The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a so-called knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, sP — it is the well-founded model. There is also a dual largest stable model, S P , which has not been considered before. The...

The seminal papers by Nelder and Wedderburn (Generalized Linear Models, JRSS A 1972) and Cox (Regression models and life tables, JRSS B 1972) both rely on the assumption that conditionally on covariate information (including time) the observations are independent. The difficulty in identifying and measuring all relevant covariates has pushed for methods that can handle both mean and covariance ...

Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for representing complex social phenomena. We generalize ERGM by also modeling nodal attributes as random variates, thus creating a random model of the full network, ...

We present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated with graphs. Our discussion of the statistical issues centers around maximum likelihood estimation.