Whittle's (1957), (1958) smoothed probability-mass-function estimate, determined by a Bayesian criterion, depends on a choice of the mean and covariance structure of a prior distribution on the unknown probabilities. A data-analytic choice is proposed (Equations (7) and (8)), based on natural stationary assumptions (Equations (4)). Adaptations and modifications for multidimensional cells are given (Section 4) and some alternatives are mentioned (Section 5).
James M. Dickey. "Smoothed Estimates for Multinomial Cell Probabilities." Ann. Math. Statist. 39 (2) 561 - 566, April, 1968. https://doi.org/10.1214/aoms/1177698417