...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.

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...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.

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...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 $a + \sum_j q_j x_j$.

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...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.

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...algorithm.⁵

The initialization method proved to have little effect on the inference results.

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...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.

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...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.

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