Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. A consequence is the occurrence of seemingly paradoxical results. The most famous example is perhaps given by the marginalization paradoxes presented by Stone and Dawid (1972). It is demonstrated here that the seemingly paradoxical results are removed by a more careful formulation of the ...

The second ECG recorded supraventricular tachycardia at the time his hemodynamic status deteriorated and decision was made to perform electrical cardioversion with 120 Joules of biphasic synchronized direct current with follow up ECG that showed atrial paced rhythm (Figure 1B). His condition improved and started on amiodarone 200 mg, anticoagulation, and subsequent follow up for ICD reprogrammi...

In this paper, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph is a vertex-coloring in which adjacent vertices are allowed to have the same color, but each color class V i satisses some condition depending on i. Such a coloring is acyclic if there are no alternating 2-colored cycles. We prove that every outerplanar graph can be acyclically 2-...

The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The expert’s opinion and trust on each pairwise correlation is described by a beta distribution. Then, by comb...

In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper r-coloring φ of a graph G. We investigate the problem of finding a proper r-coloring of G, which is “the most similar” to φ, i.e. the number k of vertices that have to be recolored is minimum possible. We observe that the problem is NP-complete for any r ≥ 3, even for bipartite pl...

A class of parametric supports in the lattice space Z is found to be inherently improper because any rational parametrization from C to C defined on such a support is improper. For a generic rational parametrization defined on an inherently improper support, we prove that its improper index is the gcd of the normalized volumes of all the simplex sub-supports and give an algorithm to obtain a pr...

An assessment of the risk of illness associated with Clostridium perfringens in ready-to-eat and partially cooked meat and poultry products was completed to estimate the effect on the annual frequency of illnesses of changing the allowed maximal 1-log growth of C. perfringens during stabilization (cooling after the manufacturing heat step). The exposure assessment modeled stabilization, storage...