In this work, a well defined procedure to assign a probability distribution to a score is presented. By considering a score 0 ≤ t ≤ 1 and using Bayesian inference together with Jaynes’ Maximum Entropy Principle, we are able to assign an estimation <t> to the score based on the available information. In order to correctly define a score t, we assume a resolution Δt that enables us to assign a a score t∗ so that t∗ −Δt/2 ≤ t ≤ t∗ + Δt/2 with a confidence p, and infer the parameters of the maximum entropy distribution as a function of p and t∗. This framework may provide insights on how to state problems with uncertain evaluation of performance in learning in several contexts.
REFERENCES
1.
M. G.
Aamodt
, D. A.
Bryan
, and A. J.
Whitcomb
, “Predicting performance with letters of recommendation
,” Public Personnel Management
22
, 81
–90
(1993
), .2.
T.
Schmader
, J.
Whitehead
, and V. H.
Wysocki
, “A linguistic comparison of letters of recommendation for male and female chemistry and biochemistry job applicants
,” Sex Roles
57
, 509
–514
(2007
).3.
D. V.
Girzadas
Jr., R. C.
Harwood
, J.
Dearie
, and S.
Garrett
, “A comparison of standardized and narrative letters of recommendation
,” Academic Emergency Medicine
5
, 1101
–1104
(1998
), https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1553-2712.1998.tb02670.x.4.
E. T.
Jaynes
, Probability Theory: The Logic of Science
(Cambridge University Press
, 2003
).5.
E. T.
Jaynes
, “Information theory and statistical mechanics
,” Phys. Rev.
106
, 620
–630
(1957
).6.
J. M.
Bernardo
et al, “Psi (digamma) function
,” Applied Statistics
25
, 315
–317
(1976
).7.
K.
Ito
and K.
Kunisch
, Lagrange multiplier approach to variational problems and applications
(SIAM
, 2008
).
This content is only available via PDF.
©2023 Authors. Published by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
