Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation

Abstract

Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I - J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min. of “extreme physical information” (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described.