A statistical test for Nested Sampling algorithms

Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood threshold. Thus, the problem of drawing from a space above a certain likelihood value arises naturally in nested sampling, making algorithms that solve this problem a key ingredient to the nested sampling framework. If the drawn points are distributed uniformly, the removal of a point shrinks the volume in a well-understood way, and the integration of nested sampling is unbiased. In this work, I develop a statistical test to check whether this is the case. This "Shrinkage Test" is useful to verify nested sampling algorithms in a controlled environment. I apply the shrinkage test to a test-problem, and show that some existing algorithms fail to pass it due to over-optimisation. I then demonstrate that a simple algorithm can be constructed which is robust against this type of problem. This RADFRIENDS algorithm is, however, inefficient in comparison to MULTINEST.Comment: 11 pages, 7 figures. Published in Statistics and Computing, Springer, September 201

OPENMENDEL: A Cooperative Programming Project for Statistical Genetics

Statistical methods for genomewide association studies (GWAS) continue to improve. However, the increasing volume and variety of genetic and genomic data make computational speed and ease of data manipulation mandatory in future software. In our view, a collaborative effort of statistical geneticists is required to develop open source software targeted to genetic epidemiology. Our attempt to meet this need is called the OPENMENDELproject (https://openmendel.github.io). It aims to (1) enable interactive and reproducible analyses with informative intermediate results, (2) scale to big data analytics, (3) embrace parallel and distributed computing, (4) adapt to rapid hardware evolution, (5) allow cloud computing, (6) allow integration of varied genetic data types, and (7) foster easy communication between clinicians, geneticists, statisticians, and computer scientists. This article reviews and makes recommendations to the genetic epidemiology community in the context of the OPENMENDEL project.Comment: 16 pages, 2 figures, 2 table

A Distributed GPU-based Framework for real-time 3D Volume Rendering of Large Astronomical Data Cubes

We present a framework to interactively volume-render three-dimensional data cubes using distributed ray-casting and volume bricking over a cluster of workstations powered by one or more graphics processing units (GPUs) and a multi-core CPU. The main design target for this framework is to provide an in-core visualization solution able to provide three-dimensional interactive views of terabyte-sized data cubes. We tested the presented framework using a computing cluster comprising 64 nodes with a total of 128 GPUs. The framework proved to be scalable to render a 204 GB data cube with an average of 30 frames per second. Our performance analyses also compare between using NVIDIA Tesla 1060 and 2050 GPU architectures and the effect of increasing the visualization output resolution on the rendering performance. Although our initial focus, and the examples presented in this work, is volume rendering of spectral data cubes from radio astronomy, we contend that our approach has applicability to other disciplines where close to real-time volume rendering of terabyte-order 3D data sets is a requirement.Comment: 13 Pages, 7 figures, has been accepted for publication in Publications of the Astronomical Society of Australi