  This paper lays the foundations for a unified framework for numerically and
computationally applying methods drawn from a range of currently distinct
geometrical approaches to statistical modelling. In so doing, it extends
information geometry from a manifold based approach to one where the simplex is
the fundamental geometrical object, thereby allowing applications to models
which do not have a fixed dimension or support. Finally, it starts to build a
computational framework which will act as a proxy for the 'space of all
distributions' that can be used, in particular, to investigate model selection
and model uncertainty. A varied set of substantive running examples is used to
illustrate theoretical and practical aspects of the discussion. Further
developments are briefly indicated.
