Abstract
The basic equation of stellar statistics connects the probability density function of a measurable quantity with the probability density of two variables, which cannot be observed directly, by the Bayes theorem of conditional probabilities. The resulting relation is a Fredholm-type integral equation of the first kind. If the two background variables are statistically independent we recover the convolution equation. The analytical solution based on the Fourier transformation is very sensitive to high-frequency noise. Eddington's solution attempts to find the unknown function in form of a series Sigma gamma jh(i)(z). Malmquist's method computes the conditional probability of the unknown variable assuming that the observed variable is given. The statistical aspect of the problem is expressed if one uses Lucy's algorithm which is a particular form of the more general EM algorithm. Dolan's matrix method solves numerically the matrix equation which approximates the integral equation. Methods are superior which retain the true statistical nature of the problem.
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