Göteborgs universitet, Naturvetenskapliga fakulteten, Institutionen för matematiska vetenskaper, Gothenburg University, Faculty of Sciences, Department of Mathematical Sciences, Fallat, Shaun, Lauritzen, Steffen, Sadeghi, Kayvan, Uhler, Caroline, Wermuth, Nanny, and Zwiernik, Piotr
We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional semi-graphoid which is upward-stable and singletontransitive. In addition, we prove that any MTP2 distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP2 distributions and discuss ways of constructing MTP2 distributions; in particular, we give conditions on the log-linear parameters of a discrete distribution which ensure MTP2 and characterize conditional Gaussian distributions which satisfy MTP2.
Peña, Jose M., Linköpings universitet, Institutionen för datavetenskap, Databas och informationsteknik, and Linköpings universitet, Tekniska högskolan
International Journal of Approximate Reasoning. 50(8):1306-1313
Engineering and Technology, Teknik och teknologier, Chain graphs, Faithfulness, Markov equivalence, Factorization equivalence, Largest chain graphs, TECHNOLOGY, and TEKNIKVETENSKAP
This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the strictly positive discrete probability distributions with the prescribed sample space that factorize according to a chain graph G with dimension d have positive Lebesgue measure wrt R-d. whereas those that factorize according to G but are not faithful to it have zero Lebesgue measure wrt R-d. This means that, in the measure-theoretic sense described, almost all the strictly positive discrete probability distributions with the prescribed sample space that factorize according to G are faithful to it.
Kärfve, Eva, Lunds universitet, Sociologi, and Lund University, Sociology
self-consecration, group, ritual interaction, faithfulness, moral system, sociology, sociologi, Samhällsvetenskap, Sociologi, Sociologi (exklusive socialt arbete, socialpsykologi och socialantropologi), Social Sciences, Sociology, and Sociology (excluding Social Work, Social Psychology and Social Anthropology)
In this paper two hypotheses concerning the structure of moral systems are suggested, First, that morality should be regarded as a normative standard, originating and moulded in ritual interaction, with the supreme function of maintaining self-consecration of the group. Consequently, the most prominent class of moral norms concerns faithfulness, basically in terms of loyalty to the group, symbolically in upholding certain beliefs and following moral commands and prohibition rules prescribved by the moral system of the particular group. These suggestions are then briefly examined when describing the moral systems of two different groups–early Christians of the first century AD, and a Rom tribal unit in contemporary Sweden. Finally, an attempt is made to find out whether an analysis in accordance with these proposals can shed light on a specific moral event, concerning the problematic issue of euthanasia.