The fundamental belief-carrying unit is the element, which corresponds to random variable in traditional statistical packages. These elements may be organised into collections which we term bases, and we usually think of elements as bases in their own right. Elements are the only kind of quantity for which we specify variances, covariances and expectations explicitly, and consequently our principal interest lies in the relationships specified over and between collections of elements, and any observations pertaining. Much of the computation in [B/D], and in particular the concept of adjustment, is aimed at elements, Thus, for example, only elements and collections of them can be adjusted.
Elements are introduced into [B/D] by the ELEMENT: command directly, or are constructed from linear combinations of other quantities via the BUILD: and COBUILD: commands. Expectations for elements can be introduced explicitly at the time of the definition within the ELEMENT: command, or may be altered at any stage via the E: command. Beliefs are typically specified over elements via the VAR: command directly, or are calculated automatically from their defining linear combination if they are constructed from other quantities. Data can be attached directly to elements using the DATA: command, or is automatically calculated if the element is constructed from other elements. Elements can be removed from [B/D] by using the XELEMENT: command.
Finally, elements are always associated with expectations, variances, and covariances with other elements, even if these values have not been specified - they are taken to be zero by default. Consequently, elements take up quite a bit of machine memory, although they are usually handled very quickly.
As an example, typical elements might be the temperature, T, and blood pressure, P, of some patient, organised into some base X. Associated with these quantities are expectations and covariances as follows:
We show the subscript (1) to indicate that we might like to associate with a collection of elements more than one variance-covariance specification. We frequently make use of this facility when we deal with exchangeable sequences. We might also have actual observations, perhaps repeated, of T and P.