arXiv subjects

Ben O'Neill

Publications and source records attributed to Ben O'Neill.

23 records · Page 2Linked to original sources

arXiv2021

Decompositions for Sum-of-Power Statistics and the Sample Central Moments

We give some useful decompositions of sum-of-powers statistics, leading to decompositions for the sample mean, sample variance, sample skewness and sample kurtosis. We solve two related problems: computing these sample moments for a pooled sample composed of subgroups with known moments; and computing these sample moments for a subgroup using known moments from other subgroups and the overall pooled sample. Each task is accomplished via decompositions of the sums-of-squares, sums-of-cubes and sums-of-quads from which the sample central moments (up to fourth order) are formed. We give decomposition results and we implement these in a user-friendly R function.

stat.AP↗

arXiv2021

The Double-Constant Matrix, Centering Matrix and Equicorrelation Matrix: Theory and Applications

This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices, which is a subclass of Toeplitz matrices. It encompasses other useful matrices such as the centering matrix and the equicorrelation matrix, which arise in statistical applications. We examine the general form of this class of matrices and derive its eigendecomposition and other important properties. We use this as a basis to look at the properties of the centering matrix and the equicorrelation matrix, and various statistics that use these matrices.

math.ST↗

arXiv2021

Multiple Linear Regression and Correlation: A Geometric Analysis

In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard regression output can be written in terms of the lengths and angles between the various input vectors, such that this geometric information is sufficient in linear regression problems. This allows us to obtain a standard formula for multiple correlation and give a geometric interpretation to this. We examine how multicollinearity affects the total explanatory power of the data, and we examine a counter-intuitive phenomena called "enhancement" where the total information from the explanatory vectors is greater than the sum of the marginal parts.

stat.ME↗

arXiv2021

An examination of the generalised pooled binomial distribution and its information properties

This paper examines the statistical properties of a distributional form that arises from pooled testing for the prevalence of a binary outcome. Our base distribution is a two-parameter distribution using a prevalence and excess intensity parameter; the latter is included to allow for a dilution or intensification effect with larger pools. We also examine a generalised form of the distribution where pools have covariate information that affects the prevalence through a linked linear form. We study the general pooled binomial distribution in its own right and as a special case of broader forms of binomial GLMs using the complementary log-log link function. We examine the information function and show the information content of individual sample items. We demonstrate that pooling reduces information content of sample units and we give simple heuristics for choosing an "optimal" pool size for testing. We derive the form of the log-likelihood function and its derivatives and give results for maximum likelihood estimation. We also discuss diagnostic testing of the positive pool probabilities, including testing for intensification/dilution in the testing mechanism. We illustrate the use of this distribution by applying it to pooled testing data on virus prevalence in a mosquito population.

stat.ME↗

arXiv2020

PoolTestR: An R package for estimating prevalence and regression modelling with pooled samples

Pooled testing (also known as group testing), where diagnostic tests are performed on pooled samples, has broad applications in the surveillance of diseases in animals and humans. An increasingly common use case is molecular xenomonitoring (MX), where surveillance of vector-borne diseases is conducted by capturing and testing large numbers of vectors (e.g. mosquitoes). The R package PoolTestR was developed to meet the needs of increasingly large and complex molecular xenomonitoring surveys but can be applied to analyse any data involving pooled testing. PoolTestR includes simple and flexible tools to estimate prevalence and fit fixed- and mixed-effect generalised linear models for pooled data in frequentist and Bayesian frameworks. Mixed-effect models allow users to account for the hierarchical sampling designs that are often employed in surveys, including MX. We demonstrate the utility of PoolTestR by applying it to a large synthetic dataset that emulates a MX survey with a hierarchical sampling design.

stat.CO↗