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

XMM-Newton observations of GB B1428+4217: confirmation of intrinsic soft X-ray absorption

We report the results of XMM-Newton observations of the X-ray bright, radio-loud blazar GB B1428+4217 at a redshift of z=4.72. We confirm the presence of soft X-ray spectral flattening at energies <0.7 keV as reported in previous ROSAT and BeppoSAX observations. At hard X-ray energies the spectrum is consistent with a power-law although we find the spectral slope varied between both XMM-Newton observations and is also significantly different from that reported previously. Whilst we cannot rule-out intrinsic cold absorption to explain the spectral depression, we favour a dust-free warm absorber. Cold absorption requires a column density ~1.4-1.6 x 10^22 cm^-2 whilst a warm absorber could have up to ~10^23 cm^-2 and an ionization parameter ~10^2. The spectrum of GB B1428+4217 shows remarkable parallels with that of the z=4.4 blazar PMN J0525-3343, in which the available evidence is also most consistent with a warm absorber model.Comment: 5 pages, 5 figures, MNRAS accepted. Minor changes to sections 3.1 and

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

The Long Wait for an Improbable Death: A Look at Delays in Executions in Kansas and Possible Reforms to Capital Punishment

This article uses Kansas as a case study to show how in Kansas, as in many other states in the United States, the execution of a death sentence is so improbable, and the delays that precede it so extraordinary, that any arguable deterrent or retributive effect capital punishment might once have had has been severely diminished. This article considers possible reforms to the capital punishment system aimed at reducing the delay between sentencing and execution, and the risks that would accompany those reforms. This article also considers whether capital punishment should still be considered a viable option for states in this position

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

Factors influencing fruit and vegetable intake among urban Fijians: A qualitative study.

Low fruit and vegetable intake is an important risk factor for micronutrient deficiencies and non-communicable diseases, but many people worldwide, including most Fijians, eat less than the World Health Organization recommended amount. The present qualitative study explores factors that influence fruit and vegetable intake among 57 urban Fijians (50 women, 7 men) of indigenous Fijian (iTaukei) and South Asian (Indian) descent. Eight focus group discussions were held in and around Suva, Fiji's capital and largest urban area, which explored motivation for eating fruit and vegetables, understandings of links to health and disease, availability and sources, determinants of product choice, and preferred ways of preparing and eating fruit and vegetables. Data were analysed using thematic content analysis. Regardless of ethnicity, participants indicated that they enjoyed and valued eating fruit and vegetables, were aware of the health benefits, and had confidence in their cooking skills. In both cultures, fruit and vegetables were essential components of traditional diets. However, increasing preferences for processed and imported foods, and inconsistent availability and affordability of high-quality, low-priced, fresh produce, were identified as important barriers. The findings indicate that efforts to improve fruit and vegetable intake in urban Fijians should target the stability of the domestic fruit and vegetable supply and access

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 /