proposed a kind of MCMC algorithm without using prior probabilities
. Duffield  proposed a kind of SCFS algorithm based on consistent prior probabilities
in small value [p.sub.0].
that it should be left to the juror to assess and incorporate his or her own prior probabilities
rather than have these supplied, explicitly or implicitly, by expert witnesses...." (169)
After the data have been collected for the current study, the analysis combines or updates the prior probabilities
with the evidence from the new data to produce the posterior probability.
Suppose that both the prior probabilities
P([[omega].sub.k]) and the conditional densities P(x|[[omega].sub.k]) are known.
Using a more general form of Bayes's Theorem, we then use the surname lists to update the prior probabilities
of membership in each of the four race/ ethnic categories with the surname list results to produce efficient, updated posterior probabilities of membership in the four groups.
The ROC convex hull can be used to determine the combinations of costs and prior probabilities
of intrusion for which one IDS is preferred over another.
However, note that the probability transfer in RbGLI is performed by taking into account the similarity between terms and not the ratio of prior probabilities
as in the case of RbCP.
We had no reason to believe that the prior probabilities
for the low- and high-water use groups are different.
The model to compute P(W) is called the language model; it is a probabilistic grammar expressing the prior probabilities
of all possible word sequences that the recognizer can potentially recognize.
Some of Hume's critics (though not Houston) deny the relevance of prior probabilities
to the evaluation of testimony, thus committing what has come to be known as the base-rate fallacy.
At the heart of Bayesianism is the claim that prior probabilities
are subjectively determined, and the most widely expressed criticism of this approach to scientific reasoning is that it must therefore fail to provide objective standards in terms of which to judge the rationality of that reasoning.
The answer depends in large part on the prior probabilities
of [H.sub.2], [H.sub.3], and [H.sub.4].