Group invariant inferred distributions via noncommutative probability

One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance method for constructing inferred distributions on parameter spaces given observed results. These inferred distributions are obtained without using Bayes' method and in particular without using a joint distribution of random variable and parameter. In the Poisson and binomial cases, the final formulas for inferred distributions coincide with the formulas for Bayes posteriors with uniform priors.Comment: Published at http://dx.doi.org/10.1214/074921706000000563 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Confucian Virtue Jurisprudence

Virtue jurisprudence is an approach to legal theory that develops the implications of virtue ethics and virtue politics for the law. Recent work on virtue jurisprudence has emphasized a NeoAristotelian approach. This essay develops a virtue jurisprudence in the Confucian tradition. The title of this essay, “Confucian Virtue Jurisprudence,” reflects the central aim of our work, to build a contemporary theory of law that is both virtue-centered and that provides a contemporary reconstruction of the central ideas of the early Confucian intellectual tradition. This essay provides a sketch of our contemporary version of Confucian virtue jurisprudence, including a view of (1) the ends of law, (2) legislation and the judiciary, (3) the nature of law. We shall argue that the highest value of Confucian ethical, political theory is the virtue of citizens and the harmony of society and individuals. From the perspective of the use of evaluative language, the Confucian doctrine of Correcting Names gives us an explanation of the mechanism of internalization of legal rules in terms of the relationship among social norms, law and thick evaluative concepts. This might throw light on our normative understanding of legislation and the judiciary,and it also provides a functional account of the nature of law