Title: Declarative Statistics,
Abstract: In this work we introduce declarative statistics, a suite of declarative
modelling tools for statistical analysis. Statistical constraints represent the
key building block of declarative statistics. First, we introduce a range of
relevant counting and matrix constraints and associated decompositions, some of
which novel, that are instrumental in the design of statistical constraints.
Second, we introduce a selection of novel statistical constraints and
associated decompositions, which constitute a self-contained toolbox that can
be used to tackle a wide range of problems typically encountered by
statisticians. Finally, we deploy these statistical constraints to a wide range
of application areas drawn from classical statistics and we contrast our
framework against established practices.