
Composition of Probability Measures on Finite Spaces
Decomposable models and Bayesian networks can be defined as sequences of...
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Regular sequences and synchronized sequences in abstract numeration systems
The notion of bregular sequences was generalized to abstract numeration...
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A dependent Lindeberg central limit theorem for cluster functionals on stationary random fields
In this paper, we provide a central limit theorem for the finitedimensi...
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Improper vs finitely additive distributions as limits of countably additive probabilities
In Bayesian statistics, improper distributions and finitely additive pro...
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Predictive distributions that mimic frequencies over a restricted subdomain (expanded preprint version)
A predictive distribution over a sequence of N+1 events is said to be "f...
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Gaussian Conditionally Markov Sequences: Dynamic Models and Representations of Reciprocal and Other Classes
Conditionally Markov (CM) sequences are powerful mathematical tools for ...
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A Topological Application of Labelled Natural Deduction
We use a labelled deduction system based on the concept of computational...
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Marginalization in Composed Probabilistic Models
Composition of lowdimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In contrast to Graphical Markov Models, which define multidomensinoal distributions in a declarative way, this approach is rather procedural. Ordering of lowdimensional distributions into a proper sequence fully defines the resepctive computational procedure; therefore, a stury of different type of generating sequences is one fo the central problems in this field. Thus, it appears that an important role is played by special sequences that are called perfect. Their main characterization theorems are presetned in this paper. However, the main result of this paper is a solution to the problem of margnialization for general sequences. The main theorem describes a way to obtain a generating sequence that defines the model corresponding to the marginal of the distribution defined by an arbitrary genearting sequence. From this theorem the reader can see to what extent these comutations are local; i.e., the sequence consists of marginal distributions whose computation must be made by summing up over the values of the variable eliminated (the paper deals with finite model).
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