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Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAOs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many related fields. Because different ADOs may determine the same Markov equivalence class, it long has been of interest to… (More)

Bayesian networks, equivalently graphical Markov models determined by acyclic digraphs or ADGs (also called directed acyclic graphs or dags), have proved to be both effective and efficient for representing complex multivariate dependence structures in terms of local relations. However, model search and selection is potentially complicated by the many-to-one… (More)

- Steven B Gillispie, Christopher G Green
- 2013

By adding a second parameter, Conway and Maxwell created a new distribution for situations where data deviate from the standard Poisson distribution. This new distribution contains a normalization constant expressed as an infinite sum whose summation has no known closed-form expression. Shmueli et al. produced an approximation for this sum but proved only… (More)

We consider the problem of a consumer wishing to evaluate bundles of options from a list of N independently selectable binary options. The consumer's goal is to find the t best bundles out of the 2 N possible bundle subsets, when ranked according to supplied utility and cost functions. Although 2 N is very large (e.g., for N = 100, 2 N ≈ 10 30), we show how… (More)

Isogonal polyhedra are those polyhedra having the property of being vertex-transitive. By this we mean that every vertex can be mapped to any other vertex via a symmetry of the whole polyhedron; in a sense, every vertex looks exactly like any other. The Platonic solids are examples, but these are bounded polyhedra and our focus here is on infinite… (More)

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