Components are notional elements. They differ from true elements in that they have no formal existence except for functional relationships specified over themselves and between themselves and true elements. Provided that the number of such functional relationships is quite limited, this is a memory-efficient way of handling belief carriers, particularly as large numbers of quantities differing only in index, say, can be represented as only one component. However, they are often handled quite slowly, and they cannot be adjusted. Their principal role is as intermediaries from which we construct elements which can be adjusted.
Components only exist via functional relationships expressed. Functional belief specifications are attached to components as follows. The FE: command is used to define their expectations, and may involve a function of some index. Beliefs are expressed over components as functions, using the FVAR: command. This command is also use for the specification of beliefs between different components and between components and elements. Again, these might involve functions of indices. A components might be associated with data in that there may be a data carrier of the same name.
Functional belief specifications can be removed using the XFVAR: command; and functional expectations can be removed by using the XFE: command.
As as a simple example, consider a sequence of quantities 
,
which we intend
to represent some error quantities. Suppose that these quantities have
expectation zero, are uncorrelated with all other quantities, and have
the following covariance structure:
Then all these quantities can be represented succinctly in [B/D] by one component, E say, with an index, for which the covariance structure can be expressed as a simple function.
Individual functionally specified beliefs can be accessed in the same way as directly specified beliefs, that is via the ex , var , and corr operators.
