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Vadim Kosoy added Note_that_the_characterization_of__.tex
about 8 years ago
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Note that the characterization of $P$ depends not only on $f$ but also on $\mu$. That is, the accuracy of an estimator depends on the prior probabilities to encounter different questions. In general, we assume that the possible questions are indexed by elements of $\Words$. Thus we need to consider a probability distribution on $\Words$. However, in the spirit of average-complexity theory we will only require our estimators to be \emph{asymptotically} optimal. Therefore instead of considering a single probability distribution we consider a family of probability distribution indexed by an integer parameter, where the role of the parameter is defining the relevant limit. We thereby arrive at the following:
\begin{definition}
A \emph{word ensemble} $\mu$ is a family of probability distributions $\{\mu^k: \Words \rightarrow [0,1]\}_{k \in \Nats}$.
\end{definition}
