J. Krob and H.v. Weizsacker. The rate of information gain in experiments with a finite parameter set. submitted, 1993. Home/Search Document Details and Download
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On risk rates and large deviations in finite Markov chain.. - Scheffel, Weizsäcker (1997) (Correct)
....transition matrix belongs to a known finite set. In the case of iid. sequences and two parameters this question was in a certain sense answered by Chernoff [Che52] Later Torgersen (e.g. Tor81] extended Chernoff s Theorem to a finite parameter set using the frame of abstract decision theory. In [KW93] it was shown that in finite parameter problems generally the decision theoretic rate and the Shannon theoretic rate coincide, where the former is measured by the minimal Bayes risk or equivalently by the deficiency distance to the most informative experiment and the latter is the rate of the ....
....be denoted by the letter V; i.e. V ffi (Q) fP 2 M : jP i;j Gamma Q i;j j ffi for all i; jg. Further we set V ffi (Q) V ffi (Q) M : So U ffi (Q) V Q ffi (Q) 3 The risk rates The following result is the starting point of this paper. It is a special case of the main result of [KW93]. Proposition 1: Let ff = ff 1 ; ff l ) be any strictly positive prior. Suppose that for every 2 Theta = f1; lg the process (X i ) i2IN 0 forms under P a Markov chain with the irreducible transition matrix where 7 is injective. Then a) lim n 1 B n (ffjX) lim ....
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J. Krob and H.v. Weizsacker. The rate of information gain in experiments with a finite parameter set. submitted, 1993.
On risk rates and large deviations in finite Markov chain - Experiments Peter Scheffel Self-citation (Weizsacker) (Correct)
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J. Krob and H.v. Weizsacker. The rate of information gain in experiments with a finite parameter set. submitted, 1993.
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