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Here we investigated the gender difference in murine cholangitis resembling human primary biliary cholangitis (PBC) caused by synthetic double-stranded RNA, and underlying hepatic innate immune responses. Female C57Bl/6 mice given repeated injections of polyinosinic-polycytidylic acid (poly I:C) for 24 weeks developed overt cholangitis with positive serum anti-mitochondria-M2 antibody, whereas male mice showed minimal pathological changes without induction in autoantibody. Poly I:C induced hepatic inflammatory cytokines and type-I interferons predominantly in females. Hepatic expression levels of toll-like receptor (TLR) 3 and melanoma differentiation-associated protein (MDA) 5 were equivalent in both genders; however, both mRNA and protein levels of retinoic acid-inducible gene (RIG)-I were nearly doubled in female livers. Following 4-week injections of poly I:C, not only hepatic RIG-I, but also TLR3 and MDA5 showed female-predominance. Moreover, hepatic RIG-I levels were 25% lower in ovariectomized mice, whereas supplementation of 17 β-estradiol enhanced hepatic RIG-I expression, as well as cytokine induction. These results clearly indicate that hepatic RIG-I expression is potentiated by estrogen, and triggers gender-dependent hepatic innate immune response against double-stranded RNA, which most likely play a pivotal role in the pathogenesis of autoimmune cholangiopathies including PBC.

In data science, an unknown information source is estimated by a predictive distribution defined from a statistical model and a prior. In an older Bayesian framework, it was explained that the Bayesian predictive distribution should be the best on the assumption that a statistical model is convinced to be correct and a prior is given by a subjective belief in a small world. However, such a restricted treatment of Bayesian inference cannot be applied to highly complicated statistical models and learning machines in a large world. In 1980, a new scientific paradigm of Bayesian inference was proposed by Akaike, in which both a model and a prior are candidate systems and they had better be designed by mathematical procedures so that the predictive distribution is the better approximation of unknown information source. Nowadays, Akaike’s proposal is widely accepted in statistics, data science, and machine learning. In this paper, in order to establish a mathematical foundation for developing a measure of a statistical model and a prior, we show the relation among the generalization loss, the information criteria, and the cross-validation loss, then compare them from three different points of view. First, their performances are compared in singular problems where the posterior distribution is far from any normal distribution. Second, they are studied in the case when a leverage sample point is contained in data. And last, their stochastic properties are clarified when they are used for the prior optimization problem. The mathematical and experimental comparison shows the equivalence and the difference among them, which we expect useful in practical applications.