For finite sets of probability measures, sufficiency is characterized by means of certain positively homogeneous convex functions. The essential tool is a discussion of equality in Jensen's inequality for conditional expectations. In particular, it is shown that characterizations of sufficiency by Csiszhr's f-divergence (1963, Publ. Math. Inst. Hung. Acad. Sci. Ser. A, 8, 85-107) and by optimal...

In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.

The safety assurance of software is ultimately demonstrated by the evidence that is put forward. There is a range of existing guidance on the types of evidence that may be used to demonstrate the safety of software, however questions remain as to the sufficiency of the evidence suggested by such guidance. We propose that the only way to determine the sufficiency of the evidence is to consider i...

Ð An explanatory mechanism is discussed that leads to a so-called sufficiency theory of certain psychological phenomena, such as standard recognition as opposed to deÂjaÁ vu, imagined novel experience, jamais vu, disturbed recognition, incorrect recognition, and hallucinationÐexperiences that have not been explained before in a satisfactory scientific manner. Sufficiency theory, in general, mea...

In [4], we have proved the necessary condition for sigraphs on union of k copies cycles of length three with one vertex in common denoted by C 3 to be graceful and sufficiency part of the theorem was discussed in certain special cases when all rim edges are negative and form a maximum matching. In this paper, we discuss the sufficiency part of the theorem on gracefulness of sigraphs on C 3 part...

In the paper a set of necessary and sufficient conditions for vsufficiency (equiv. sv-sufficiency) of jets of map-germs f : (Rn, 0) → (Rm, 0) is proved which generalize both the Kuiper-Kuo and the Thom conditions in the function case (m = 1) so as the Kuo conditions in the general map case (m > 1). Contrary to the Kuo conditions the conditions proved in the paper do not require to verify any in...

I discuss how the Multiple Pathway Anchoring and Adjustment model is similar to and different from the Feldman and Lynch accessibility-diagnosticity model, elaborated as an anchoring and adjustment model by Lynch, Marmorstein, andWeigold. Cohen and Reed’s concept of representational sufficiency embraces both attitude coherence and retrieval fluency; these map to prior operationalizations of dia...

Vitamin D is vital for human health, and its deficiency may result in hypocalcemic seizures and rickets in infants and children. The optimal cut-off of serum 25(OH)D levels to define vitamin D deficiency are yet to be established. While, the Endocrine Society of USA has suggested serum 25(OH)D < 20 ng/mL to define vitamin D deficiency [1], the Institute of Medicine (IOM), USA recommends a cut-o...

Suppose we are given the conditional proba­ bility of one variable given some other vari­ ables. Normally the full joint distribution over the conditioning variables is required to determine the probability of the conditioned variable. Under what circumstances are the marginal distributions over the conditioning variables sufficient to determine the probabil­ ity of the conditioned variable? Su...