On the weak convergence of stochastic processes without discontinuities of the second kind

Subspaces D α , α > 0, of D [0, 1] are defined and given complete metrics d α which are stronger than the Prokhorov metric. The spaces ( D α d α ) are shown to be separable, and their pre-compact subsets are characterized. A condition which is known to guarantee weak pre-compactness of sets of probability measures over D [0, 1] is shown to also guarantee weak pre-compactness of probability measures over D α for appropriate values of α. Applications are made to the weak convergence of measures induced by stochastic processes, and some examples are included.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47645/1/440_2004_Article_BF00538382.pd

Evaluation of ADAMTS-9 Expression in Post-Mortem Brain Tissue

Background: Extracellular Matrix (ECM) modifications have been reported in the Central Nervous System (CNS) of multiple sclerosis (MS) within post mortem brain tissue due to both the increased synthesis of ECM proteoglycans, and release activation of matrix metalloproteinase (MMPs). Multiple sclerosis (MS) is chronic inflammatory demyelinating disease written off as inflammation and demyelination disease, mainly located in central nervous system (CNS) white matter (WM). This study aims to clarify the potential pathophysiologic role of adisintegrin And metalloproteinase with thromboSpondin motif-9 (ADAMTS-9) in MS. Materials and methods: Immunohistochemistry was performed to study the expression of ADAMTS-9 in both normal and MS white matter by confocal microscopic using specific antibodies. Fifty frozen blocks of brain tissue were obtained from the UK MS Society Tissue. All tissues blocks were marked by immunohistological material including antibodies to Human leukocyte antigen (HLA-DR) to assess the macrophage activation, Glial fibrillary acidic protein (GFAP) for astrocyte, neurofilaments (NF) for neurons and Von Willbrand factor (VWF) for endothelial. Results: In MS lesions, ADMTS-9 expression was increased in comparison to control samples. The expression of ADAMTS-9 was increased in active lesions as well as was associated with different cells from neuron, endothelial covering blood vessels astrocyte and microglia. Conclusion: The expression of ADAMTS-9 at the protein level was increased in active inflammatory lesions with evidence of myelin breakdown, suggesting that up-regulation of ADAMTS-9 may be a general phenomenon induced by CNS injurie

On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities

In order to construct fixed-width (2d) confidence intervals for the mean of an unknown distribution function F , a new purely sequential sampling strategy is proposed first. The approach is quite different from the more traditional methodology of Chow and Robbins (1965, Ann. Math. Statist. , 36 , 457–462). However, for this new procedure, the coverage probability is shown (Theorem 2.1) to be at least (1-α)+ Ad 2 + o (d 2 ) as d →0 where (1-α) is the preassigned level of confidence and A is an appropriate functional of F , under some regularity conditions on F . The rates of convergence of the coverage probability to (1-α) obtained by Csenki (1980, Scand. Actuar. J. , 107–111) and Mukhopadhyay (1981, Comm. Statist. Theory Methods , 10 , 2231–2244) were merely O (d 1/2-q ), with 0< q <1/2, under the Chow-Robbins stopping time τ * . It is to be noted that such considerable sharpening of the rate of convergence of the coverage probability is achieved even though the new stopping variable is O p (τ * ). An accelerated version of the stopping rule is also provided together with the analogous second-order characteristics. In the end, an example is given for the mean estimation problem of an exponential distribution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47956/1/10463_2004_Article_BF00050850.pd

Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

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-

Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling With Censoring

International audienceWhat population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time $t_0$ represents not the target density $f(t)$ but its length-biased version proportional to $tf(t)$, for $t>0$. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent consoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators

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