Inference for bounded parameters

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the construction of a confidence interval. We argue that the likelihood function and $p$-value function provide a comprehensive presentation of the information available from the model and the data. This is illustrated for Gaussian and Poisson models with lower bounds for the mean parameter

On the future of astrostatistics: statistical foundations and statistical practice

This paper summarizes a presentation for a panel discussion on "The Future of Astrostatistics" held at the Statistical Challenges in Modern Astronomy V conference at Pennsylvania State University in June 2011. I argue that the emerging needs of astrostatistics may both motivate and benefit from fundamental developments in statistics. I highlight some recent work within statistics on fundamental topics relevant to astrostatistical practice, including the Bayesian/frequentist debate (and ideas for a synthesis), multilevel models, and multiple testing. As an important direction for future work in statistics, I emphasize that astronomers need a statistical framework that explicitly supports unfolding chains of discovery, with acquisition, cataloging, and modeling of data not seen as isolated tasks, but rather as parts of an ongoing, integrated sequence of analyses, with information and uncertainty propagating forward and backward through the chain. A prototypical example is surveying of astronomical populations, where source detection, demographic modeling, and the design of survey instruments and strategies all interact.Comment: 8 pp, 2 figures. To appear in "Statistical Challenges in Modern Astronomy V," (Lecture Notes in Statistics, Vol. 209), ed. Eric D. Feigelson and G. Jogesh Babu; publication planned for Sep 2012; see http://www.springer.com/statistics/book/978-1-4614-3519-

An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations

We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure's headstart is not restricted to a bounded range, nor is there a "ceiling" value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th German-Polish Workshop on Stochastic Models, Statistics and Their Application

Study protocol to investigate the effect of a lifestyle intervention on body weight, psychological health status and risk factors associated with disease recurrence in women recovering from breast cancer treatment

Background Breast cancer survivors often encounter physiological and psychological problems related to their diagnosis and treatment that can influence long-term prognosis. The aim of this research is to investigate the effects of a lifestyle intervention on body weight and psychological well-being in women recovering from breast cancer treatment, and to determine the relationship between changes in these variables and biomarkers associated with disease recurrence and survival. Methods/design Following ethical approval, a total of 100 patients will be randomly assigned to a lifestyle intervention (incorporating dietary energy restriction in conjunction with aerobic exercise training) or normal care control group. Patients randomised to the dietary and exercise intervention will be given individualised healthy eating dietary advice and written information and attend moderate intensity aerobic exercise sessions on three to five days per week for a period of 24 weeks. The aim of this strategy is to induce a steady weight loss of up to 0.5 Kg each week. In addition, the overall quality of the diet will be examined with a view to (i) reducing the dietary intake of fat to ~25% of the total calories, (ii) eating at least 5 portions of fruit and vegetables a day, (iii) increasing the intake of fibre and reducing refined carbohydrates, and (iv) taking moderate amounts of alcohol. Outcome measures will include body weight and body composition, psychological health status (stress and depression), cardiorespiratory fitness and quality of life. In addition, biomarkers associated with disease recurrence, including stress hormones, estrogen status, inflammatory markers and indices of innate and adaptive immune function will be monitored. Discussion This research will provide valuable information on the effectiveness of a practical, easily implemented lifestyle intervention for evoking positive effects on body weight and psychological well-being, two important factors that can influence long-term prognosis in breast cancer survivors. However, the added value of the study is that it will also evaluate the effects of the lifestyle intervention on a range of biomarkers associated with disease recurrence and survival. Considered together, the results should improve our understanding of the potential role that lifestyle-modifiable factors could play in saving or prolonging lives

Intracerebral Human Regulatory T Cells: Analysis of CD4+CD25+FOXP3+ T Cells in Brain Lesions and Cerebrospinal Fluid of Multiple Sclerosis Patients

Impaired suppressive capacity of CD4+CD25+FOXP3+ regulatory T cells (Treg) from peripheral blood of patients with multiple sclerosis (MS) has been reported by multiple laboratories. It is, however, currently unresolved whether Treg dysfunction in MS patients is limited to reduced control of peripheral T cell activation since most studies analyzed peripheral blood samples only. Here, we assessed early active MS lesions in brain biopsies obtained from 16 patients with MS by FOXP3 immunohistochemistry. In addition, we used six-color flow cytometry to determine numbers of Treg by analysis of FOXP3/CD127 expression in peripheral blood and cerebrospinal fluid (CSF) of 17 treatment-naïve MS patients as well as quantities of apoptosis sensitive CD45ROhiCD95hi cells in circulating and CSF Treg subsets. Absolute numbers of FOXP3+ and CD4+ cells were rather low in MS brain lesions and Treg were not detectable in 30% of MS biopsies despite the presence of CD4+ cell infiltrates. In contrast, Treg were detectable in all CSF samples and Treg with a CD45ROhiCD95hi phenotype previously shown to be highly apoptosis sensitive were found to be enriched in the CSF compared to peripheral blood of MS patients. We suggest a hypothetical model of intracerebral elimination of Treg by CD95L-mediated apoptosis within the MS lesion

Gene expression profiling of the astrocyte transcriptome in multiple sclerosis normal appearing white matter reveals a neuroprotective role

Multiple sclerosis (MS) is a chronic, inflammatory, demyelinating disease of the central nervous system (CNS). White matter lesions in MS are surrounded by areas of non-demyelinated normal appearing white matter (NAWM) with complex pathology, including blood brain barrier dysfunction, axonal damage and glial activation. Astrocytes, the most abundant cell type within the CNS, may respond and/or contribute to lesion pathogenesis. We aimed to characterise the transcriptomic profile of astrocytes in NAWM to determine whether specific glial changes exist in the NAWM which contribute to lesion development or prevent disease progression. Astrocytes were isolated from control and NAWM by laser capture microdissection (LCM), using glial fibrillary acidic protein (GFAP) as a marker, and the astrocyte transcriptome determined using microarray analysis. 452 genes were significantly differentially expressed (208 up-regulated and 244 down-regulated, FC ≥ 1.5 and p-value ≤ 0.05). Within the NAWM, astrocytes were associated with significant upregulation of genes involved in the control of iron homeostasis (including metallothionein-1 and -2, ferritin light chain and transferrin), oxidative stress responses, the immune response and neurotrophic support. These findings suggest a neuroprotective role of astrocytes in the NAWM in M

Shedding Light on the Galaxy Luminosity Function

From as early as the 1930s, astronomers have tried to quantify the statistical nature of the evolution and large-scale structure of galaxies by studying their luminosity distribution as a function of redshift - known as the galaxy luminosity function (LF). Accurately constructing the LF remains a popular and yet tricky pursuit in modern observational cosmology where the presence of observational selection effects due to e.g. detection thresholds in apparent magnitude, colour, surface brightness or some combination thereof can render any given galaxy survey incomplete and thus introduce bias into the LF. Over the last seventy years there have been numerous sophisticated statistical approaches devised to tackle these issues; all have advantages -- but not one is perfect. This review takes a broad historical look at the key statistical tools that have been developed over this period, discussing their relative merits and highlighting any significant extensions and modifications. In addition, the more generalised methods that have emerged within the last few years are examined. These methods propose a more rigorous statistical framework within which to determine the LF compared to some of the more traditional methods. I also look at how photometric redshift estimations are being incorporated into the LF methodology as well as considering the construction of bivariate LFs. Finally, I review the ongoing development of completeness estimators which test some of the fundamental assumptions going into LF estimators and can be powerful probes of any residual systematic effects inherent magnitude-redshift data.Comment: 95 pages, 23 figures, 3 tables. Now published in The Astronomy & Astrophysics Review. This version: bring in line with A&AR format requirements, also minor typo corrections made, additional citations and higher rez images adde