Johann Heinrich Lambert: An Admirable Applied Statistician

Johann Heinrich Lambert is best known for his work in physics. The law of Bouguer-Lambert-Beer on the absorbtion of light may be his most famous achievement. He is also well known in mathematics, for example for his proof of π and e being irrational numbers, for his work on non-additive probabilities and for his contribution to non-Euclidean geometry. He worked on numerous problems of natural science, for example in astronomy and in cartography (Lambertprojection). Last but not least, Lambert was a philosopher with a keen interest in epistemology. However, his work in statistics has long gone unattended. But Lambert was an eminent applied statistician and this in a very modern sense of statistical data analysis. His studies of measurement and how to gain insight into the laws of nature in spite of measurement error lead him to formulate the principle of maximum likelihood and to devise a rule for treating outliers. In addition, he wrote about fitting a line to bivariate measurements and developed a theory of errors. Several aspects may have hindered the recognition of Lambert as a statistician. First, the discipline of statistics did not exist at that time. Probability theory was established by Jacob Bernoulli in 1713. But when Lambert published his masterpiece, the Photometria, in 1760 statistics did not exist. Second, Carl Friedrich Gauss developed the normal distribution, showing that the arithmetic mean is the optimal estimator under the normal distribution and established the least squares principle in 1795. Thus the work of Lambert was overshadowed by the work of