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We present a theoretical analysis of the relationship between incoming radiance and irradiance. Specifically, we address the question of whether it is possible to compute the incident radiance from knowledge of the irradiance at all surface orientations. This is a fundamental question in computer vision and inverse radiative transfer. We show that the(More)
A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In the recent years, eecient Markov chain Monte Carlo method for the computation of the posterior distribution has been developed. The method has been applied to data arising from diierent elds of interest. The(More)
We consider the problem of Bayesian inference about the centre of symmetry of a symmetric density on the real line based on independent identically distributed observations. A result of Diaconis and Freedman shows that the posterior distribution of the location parameter may be inconsistent if (symmetrized) Dirichlet process prior is used for the unknown(More)
In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of posterior distributions. In this paper, we build up some conceptual issues in consistency of posterior distributions,(More)
Jim Hannan is a professor who has lived an interesting life and one whose fundamental research in repeated games was not fully appreciated until late in his career. During his service as a meteorologist in the Army in World War II, Jim played poker and made weather forecasts. It is curious that his later research included strategies for repeated play that(More)
Neglected tropical diseases (NTDs), malaria, and tuberculosis have a devastating effect on an estimated 1.6 billion people worldwide. The World Intellectual Property Organization (WIPO) Re:Search consortium accelerates the development of new drugs, vaccines, and diagnostics for these diseases by connecting the assets and resources of pharmaceutical(More)
The process of blood coagulation in mammals is complicated, and involves the interaction of more than a dozen coagulation factors as well as a number of proteins from the kinin-kallikrein system and protein inhibitors. Attempts to model coagulation mathematically have previously focused on a smaller subset of interactions, perhaps one of the pathways or(More)
We show that the equivalence of two notions of sufficiency is related to the separation of two orthogonal, strongly convex sets of probability measures by a universally measurable set. Consider a measurable space (äf, sé), and let M(%?) be the set of all probability measures on (%? , sé). Equip M(JT) with the canonical cr-algebra Jf generated by the(More)
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