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Node assignment problem in Bayesian networks

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EN
This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.
EN
The paper deals with construction of exact confidence intervals for the variance component σ₁² and ratio θ of variance components σ₁² and σ² in mixed linear models for the family of normal distributions $𝒩_t(0, σ₁²W + σ²I_t)$. This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two classes of bayesian interval estimators depending on a prior distribution on (σ₁², σ²) for: 1) the variance components ratio θ - built by using test statistics obtained from the decomposition of a quadratic form y'Ay for the Bayes locally best estimator of σ₁², Michalski and Zmyślony (1996), 2) the variance component σ₁² - constructed using Bayes point estimators from BIQUE class (Best Invariant Quadratic Unbiased Estimators, see Gnot and Kleffe, 1983, and Michalski, 2003). In the paper an idea of construction of confidence intervals using generalized p-values is also presented (Tsui and Weerahandi, 1989, Zhou and Mathew, 1994). Theoretical results for Bayes interval estimators and for some generalized confidence intervals by simulations studies for some experimental layouts are illustrated and compared (cf Arendacká, 2005).
EN
In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by Wu (2001) seems to perform most stably.
EN
In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between this test and the classical t-test for independence of normal variables is shown. Moreover, the confidence interval for correlation coefficient is given. The results follow from the unified theory of testing hypotheses both for fixed effects and variance components presented in papers [6] and [7].
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