REMARKS ON THE PROBLEM OF 'HOMOGENIZATION OF BERNOULLI TRIALS'.
STANFORD UNIV CALIF DEPT OF STATISTICS
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The report presents some preliminary results and suggestions of possible methods for further analysis of the following problem. We have two coins with different values for the probability of Heads. One of the two coins is chosen at random and tossed an unknown number of times. Then the other coin is tossed an unknown number of times. Then the first coin is tossed again, and so on, the coins being alternated for a very large total number of tosses. The numbers of times that each coin is tossed will in general be different. All tosses are assumed to be statistically independent. We thus have available a very long sequence of observed Heads and Tails. The problem is to divide the complete sequence of very many tosses into subsequences where we are reasonably sure that the same coin has been used for all the tosses in the subsequence. It is not crucial to detect exactly when a change of coin occurs, and an appropriate loss function for the problem might be simply the total number of misclassifications. Author
- Statistics and Probability