TY - GEN
T1 - A Historical Perspective on the Schützenberger-van Trees Inequality
T2 - 7th International Conference on Geometric Science of Information, GSI 2025
AU - Rioul, Olivier
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.
PY - 2026/1/1
Y1 - 2026/1/1
N2 - The Bayesian Cramér-Rao Bound (BCRB) is generally attributed to Van Trees who published it in 1968. According to Stigler’s law of eponymy, no scientific discovery is named after its first discoverer. This is the case not only for the Cramér-Rao bound itself—due in particular to the French mathematicians Fréchet and Darmois—but also for the van Trees inequality: The French physician, geneticist, epidemiologist and mathematician Marcel-Paul (Marco) Schützenberger, in a paper of just fifteen lines written in 1956—more than a decade before van Trees—had not only derived the BCRB but, as a close examination of his proof shows, used a very original approach based on the Weyl-Heisenberg uncertainty principle on the square root of the posterior distribution. This work reviews and extends Schützenberger’s approach to Fisher information matrices, which opens up new perspectives.
AB - The Bayesian Cramér-Rao Bound (BCRB) is generally attributed to Van Trees who published it in 1968. According to Stigler’s law of eponymy, no scientific discovery is named after its first discoverer. This is the case not only for the Cramér-Rao bound itself—due in particular to the French mathematicians Fréchet and Darmois—but also for the van Trees inequality: The French physician, geneticist, epidemiologist and mathematician Marcel-Paul (Marco) Schützenberger, in a paper of just fifteen lines written in 1956—more than a decade before van Trees—had not only derived the BCRB but, as a close examination of his proof shows, used a very original approach based on the Weyl-Heisenberg uncertainty principle on the square root of the posterior distribution. This work reviews and extends Schützenberger’s approach to Fisher information matrices, which opens up new perspectives.
UR - https://www.scopus.com/pages/publications/105035324252
U2 - 10.1007/978-3-032-03921-7_29
DO - 10.1007/978-3-032-03921-7_29
M3 - Conference contribution
AN - SCOPUS:105035324252
SN - 9783032039200
T3 - Lecture Notes in Computer Science
SP - 280
EP - 289
BT - Geometric Science of Information - 7th International Conference, GSI 2025, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 29 October 2025 through 31 October 2025
ER -