The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.

Two types of representations can be used to specify spatial relations: Coordinate spatial relations representations specify the precise distance between two objects, whereas categorical spatial relations representations assign a category (such as above or below) to specify a spatial relation between two objects. Computer simulation models suggest that coordinate spatial relations representation...

The grade of membership (GoM) model uses fuzzy sets as memberships of each individual to extreme profiles (or classes) on the likelihood function of multivariate multinomial distributions. The GoM clustering algorithm derived from the GoM model is used in cluster analysis for categorical data, but it is iterated with complicated calculations. In this paper we create another approach, termed a f...

A Bayesian methodology is used to assess the information content of categorical, probabilistic forecasts of specific variables derived from a general circulation model (GCM) forecast ensemble, and to combine a ‘‘prior’’ forecast (climatological probabilities of each category) with a categorical probabilistic forecast derived from a GCM ensemble to develop posterior, or ‘‘regularized’’ categoric...

Complex categorical variables are usually classified into many classes with interclass dependencies, which conventional geostatistical methods have difficulties to incorporate. A two-dimensional Markov chain approach has emerged recently for conditional simulation of categorical variables on line data, with the advantage of incorporating interclass dependencies. This paper extends the approach ...

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