Laws of the Statistical Universe: Gravitational Forces of the Data World

Abstract

AbstractThe physical universe has had its laws since Newton (1687). The statisticaluniverse — the universe of data, observations, and inference in which every scientificmeasurement operates — has had none. Every statistical method has been a tool. Noone has established the foundational laws that govern the data world as a scientificuniverse.This paper establishes four such laws, all derived from one structural primitive —the Zulfia Deviation:∆(θ, x) = x − MZ [θ]This is not an error. It is not a residual. It is the gravitational field of the statisticaluniverse — the telescope through which the structure of the data world becomesvisible for the first time.From this one field we derive: Law I (Statistical Existence): a parameterexists in the statistical universe if and only if its deviation from data is defined; LawII (Statistical Gravitation): data exerts a measurable gravitational force on everyestimate, proportional to evidence and deviation; Law III (Statistical Curvature):the deviation field curves the inference space and determines the precision of allmeasurement; Law IV (Statistical Reaction): every statistical force generates anequal and opposite reaction, visible as systematic error when models are wrong.Zulfiqar Ali Khan Laws of the Statistical Universe (ZSU)These four laws are to statistical inference what Newton’s laws are to mechanics.Science cannot be wrong when its laws are correct. These are the correct laws of thestatistical universe.