A curated set of astronomical tools and a historical timeline tracing the co-development of statistics and astronomy, drawn from The History of Statistics: The Measurement of Uncertainty before 1900 by Stephen M. Stigler.
The following chronology, sourced from The History of Statistics: The Measurement of Uncertainty before 1900 by Stephen M. Stigler, traces how astronomical problems — from calendar reform to planetary orbit-fitting — drove the development of least squares, error theory, and probability.
Antiquity were lunisolar, based on moon phase and position of the sun
Julius Caesar made reforms (Julian calendar) based on an algorithm of introducing a leap day every four years but added an extra day every 128 years causing seasonal equinoxes to fall at wrong time of year
Errors decrease with aggregation rather than increase
Tobias Mayer and Euler
Method of averages - combination of different observations under same equations
The inequalities of the motions of Jupiter and Saturn
The librations (the moon’s face varies, wobbles) of the Moon
Latitude measures angular elevation above horizon
Longitude based on Moon features and position with stars
Created a table of equations of condition
Uses the symbol plus/minus x (margin of error?)
Let error be the limit of accuracy for the mean
Post 1750 mathematical astronomers averaged simple measurements, combining several days of observations into a single number, as well as doing the same with equations
Laplace
The Mechanics of the Planets
Analytical Theory of Probability
Mayer’s 27 equations of conditions of moon crater observations
Least Absolute Deviation - the combination of different observations under different conditions
Legendre (Least Squares Method)
The first clear and concise exposition of the method of least squares was published by Legendre in 1805. The technique is described as an algebraic procedure for fitting linear equations to data and Legendre demonstrates the new method by analyzing the same data as Laplace for the shape of the Earth.
Jacob Bernoulli
Ars Conjectandi - the formalization of the mathematical theory of probability
Law of large numbers - the greater the number of observations the less the uncertainty in the result
De Moivre - stated and proved the normal approximation to the Binomial distribution
Simpson
Development of quantified uncertainty and mathematical theory of inference
A new problem was to combine discordant observations, if five observers record five different times for the passage of a star past a crosshair in a telescope, how are these numbers reconciled?
Introduces annuity tables (insurance)
Wrote a letter on the advantage of taking the mean of a number of observation (astronomical)
Distribution of errors accounts for small and large errors
Simpson’s Paradox - a trend that appears in multiple groups may disappear when the groups are combined
Inverse Probability (Bayesian Inference, inferential statistics), probability distribution of an unobserved variable
Fisher - fundamental paradox of inverse probability is the source of confusion between statistical terms that refer to the true value to be estimated with the actual value arrived at by the estimation method, which is subject to error
The Gaussian distribution came about from Laplace’s distribution of errors when sampling the mean, Gauss’ observation of measurement error and de Moivre’s attempt to approximate the binomial distribution with largeaN