Figure: A belief network and its corresponding Q-DAG in which variable
is declared to be both query and evidence.
The construction of a Q-DAG requires the identification of query and evidence variables. This may give an incorrect impression that we must know up front which variables are observed and which are not. This could be problematic in (1) applications where one may lose a sensor reading, thus changing the status of a variable from being observed to being unobserved; and (2) applications where some variable may be expensive to observe, leading to an on-line decision on whether to observe it or not (using some value-of-information computation).
Figure: A belief network and its corresponding Q-DAG in which
variable is declared to be both query and evidence.
Both of these situations can be dealt with in a Q-DAG framework. First, as
we mentioned earlier, Q-DAGs allow us to handle missing evidence
through the use of the 
notation which denotes an unknown value of
a variable. Therefore, Q-DAGs can handle missing sensor readings.
Second, a variable can be declared to be both query and evidence.
This means that we can incorporate evidence about this variable when it is
available, and also compute the probability distribution of the variable
in case evidence is not available. Figure [*] depicts a Q-DAG in
which variable 
is declared to be a query variable, while variable
is declared to be both an evidence and a query variable (both variables
have 
and 
as their values). In this case, we have two ESNs
for variable and also two query nodes
(see Figure [*]).
This Q-DAG can be used in two ways:
and
when no evidence is available about . Under this situation,
the values of 
and 
are set to 1, and we have
when evidence is available
about . For example, suppose that we observe to be .
The value of will then be set to 0 and the value of
will be set to 1, and we have
Utility_Of_Observing
The ability to declare a variable as both an evidence and a query
variable seems to be essential in applications where
(1) a decision may need to be made on whether to collect evidence about
some variable ; and
(2) making the decision requires knowing the probability distribution of
variable .
For example, suppose that we are using the following formula
[PearlPearl1988, Page 313,] to compute the utility of observing variable
:
where 
is the utility for the decision maker of finding that
variable has value 
. Suppose that 
and
. We can use the Q-DAG to compute the probability
distribution of and use it to evaluate 
:
which leads us to observe variable . Observing , we find that
its value is . We can then accommodate this evidence into the Q-DAG
and continue with our analysis.