- ...model.
^{1} - The acronym ``QMR-DT'' that
we use in this paper refers to the ``decision-theoretic'' reformulation
of the QMR by Shwe, et al. (1991). Shwe, et al. replaced
the heuristic representation employed in the original QMR model
(Miller, Fasarie, & Myers, 1986) by a probabilistic representation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...QMR-DT.
^{2} - D'Ambrosio (1994) reports
``mixed'' results using incremental SPI on the QMR-DT, for a somewhat
more difficult set of cases than Heckerman (1989) and Henrion (1991),
but still with a restricted number of positive findings.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...decoupled.
^{3} - Jensen's
inequality, which states that
$f(a + \sum_j q_j x_j) \geq \sum_j q_j f(a + x_j)$,
for concave $f$, where $\sum q_j = 1$, and $0 \leq q_j \leq 1$,
is a simple consequence of Eq. (8), where $x$ is taken to be $a + \sum_j q_j x_j$.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...exactly.
^{4} - Given that a significant fraction of the positive
findings are being treated exactly in these simulations, one may wonder
what if any additional accuracy is due to the variational
transformations. We address this concern later in this section and
demonstrate that the variational transformations are in fact responsible
for a significant portion of the accuracy in these cases.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...algorithm.
^{5} - The initialization method proved to have
little effect on the inference results.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...inference.
^{6} - We also investigated Gibbs
sampling (Pearl, 1988). The results from Gibbs sampling were
not as good as the results from likelihood-weighted sampling,
and we report only the latter results in the remainder of
the paper.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...method.
^{7} - It should be noted that this is a conservative
comparison, because the partially-exact method in fact benefits from
the variational transformation-the set of exactly treated positive
findings is selected on the basis of the accuracy of the variational
transformations, and these accuracies correlate with the diagnostic
relevance of the findings.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Sun May 9 16:22:01 PDT 1999