Abstract
The Markov-Polya urn scheme is considered, in which the balls are sequentially and equiprobably drawn from an urn initially containing a given numberaj of balls of thejth color,j = 1,…,N, and after each draw the ball is returned into the urn together withs new balls of the same color. It is assumed that at the beginning only the total number of balls in the urn is known and one must estimate its structure ā = (a1, …,aN) by observing the frequencies inn trials of the balls of corresponding colors. Various approaches including the Bayes and minimax ones for estimatingā under a quadratic loss function are discussed. The connection of the obtained results with known ones for multinomial and multivariate hypergeometric distributions is also discussed.
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