The sequential design procedure which selects one of two experiments
e0 and
e1 at each stage in order to maximize the sum of
n observations is considered, where the distributions of
e0 and
e1 are uniform distributions on the intervals (0,
u) and (0, 1) respectively. The value of
u is unknown and is assumed to have a Pareto distribution with parameters
w and α as a prior distribution. This problem is formulated by the dynamic programming and is solved recursively. The expected sum of
n observations is given as function of
w, α and
n, and the optimal strategy is to perform
e0 if and only if
w_??_
wn (α).
wn (α) is strictly increasing in α and non-decreasing in
n, and the value of
wn (α) is calculated for several values of
w and α and tabulated.
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