Geodesic
Sequential discrimination of hypotheses with control of observations
Izvestiya. Mathematics , Tome 15 (1980) no. 3, pp. 419-440.

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The problem of sequential discrimination of $N$ hypotheses $\{\theta_i\}$ is considered, using a family of measures $\mathscr F=\{F_\alpha\}$, $\alpha\in\mathfrak A$, defined on a measurable space $(X,\mathscr B)$. For observation at a particular instant of the time sequence one of the measures in $\mathscr F$ is assigned to each hypothesis $\theta_i$, and it is decided to use the results of the preceding observations. For given error probability $\mathbf P_e=\mathbf P(\hat\theta\ne\theta_\text{true})$ in making a decision the author studies the smallest possible average number $\mathbf E\tau$ of observations (in the Bayesian or minimax formulation). Asymptotically optimal results (as $\mathbf P_e\to0$, $N\to\infty$) are obtained for a rather large class of cases. Bibliography: 12 titles. 
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M. V. Burnashev. Sequential discrimination of hypotheses with control of observations. Izvestiya. Mathematics , Tome 15 (1980) no. 3, pp. 419-440. http://geodesic.mathdoc.fr/item/IM2_1980_15_3_a0/

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