Riemannian Gaussian distributions on the space of positive-definite quaternion matrices

Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positive-definite quaternion matrices. In order to do so, it develops the Riemannian geometry of the space of positive-definite quaternion matrices, which is shown to be a Riemannian symmetric space of non-positive curvature. The paper gives original formulae for the Riemannian metric of this space, its geodesics, and distance function. Then, it develops the theory of Riemannian Gaussian distributions, including the exact expression of their probability density, their sampling algorithm and statistical inference.Comment: 8 pages, submitted to GSI 201

A review of social cohesion initiatives and challenges with a focus on Jordan and education

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Megacystis microcolon intestinal hypoperistalsis syndrome: a report of a variant

Megacystis microcolon intestinal hypoperistalsis syndrome is a very rare cause of functional intestinal obstruction in newborns. It is associated with nonobstructed distended urinary bladder, microcolon, and decreased or absent intestinal peristalsis. The prognosis is poor and most patients die early because of sepsis or total parental nutrition-related complications. This report describes a new case of megacystis microcolon intestinal hypoperistalsis syndrome associated with meconium ileus, dilated stomach, and megaesophagus.Keywords: intestinal hypoperistalsis syndrome, megacystis, microcolo

Mis-specification and goodness-of-fit in logistic regression

PhD ThesisThe logistic regression model has become a standard model for binary outcomes in many areas of application and is widely used in medical statistics. Much work has been carried out to examine the asymptotic behaviour of the distribution of Maximum Likelihood Estimates (MLE) for the logistic regression model, although the most widely known properties apply only if the assumed model is correct. There has been much work on goodness-of-fit tests to address the last point. The first part of this thesis investigates the behaviour of the asymptotic distribution of the (MLE) under a form of model mis-specification, namely when covariates from the true model are omitted from the fitted model. When the incorrect model is fitted the maximum likelihood estimates converge to the least false values. In this work, key integrals cannot be evaluated explicitly but we use properties of the skew-Normal distribution and the approximation of the Logit by a suitable Probit function to obtain a good approximation for the least false values. The second part of the thesis investigates the assessment of a particular goodness-of-fit test namely the information matrix test (IM) test as applied to binary data models. Kuss (2002), claimed that the IM test has reasonable power compared with other statistics. In this part of the thesis we investigate this claim, consider the distribution of the moments of the IM statistic and the asymptotic distribution of the IM test (IMT) statistic. We had dificulty in reproducing the results claimed by Kuss (2002) and considered that this was probably due to the near singularity of the variance of IMT. We define a new form of the IMT statistic, IMTR, which addresses this issue

Decompounding on compact Lie groups

Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The proposed solution is based on a char- acteristic function method. The treated problem is important to recent models of the physical inverse problem of multiple scattering.Comment: 26 pages, 3 figures, 25 reference