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A Historical Perspective on the Schutzenberger-van Trees Inequality: A Posterior Uncertainty Principle
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DOI：10.1007/978-3-032-03921-7_29.png)
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Abstract
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The Bayesian Cramer-Rao Bound (BCRB) is generally attributed to Van Trees who published it in 1968. According to Stiglers law of eponymy, no scientific discovery is named after its first discoverer. This is the case not only for the Cramer-Rao bound itself-due in particular to the French mathematicians Frechet and Darmois-but also for the van Trees inequality: The French physician, geneticist, epidemiologist and mathematician Marcel-Paul (Marco) Schutzenberger, 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 Schutzenbergers approach to Fisher information matrices, which opens up new perspectives.
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