Phase I and Phase II control charts for the variance and generalized variance

By extending the results of Human, Chakraborti and Smit (2010), Phase I control charts are derived for the generalized variance when the mean vector and covariance matrix of multivariate normally distributed data are unknown and estimated from m independent samples, each of size n. In Phase II predictive distributions based on a Bayesian approach are used to construct Shewart-type control limits for the variance and generalized variance. The posterior distribution is obtained by combining the likelihood (the observed data in Phase I) and the uncertainty of the unknown parameters via the prior distribution. By using the posterior distribution the unconditional predictive density functions are derived

Thyroidal iodoproteins in a congenital goitre

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Calibration artefacts in radio interferometry. I. Ghost sources in WSRT data

This work investigates a particular class of artefacts, or ghost sources, in radio interferometric images. Earlier observations with (and simulations of) the Westerbork Synthesis Radio Telescope (WSRT) suggested that these were due to calibration with incomplete sky models. A theoretical framework is derived that validates this suggestion, and provides predictions of ghost formation in a two-source scenario. The predictions are found to accurately match the result of simulations, and qualitatively reproduce the ghosts previously seen in observational data. The theory also provides explanations for many previously puzzling features of these artefacts (regular geometry, PSF-like sidelobes, seeming independence on model flux), and shows that the observed phenomenon of flux suppression affecting unmodelled sources is due to the same mechanism. We demonstrate that this ghost formation mechanism is a fundamental feature of calibration, and exhibits a particularly strong and localized signature due to array redundancy. To some extent this mechanism will affect all observations (including those with non-redundant arrays), though in most cases the ghosts remain hidden below the noise or masked by other instrumental artefacts. The implications of such errors on future deep observations are discussed.Comment: 19 pages, 15 figures, submitted to MNRA

Bayesian testing for process capability indices

Process capability indices have been widely used in the manufacturing industry. They measure the ability of a manufacturing process to produce items that meet certain specifications. A capability index relates the voice of the customer (specification limits) to the voice of the process. There is a need to understand and interpret process capability indices. Most of the existing work in this area has been devoted to classical frequentist large sample theory. An alternative approach to the problem of making inference about capability indices is the Bayesian approach. In this paper a Bayesian version of Tukey’s method is used for constructing simultaneous credibility intervals for all pairwise differences. A Bayesian procedure for testing all possible contrasts is also given. The problem of selecting the best supplier(s) has received considerable attention in the literature, but mainly from a classical frequentist point of view. A Bayesian simulation procedure is also illustrated to find the best supplier or group of suppliers.This method seems much easier to perform than the Monte Carlo integration method given in Wu, Shiau, Pearn and Hung (2016). In section 10, a sensitivity analysis regarding the prior choice is considered and in the last section, t-distributed data are analysed

Exact first-order density matrix for a d-dimensional harmonically confined Fermi gas at finite temperature

We present an exact closed form expression for the {\em finite temperature} first-order density matrix of a harmonically trapped ideal Fermi gas in any dimension. This constitutes a much sought after generalization of the recent results in the literature, where exact expressions have been limited to quantities derived from the {\em diagonal} first-order density matrix. We compare our exact results with the Thomas-Fermi approximation (TFA) and demonstrate numerically that the TFA provides an excellent description of the first-order density matrix in the large-N limit. As an interesting application, we derive a closed form expression for the finite temperature Hartree-Fock exchange energy of a two-dimensional parabolically confined quantum dot. We numerically test this exact result against the 2D TF exchange functional, and comment on the applicability of the local-density approximation (LDA) to the exchange energy of an inhomogeneous 2D Fermi gas.Comment: 12 pages, 3 figures included in the text, RevTeX4. Text before Eq.(25) corrected. Additional equation following Eq.(25) has been adde

Realistic modeling of leakage and intrusion flows through leak openings in pipes

The hydraulics of leakage and intrusion flows through leak openings in pipes is complicated by variations in the leak areas owing to changes in pressure. This paper argues that the pressure–area relationship can reasonably be assumed to be a linear function, and a modified orifice equation is proposed for more realistic modeling of leakage and intrusion flows. The properties of the modified orifice equation are explored for different classes of leak openings. The implications for the current practice of using a power equation to model leakage and intrusion flows are then investigated. A mathematical proof is proposed for an equation linking the parameters of the modified orifice and power equations using the concept of a dimensionless leakage number. The leakage exponent of a given leak opening is shown to generally not be constant with variations in pressure and to approach infinity when the leakage number approaches a value of minus one. Significant modeling errors may result if the power equation is extrapolated beyond its calibration pressure range or at high exponent values. It is concluded that the modified orifice equation and leakage number provide a more realistic description of leakage and intrusion flows, and it is recommended that this approach be adopted in modeling studies

Human cytomegalovirus immunoglobulin G response and pulmonary tuberculosis in adolescents: a case-control study

Background Emerging evidence suggests a link between infection with herpes viruses, particularly human cytomegalovirus (HCMV) and Epstein Barr Virus (EBV), and progression to tuberculosis (TB) disease. Methods An unmatched case-control study was conducted amongst adolescents aged 10-19 years enrolled in an observational study (Teen TB), between November 2020 and November 2021, in Cape Town, South Africa. Fifty individuals with pulmonary TB and 51 healthy TB-exposed individuals without TB were included. Demographics and clinical data were obtained, and serum samples collected at enrolment were tested for HCMV IgG and EBV Nuclear Antigen (EBNA) IgG using two automated enzyme immunoassays. Odds ratios (ORs) were estimated using unconditional logistic regression. Results The median age of 101 participants was 15 years (interquartile range [IQR] 13 to 17); 55 (54%) were female. All participants were HCMV IgG seropositive and 95% were EBNA IgG seropositive. Individuals with TB had higher HCMV IgG titres than healthy controls (p=0.04). Individuals with upper tertile HCMV IgG titres had a 3.7 times greater odds of pulmonary TB compared to those with IgG titres in the lower tertile (95%CI: 1.05–12.84; p=0.04). There was a trend for increasing odds of pulmonary TB with increasing titres of HCMV IgG (p=0.04). In contrast, there was no association between TB and higher EBNA IgG values. Conclusions There is a high prevalence of sensitisation to HCMV and EBV amongst adolescents in this high-TB burden setting. Higher HCMV IgG titres were associated with pulmonary TB in adolescents

Contemporary Discourses in Qualitative Research: Lessons for Health Research in Nigeria

Quantitative research has permeated and dominated health research in Nigeria. One of the oldest and the most commonly used quantitative research designs are KAP (knowledge, attitude and practice) surveys. Although KAP surveys are important approaches to assessing distribution of community knowledge in large-scale projects, such surveys are often inundated by challenges, especially with regard to accurate measurement and understanding of social construction of health and illness. This paper examines contemporary ontological, epistemological, axiological and methodological discourses in the qualitative research approach and argues for adequate utilisation of the qualitative approach in health research in Nigeria. The qualitative approach deepens understanding of cultural milieu regarding health beliefs and socio-cultural issues surrounding medical therapy, as well as health seeking behaviour. Therefore, this paperargues for a more participatory research methodology in the understanding of health, illness and disease in Nigeria. Some case studies of qualitative research from Nigeria and abroad were reviewed from which health researchers (clinical managers and health social scientists and public health experts) could learn. The paper is thus a contribution to the ongoing discourses in global qualitative health research.Keywords: Qualitative research; quantitative research; ontology; epistemology; developing countries; Nigeria