Random fields of multivariate test statistics, with applications to shape analysis

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the $P$-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main result is a very simple method for calculating this, which not only gives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999) 925--942] for Hotelling's $T^2$, but also random fields of Roy's maximum root, maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021--1057], multilinear forms [Ann. Statist. 29 (2001) 328--371], $\bar{\chi}^2$ [Statist. Probab. Lett 32 (1997) 367--376, Ann. Statist. 25 (1997) 2368--2387] and $\chi^2$ scale space [Adv. in Appl. Probab. 33 (2001) 773--793]. The trick involves approaching the problem from the point of view of Roy's union-intersection principle. The results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma.Comment: Published in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An analysis of HCPC fitness to practise hearings: Fit to Practise or Fit for Purpose?

All professions regulated by the HCPC have ‘protection of title’. This means that only those on its relevant register can legally work as or call themselves a social worker. As such, the HCPC’s Fitness to Practise panel wields a lot of power over individuals brought before it, effectively being able to prevent them from gaining employment as a social worker or imposing conditions on their practice. This article reports the findings from a study which examined publically available notes of HCPC fitness to practise hearings. The aim was to analyse what happens when an initial investigation finds that there is a case to answer, what factors influence the findings of the Fitness to Practise panel and how the outcome of the hearing then affects the social worker subject to the HCPC process. Using thematic analysis, our findings suggest that the seriousness of the alleged misconduct does not necessarily relate to the severity of sanction applied. It is the social worker’s engagement with the process, her insight into the issues and her credibility as a witness that appears to have the most significant bearing on the level of sanction applied

Tilted Euler characteristic densities for Central Limit random fields, with application to "bubbles"

Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above $u$, denoted $\mathbb{E}\varphi(A_u)$. Under isotropy, one can use the expansion $\mathbb{E}\varphi(A_u)=\sum_k\mathcal{V}_k\rho_k(u)$, where $\mathcal{V}_k$ is an intrinsic volume of the parameter space and $\rho_k$ is an EC density of the field. EC densities are available for a number of processes, mainly those constructed from (multivariate) Gaussian fields via smooth functions. Using saddlepoint methods, we derive an expansion for $\rho_k(u)$ for fields which are only approximately Gaussian, but for which higher-order cumulants are available. We focus on linear combinations of $n$ independent non-Gaussian fields, whence a Central Limit theorem is in force. The threshold $u$ is allowed to grow with the sample size $n$, in which case our expression has a smaller relative asymptotic error than the Gaussian EC density. Several illustrative examples including an application to "bubbles" data accompany the theory.Comment: Published in at http://dx.doi.org/10.1214/07-AOS549 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probability distribution of the maximum of a smooth temporal signal

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a non-zero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=.Comment: Final version (1 major typo corrected; better introduction). Accepted in Phys. Rev. Let

Income differences in food consumption in the 1995 Australian national nutrition survey

Objective: To assess the relationships between an index of per capita income and the intake of a variety of individual foods as well as groups of food for men and women in different age groups. Design: Cross-sectional national survey of free-living men and women. Subjects: A sample of 5053 males and 5701 females aged 18 y and over who completed the Australian National Nutrition Survey 1995. Methods: Information about the frequency of consumption of 88 food items was obtained. On the basis of scores on the Food Frequency Questionnaire, regular and irregular consumers of single foods were identified. The relationships between regularity of consumption of individual foods and per capita income were analysed via contingency tables. Food variety scores were derived by assigning individual foods to conventional food group taxonomies, and then summing up the dichotomised intake scores for individual foods within each food group. Two-way ANOVA (income age group) were performed on the food variety scores for males and females, respectively. Results: Per capita income was extensively related to the reported consumption of individual foods and to total and food group variety indices. Generally, both men and women in low income households had less varied diets than those in higher-income households. However, several traditional foods were consumed less often by young high-income respondents, especially young women. Conclusions: Major income differentials in food variety occur in Australia but they are moderated by age and gender. Younger high-income women, in particular, appear to have rejected a number of traditional foods, possibly on the basis of health beliefs. The findings also suggest that data aggregation has marked effects on income and food consumption relationships.<br /

A Lyman-alpha blob in the GOODS South field: evidence for cold accretion onto a dark matter halo

We report on the discovery of a z = 3.16 Lyman-alpha emitting blob in the GOODS South field. The blob has a total Ly-alpha luminosity of ~ 10^(43) erg s^(-1) and a diameter larger than 60 kpc. The available multi-wavelength data in the GOODS field consists of 13 bands from X-rays (Chandra) to infrared (Spitzer). Unlike other discovered Ly-alpha blobs, this blob shows no obvious continuum counter-part in any of the broad-bands. In particular, no optical counter-parts are found in the deep HST/ACS imaging available. For previously published blobs, AGN (Active Galactic Nuclei) or 'superwind' models have been found to provide the best match with the data. We here argue that the most probable origin of the extended Ly-alpha emission from the blob in the GOODS South field is cold accretion onto a dark matter halo.Comment: 4 pages, 2 tables, 2 figures, Accepted to A&A Letters, minor changes to tex

Allogeneic Stem Cells Alter Gene Expression and Improve Healing of Distal Limb Wounds in Horses.

Distal extremity wounds are a significant clinical problem in horses and humans and may benefit from mesenchymal stem cell (MSC) therapy. This study evaluated the effects of direct wound treatment with allogeneic stem cells, in terms of gross, histologic, and transcriptional features of healing. Three full-thickness cutaneous wounds were created on each distal forelimb in six healthy horses, for a total of six wounds per horse. Umbilical cord-blood derived equine MSCs were applied to each wound 1 day after wound creation, in one of four forms: (a) normoxic- or (b) hypoxic-preconditioned cells injected into wound margins, or (c) normoxic- or (d) hypoxic-preconditioned cells embedded in an autologous fibrin gel and applied topically to the wound bed. Controls were one blank (saline) injected wound and one blank fibrin gel-treated wound per horse. Data were collected weekly for 6 weeks and included wound surface area, thermography, gene expression, and histologic scoring. Results indicated that MSC treatment by either delivery method was safe and improved histologic outcomes and wound area. Hypoxic-preconditioning did not offer an advantage. MSC treatment by injection resulted in statistically significant increases in transforming growth factor beta and cyclooxygenase-2 expression at week 1. Histologically, significantly more MSC-treated wounds were categorized as pro-healing than pro-inflammatory. Wound area was significantly affected by treatment: MSC-injected wounds were consistently smaller than gel-treated or control wounds. In conclusion, MSC therapy shows promise for distal extremity wounds in horses, particularly when applied by direct injection into the wound margin. Stem Cells Translational Medicine 2018;7:98-108

Bayesian Blocks, A New Method to Analyze Structure in Photon Counting Data

I describe a new time-domain algorithm for detecting localized structures (bursts), revealing pulse shapes, and generally characterizing intensity variations. The input is raw counting data, in any of three forms: time-tagged photon events (TTE), binned counts, or time-to-spill (TTS) data. The output is the most likely segmentation of the observation into time intervals during which the photon arrival rate is perceptibly constant -- i.e. has a fixed intensity without statistically significant variations. Since the analysis is based on Bayesian statistics, I call the resulting structures Bayesian Blocks. Unlike most, this method does not stipulate time bins -- instead the data themselves determine a piecewise constant representation. Therefore the analysis procedure itself does not impose a lower limit to the time scale on which variability can be detected. Locations, amplitudes, and rise and decay times of pulses within a time series can be estimated, independent of any pulse-shape model -- but only if they do not overlap too much, as deconvolution is not incorporated. The Bayesian Blocks method is demonstrated by analyzing pulse structure in BATSE $\gamma$-ray data. The MatLab scripts and sample data can be found on the WWW at: http://george.arc.nasa.gov/~scargle/papers.htmlComment: 42 pages, 2 figures; revision correcting mathematical errors; clarifications; removed Cyg X-1 sectio