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In this paper, in the Formula at the beginning of 2.2, we have



$i=0,1$ - the number of probability formula

$O_t$ - the state at moment $t$

$b_i(O_t)$ - two probabilities or estimations for the state $O_t$

The result ($B$) is named "likelihood". How can likelihood be obtained from 2 numbers? Is this a weighted average like

$b_i(O_t)= 0*b_0(O_t) + 1*b_1(O_t)$


$b_i(O_t)= -1*b_0(O_t) + 1*b_1(O_t)$

or something?

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It looks like some sort of indexing similar to the idea of vectors. – azetina Jul 5 '12 at 14:41

This is a good example of why it makes sense to quote texts with more context, since it's often the context that supplies the clues for interpretation.

$B$ is referred to not just as a likelihood, but as "the likelihood [...] of [...] the frame [...] being a speech or a noise frame". This is rather badly phrased (like some other things in that paper), but it's clear that a single number cannot be simultaneously the likelihood of being a speech or a noise frame, so $B$ is the pair of likelihoods for these two cases. The curly brace notation for this pair is somewhat unfortunate in my view.

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My guess is that he meant it as $B_i:=b_i(O_t)$

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