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Abstract. We consider normal ≡ Gaussian seemingly unrelated regressions (SUR) models with incomplete data (ID). Imposing a natural minimal set of conditional independence con-straints, we find restricted SUR/ID models for which the likelihood function and the parameter space factors into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a uni-modal likelihood and permits explicit likelihood inference. The restricted model may be used to directly model the data actually observed. Alternatively, the maximum likelihood estimates in the restricted model can yield improved starting values for iterative methods to maximize the likelihood of the unrestricted SUR/ID model. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem. The results are presented in the framework of both lattice conditional independence models and graphical Markov models based on acyclic directed graphs. Date: October 1, 2003. Key words and phrases. Acyclic directed graph, graphical model, incomplete data, lattice conditional indepen-dence model, MANOVA, maximum likelihood estimator, multivariate analysis, multivariate linear model, missing data, seemingly unrelated regressions.

Abstract: Ideally, learning resources should be built over a shared pool of fine reusable granular learning objects. However, in order to avoid contextual lacks, dynamic creation of such resources would mostly rely on the conceptual relationships among learning objects inside a repository. These conceptual relationships, as well as the learning objects creation, are best established if students ’ learning styles are considered. Common standards like Sharable Content Object Reference Model (SCORM) do not have tools to provide conceptual relationships among fine granular learning objects. This paper presents a conceptual lattice-based architecture for using SCORM to provide an effective mapping of conceptual relationships among learning objects.

Abstract. We show that every abstract interpretation possesses an internal logic, whose proof theory is defined by the partial ordering on the abstract domain’s elements and whose model theory is defined by the domain’s concretization function. We explain how program validation and transformation depend on this logic. Next, when a logic external to the abstract interpretation is imposed, we show how to synthesize a sound, underapproximating, set-based variant of the external logic and give conditions when the underapproximating logic can be embedded within the original abstract domain, inverted. We show how model-checking logics depend on this construction. The intent of this paper is tutorial, to integrate little-publicized results into a standard framework that can be used by practitioners of static analysis. Perhaps the central issue in program validation and transformation is how to apply the results of a static program analysis to prove that a desired validation/transformation property holds true: How does the domain of logical properties “connect ” to the domain of values used in the static analysis? Here are three examples: (i) we use data-flow analysis to compute sets of available expressions and use the sets to decide properties of register allocation [20]; (ii) we complete a state-space exploration and use it to model check a temporal-logic formula that defines a safety property [4] or program-transformation criterion [15]; (iii) we apply predicate abstraction with counter-example-guided refinement (CEGAR) to generate an assertion set that proves a safety property [1, 2,19,28]. This paper asserts that the value domain used by a static analysis and the logic used for validation and transformation should be one and the same — the logic should be internal to the value domain. If the values and logical properties differ, then the logic must be defined externally, and this paper shows how. domain for static analysis (e.g., sign values or sets of available expressions or names of state partitions); and let γ: A → P(Σ) be the concretization function that maps each a ∈ A to the values it models in Σ. In this paper, we demonstate that

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.

The relations among the classes of multivariate conditional independence models determined by directed acyclic graphs (DAG). undirected graphs (UDG). decomposable graphs (DEC). and finite distributive lattices (LCI) are investigated. First. LCI models that admit positive joint densities are characterized in terms of an appropriate factorization of the density. This factorization is then recognized as a particular form of the recursi ve factorization that characterizes DAG models. thereby establ ishing that the LCI models comprise a subclass of the class of DAG models. precisely. the class of LCI models coincides with the subclass of transitive DAG models. Furthermore. the class of LCI models has nontrivial intersection with the class of DEC models. A series of examples illustrating these relations are presented. Key words and phrases: conditional independence model. rnuttivartate distribution.

Boundary algebra is a new and simple notation for the Boolean algebra 2 and the truth functors. The primary arithmetic [PA] is built up from the atoms, ‘() ’ and the blank page, by enclosure between ‘( ‘ and ‘)’, denoting the primitive notion of distinction, and concatenation. Inserting letters denoting the presence or absence of () into a PA formula yields boundary algebra [BA], a simpler notation for Spencer-Brown’s (1969) primary algebra [pa]. The BA axioms are “()()=()”, and “(()) [=⊥] may be written or erased at will.” Repeated application of these axioms to a PA formula yields a member of B={(),⊥}, its simplification. If (a)b [dually (a(b))] ⇔ a≤b, then ⊥≤() [()≤⊥] follows trivially, so that B is a poset. BA is a self-dual notation for the Boolean algebra 2: (a) ⇔ a′, () ⇔ 1 [0] so that B is the carrier for 2, and ab ⇔ a∪b [a∩b]. The basis abc=bca (Dilworth 1938), a(ab) = a(b) (Bricken 2002), and a(a)=() facilitates clausal reasoning and proof by calculation. BA also simplifies the usual normal forms and Quine’s (1982) truth value analysis. () ⇔ true [false] yields boundary logic.

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Information and Computation journal homepage: www.elsevier.com/locate/ic

Abstract not found