The QMR-DT network (Shwe et al., 1991) is a two-level or bi-partite
graphical model (see Figure 1). The top level of the graph
contains nodes for the *diseases*, and the bottom level contains
nodes for the *findings*.

There are a number of conditional independence assumptions reflected
in the bi-partite graphical structure. In particular, the diseases
are assumed to be marginally independent. (I.e., they are independent in the
absence of findings. Note that diseases are *not* assumed to
be mutually exclusive; a patient can have multiple diseases).
Also, given the states of the disease nodes, the findings are assumed
to be conditionally independent. (For a discussion regarding the medical
validity and the diagnostic consequences of these and other assumptions
embedded into the QMR-DT belief network, see Shwe et al., 1991).

**Figure 1:** The QMR belief network is a two-level graph where the
dependencies between the diseases and their associated findings have
been modeled via noisy-OR gates.

To state more precisely the probability model implied by the QMR-DT model, we write the joint probability of diseases and findings as:

where *d* and *f* are binary (1/0) vectors referring to presence/absence
states of the diseases and the positive/negative states or outcomes of
the findings, respectively. The conditional probabilities are
represented by the ``noisy-OR model'' (Pearl, 1988):

where is the set of diseases that are parents of the finding
in the QMR graph, is the probability that
the disease *j*, if present, could alone cause the finding to have a
positive outcome, and is the ``leak''
probability, i.e., the probability that the finding is caused by means
other than the diseases included in the QMR model. In the final
line, we reparameterize the noisy-OR probability model using an
exponentiated notation. In this notation, the model parameters are
given by .

Sun May 9 16:22:01 PDT 1999