Description

Kjøbenhavn: B. Lunos Kgl. Hof.-Bogtrykkeri, 1880. 265 by 210mm (10½ by 8¼ inches). Blue-green boards; 382-408. Offprint from Det Kongelige Danske videnskabernes Selskabs Skrifter vol. 12, no. 5. In Danish. Very good with pages browned and unopened at top.

Thorvald Thiele (1838–1910) was a Danish astronomer and mathematician. Thiele made notable contributions to the study of statistics and randomness.

Thiele describes the problem of determining the distance from Copenhagen to Lund (Sweden) and in the process solves the problem of estimating the regression coefficients and predicting the values of Brownian motion by the method of least squares (i.e. Kalman filtering). Thiele presents an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement.

Oxford Professor Steffen Lauritzen wrote the following about Thiele:

His first paper on the method of least squares [the one on offer here] is a brilliant tour de force. There he derives both Brownian motion with independent and normally distributed increments and variances proportional to time as well as recursive computational procedures for filtering and prediction now known as the Kalman filter and smoother. He also derives iterative methods for estimating the ratio between system and measurement noise.

See also, Lauritzen “Time Series Analysis in 1880: A Discussion of Contributions Made by T.N. Thiele” International Statistical Review 49 (1981), pp. 319–331.

Scarce with no other copies for sale at the time of cataloguing and no auction records in Rare Book Hub. OCLC locates merely two copies of this offprint in American institutions: UC Berkeley and the American Institute of Physics.

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