A Note on “Shaved Dice” Inference

ABSTRACT

Two dice are rolled repeatedly, only their sum is registered. Have the two dice been “shaved,” so two of the six sides appear more frequently? Pavlides and Perlman discussed this somewhat complicated type of situation through curved exponential families. Here, we contrast their approach by regarding data as incomplete data from a simple exponential family. The latter, supplementary approach is in some respects simpler, it provides additional insight about the relationships among the likelihood equation, the Fisher information, and the EM algorithm, and it illustrates the information content in ancillary statistics.

KEYWORDS:

• Ancillarity
• Curved exponential families
• EM algorithm
• Incomplete data model
• ML estimation
• Multinomial model