizione: Paper
Dimensione 2.45 MB
Formato Adobe PDF
2.45 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/67003
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 17
social impact