Typical analyses including exchangeable quantities involve
representations where we can resolve the information over the
exchangeable quantities into mean and residual components. In
particular, an exchangeable sequence can be treated as a special kind of
element, where the sequence is summarised by its name, expectation,
mean-component variance, and mean-plus-residual variance, together
with the notion of repetition. Such elements are distinguished from
ordinary elements by being associated with a pair of
variance-covariance specifications over itself and with other
quantities.
To this purpose, [B/D] allows the creation of several alternative
variance-covariance specifications over the same named quantity.
Different belief storage areas, named belief store 1, belief store
2, 
, are set aside for this purpose. In this example, for all
the quantities involved in the model we intend storing overall variances
(for the mean plus residual components) in belief store 1, and any
underlying mean component variances in belief store 2.
Thus, the model definition part of the [B/D] program for this example,
shown in Figure 7, begins with the creation of one element
named A to represent all three intercepts 
. A has overall
variance 0.058 (comprising 0.020 as the residual variance, and 0.038
as the underlying mean component variance) which we enter into
variance-covariance store 1. Its mean-component variance is entered
into store 2, and its prior expectation is set at 1.4.
The remainder of the code shown in Figure 7 deals with the
specification and creation of the error structure as follows. The
non-zero beliefs are introduced as constants, and the elements 
and 
are defined to terminate the random walk and
autoregressive components (5), (6). Otherwise,
beliefs over the error quantities are defined functionally, using the
FVAR: command. These error
quantities are essentially residual only and will relate to belief store
1: there is no need to enter zero variances into belief store 2 for
their notional mean components because unspecified variances and covariances
are taken to be zero by default.
We specify the expectation and variances and covariances over the slopes
functionally, using the FVAR: and FE: commands. The
overall (i.e. mean plus residual) variance structure is stored in belief
store 1, and the variance structure for the underlying mean components
is stored in belief store 2. The term named ``#rho'', intended to be
the correlation 
between neighbouring slopes, is a function
which will be defined as appropriate before entry to the main creation
and analysis subroutine.
Linear and linear recursive relationships may be established by [B/D]
assignments by using the ASSIGN: command. When particular
recursive relationships are encountered, the program tries, by tracking
back through the recursion, to construct from it a definition which is
finally non-recursive because of termination criteria already set. From
the three assignments shown in Figure 7, and the earlier
explicit and functional belief specifications, [B/D] is now able to
deduce expectations, variances, and covariances for the 
.
Recall that the element whose name is ``H.1'' was explicitly introduced
earlier to act as a termination criterion for the recursive component.
For example, when the program later calls for 
it deduces that
by using the recursive assignment and
this termination criterion.
