  The cluster expansion formalism used in materials science is reconstructed on
an axiomatic basis with the aims of clarifying underlying concepts and
improving computational procedures, and without using conventional cluster
functions. Instead, cluster components of configuration functions are defined
in an intrinsic manner, which can be viewed as Moebius inversion of conditional
expectation. The associated method for fitting a model to a configurational
sample is grounded entirely in Hilbert space geometry. By constructing models
directly from the given data, we avoid an underdetermination problem to which
the conventional approach is subject. Tensor observables are treated on an
equal footing with scalar observables.
