Statistical Spectral Analysis
William A. Gardner
Prentice Hall
A good deal of our statistical theory, although it is mathematical in nature, originated not in mathematics but in problems of astronomy, geomagnetism and meteorology: examples of fruitful problems in these subjects have included the clustering of stars, also galaxies, on the celestial sphere, tidal analysis, the correlation of fluctuations of the Earth's magnetic field with other solar-terrestrial effects, and the determination of seasonal variations and climatic trends from weather data. All three of these fields are observational. Great figures of the past, such as С F. Gauss A777-1855) (who worked with both astronomical and geomagnetic data, and discovered the method of least square fitting of data, the normal error distribution, and the Fast Fourier Transform algorithm), have worked on observational data analysis and have contributed much to our body of knowledge on time series and randomness. Much other theory has come from gambling, gunnery, and agricultural research, fields that are experimental. Measurements of the fall of shot on a firing range will reveal a pattern that can be regarded as a sample from a normal distribution in two dimensions, together with whatever bias is imposed by pointing and aiming, the wind, air temperature, atmospheric pressure and Earth rotation. The deterministic part of any one of these influences may be characterized with further precision by further firing tests. In the experimental sciences, as well as in the observational, great names associated with the foundations of statistics and probability also come to mind. Experimental subjects are traditionally distinguished from observational ones by the property that conditions are under the control of the experimenter.