Approximating multivariate posterior distribution functions from Monte Carlo samples for sequential Bayesian inference

An important feature of Bayesian statistics is the opportunity to do sequential inference: the posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods are used for inference, we only have a set of samples from the posterior distribution. To do sequential inference, we then either have to evaluate the second posterior at only these locations and reweight the samples accordingly, or we can estimate a functional description of the posterior probability distribution from the samples and use that as prior for the second inference. Here, we investigated to what extent we can obtain an accurate joint posterior from two datasets if the inference is done sequentially rather than jointly, under the condition that each inference step is done using Monte Carlo sampling. To test this, we evaluated the accuracy of kernel density estimates, Gaussian mixtures, vine copulas and Gaussian processes in approximating posterior distributions, and then tested whether these approximations can be used in sequential inference. In low dimensionality, Gaussian processes are more accurate, whereas in higher dimensionality Gaussian mixtures or vine copulas perform better. In our test cases, posterior approximations are preferable over direct sample reweighting, although joint inference is still preferable over sequential inference. Since the performance is case-specific, we provide an R package mvdens with a unified interface for the density approximation methods

Book review

NEW DICTIONARY OF SOUTH AFRICAN BIOGRAPHY, volume 2 (edited by Nelly E Sonderling; foreword by Kader Asmal). Pretoria: Vista University, 1999. ISBN 1-86828-133-7 (296 pages)

Heraclitean logos and flux in T.S. Eliot’s Four Quartets: 'cosmic consciousness' and 'the still point of the turning world'

T.S. Eliot prefaces “Burnt Norton”, the first of his Four Quartets, with two quotations from the Greek philosopher, Heraclitus. By means of these epigrams, Eliot points us to the Heraclitean opposition and paradoxical interdependence between logos and flux as a paradigm in the poem, a paradigm that he uses for an investigation and articulation of a number of philosophical contemplations. In this paper, I discuss Eliot’s different configurations of the logos/flux paradigm in the poem, firstly to illuminate the relationship between temporality and eternity, secondly, to elaborate the relationship between God and humanity, and thirdly to express the relationship between structured art and chaotic experience. In each instance it is not only the opposition between the two elements that is important, but also the point of contact, the intersection. There is some evidence that Eliot’s depiction of this intersection as, for example, the “moment in and out of time”, is based on personal experience of a transcendent, mystical nature. His expression of this experience is also investigated by comparing it to similar experiences described by others, notably by a Canadian psychiatrist, Richard Maurice Bucke. A comparison of Bucke’s description in his evolutionist text of 1901 and Eliot’s poetic rendering reveals not only surprising similarities but also essential differences which highlights Eliot’s purely Christian interpretation in the face of Bucke’s more universalist approach. For T.S. Eliot, eternity or timelessness can only be accessed through the temporal experience of human consciousness, in fleeting moments of exaltation in daily life, in the charged, timeless configurations of art as an imitation of divine creation, and finally in Christ, who embodies the love of God and is for Eliot the ultimate transection of the temporal and eternal, the flux and the logos

On the design of a real-time volume rendering engine

An architecture for a Real-Time Volume Rendering Engine (RT-VRE) is given, capable of computing 750 × 750 × 512 samples from a 3D dataset at a rate of 25 images per second. The RT-VRE uses for this purpose 64 dedicated rendering chips, cooperating with 16 RISC-processors. A plane interpolator circuit and a composition circuit, both capable to operate at very high speeds, have been designed for a 1.6 micron VLSI process. Both the interpolator and composition circuit are back from production. They have been tested and both complied with our specifications

Diaphragmatic Hernia Masquerading as Pleural Effusion

Rupture of the diaphragm is almost always due to major trauma. We present here an unusual and rare case of late presentation of diaphragmatic hernia after an innocuous injury. The patient was initially misdiagnosed as a left pleural effusion on the basis of chest X.ray and ultrasound findings. Finally, the diagnosis was confirmed on computerized scanning.Keywords: Pleural effusion, CT scan, diaphragmatic herni

Flow-gauging structures in South African rivers Part 1: An overview

Accurate hydrological information is of paramount importance in a dry country such as South Africa. Flow measurements in rivers are complicated by the high variability of flows as well as by sediment and debris loads. It has been found necessary to modify and even substitute certain internationally accepted gauging structure designs to overcome local practical problems and improve accuracies.This, Part 1 of a paper in 2 parts, concentrates on the attributes of different types of gauging structures and the informationprovided on the different structures will assist the reader with the selection of an appropriate structure. The historical development of the gauging structure network in South African rivers is briefly discussed. Gauging structures used in South African rivers and basic design criteria for the preferred structures at this stage, based on past experience, are discussed:• Crump weirs• Sharp-crested weirs• Sluicing flumes.This paper reflects the lessons that have been learnt by DWAF and other South African organisations and should be of value to others who have to perform flow measurements under similar climatic conditions. Factors that may adversely impact on gauging accuracy are also pointed out in the conclusion. Part 2 of the paper contains information on the calibration theory and techniques to rate the preferred gauging structures