The Cramér-Rao lower bound on variance: Adam and Eve's “uncertainty principle”
Michael R. Powers
Purpose – The editorial aims to describe the importance of the Cramér-Rao lower bound (CRLB) in matters of risk, and consider why this inequality generally receives less attention than it deserves. Design/methodology/approach – The CRLB is discussed in the context of other celebrated equations, one of which (Heisenberg's uncertainty principle) is actually implied by the CRLB. A hypothetical world with no randomness on the macroscopic level is then imagined, and the role of the CRLB in that world is considered. Findings – It is found that in a world with no macroscopic uncertainty, the CRLB would play a central role in describing the “counterintuitive” concept of randomness. Originality/value – The editorial identifies and explores an important epistemological result that is under-appreciated.
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