Attribute charts for monitoring the mean vector of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Study on Bivariate Normal Distribution

Let (X, Y) be bivariate normal random vectors which represent the responses as a result of Treatment 1 and Treatment 2. The statistical inference about the bivariate normal distribution parameters involving missing data with both treatment samples is considered. Assuming the correlation coefficient ρ of the bivariate population is known, the MLE of population means and variance (ξ, η, and σ2) are obtained. Inferences about these parameters are presented. Procedures of constructing confidence interval for the difference of population means ξ – η and testing hypothesis about ξ – η are established. The performances of the new estimators and testing procedure are compared numerically with the method proposed in Looney and Jones (2003) on the basis of extensive Monte Carlo simulation. Simulation studies indicate that the testing power of the method proposed in this thesis study is higher.

Gráfico de controle de VMAX para o monitoramento da matriz de covariâncias

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Fatty liver characterization and classification by ultrasound

Steatosis, also known as fatty liver, corresponds to an abnormal retention of lipids within the hepatic cells and reflects an impairment of the normal processes of synthesis and elimination of fat. Several causes may lead to this condition, namely obesity, diabetes, or alcoholism. In this paper an automatic classification algorithm is proposed for the diagnosis of the liver steatosis from ultrasound images. The features are selected in order to catch the same characteristics used by the physicians in the diagnosis of the disease based on visual inspection of the ultrasound images. The algorithm, designed in a Bayesian framework, computes two images: i) a despeckled one, containing the anatomic and echogenic information of the liver, and ii) an image containing only the speckle used to compute the textural features. These images are computed from the estimated RF signal generated by the ultrasound probe where the dynamic range compression performed by the equipment is taken into account. A Bayes classifier, trained with data manually classified by expert clinicians and used as ground truth, reaches an overall accuracy of 95% and a 100% of sensitivity. The main novelties of the method are the estimations of the RF and speckle images which make it possible to accurately compute textural features of the liver parenchyma relevant for the diagnosis.

Association of adiposity genetic variants with menarche timing in 92,105 women of European descent.

Obesity is of global health concern. There are well-described inverse relationships between female pubertal timing and obesity. Recent genome-wide association studies of age at menarche identified several obesity-related variants. Using data from the ReproGen Consortium, we employed meta-analytical techniques to estimate the associations of 95 a priori and recently identified obesity-related (body mass index (weight (kg)/height (m)(2)), waist circumference, and waist:hip ratio) single-nucleotide polymorphisms (SNPs) with age at menarche in 92,116 women of European descent from 38 studies (1970-2010), in order to estimate associations between genetic variants associated with central or overall adiposity and pubertal timing in girls. Investigators in each study performed a separate analysis of associations between the selected SNPs and age at menarche (ages 9-17 years) using linear regression models and adjusting for birth year, site (as appropriate), and population stratification. Heterogeneity of effect-measure estimates was investigated using meta-regression. Six novel associations of body mass index loci with age at menarche were identified, and 11 adiposity loci previously reported to be associated with age at menarche were confirmed, but none of the central adiposity variants individually showed significant associations. These findings suggest complex genetic relationships between menarche and overall obesity, and to a lesser extent central obesity, in normal processes of growth and development.

Unraveling dynamics of human physical activity patterns in chronic pain conditions.

Chronic pain is a complex disabling experience that negatively affects the cognitive, affective and physical functions as well as behavior. Although the interaction between chronic pain and physical functioning is a well-accepted paradigm in clinical research, the understanding of how pain affects individuals' daily life behavior remains a challenging task. Here we develop a methodological framework allowing to objectively document disruptive pain related interferences on real-life physical activity. The results reveal that meaningful information is contained in the temporal dynamics of activity patterns and an analytical model based on the theory of bivariate point processes can be used to describe physical activity behavior. The model parameters capture the dynamic interdependence between periods and events and determine a 'signature' of activity pattern. The study is likely to contribute to the clinical understanding of complex pain/disease-related behaviors and establish a unified mathematical framework to quantify the complex dynamics of various human activities.

Tuotekehitys- ja innovaatioprosessin kehittäminen yrityksessä

Tutkimus käsittelee tuotekehitys- ja innovaatioprosessin kehittämistä ja sen vakiinnuttamista kohdeyrityksissä A ja B. Työssä luodaan ensin kirjallisuustutkimuksena yleinen teoreettinen viitekehys ja lähtötilannemalli tuotekehitys- ja innovaatioprosessin referenssimallille. Tämän vaiheen aikanakäsitellään erilaisia elementtejä ja vaiheita, joita tarvitaan kehitysprosessinkuvaamiseen ja sen kehittämiseen. Prosessimallissa ovat keskeisessä osassa päätöspisteet, joiden arviointikriteereitä ja -tekniikoita työssä käsitellään osana portfolion hallinnan eri mahdollisuuksia. Kehitettyä teoreettista mallia lähdetään implementoimaan työn toisessa osassa kohdeyrityksiin A ja B. Implementoinninyhteydessä käydään läpi sekä prosessikuvaus että siihen liittyvät päätöskriteerit. Tutkimuksen lopputuloksena on yrityksille tuotettu esitys innovaatioprosessista ja sen eri osa-alueista tarkemmalla tasolla sekä tutkimuksen puitteissa rakennettu portfoliotyökalu, jolla kehitysprojekteja voidaan hallinnoida niiden eri vaiheissa.

Role of matrix metalloproteinases in the development of airway inflammation and remodeling

Matrix metalloproteinases (MMPs) are a major group of proteases known to regulate extracellular matrix (ECM) turnover and so they have been suggested to be important in the process of lung disease associated with tissue remodeling. This has led to the concept that modulation of airway remodeling including excessive proteolysis damage to the tissue may be of interest for future treatment. Within the MMP family, macrophage elastase (MMP-12) is able to degrade ECM components such as elastin and is involved in tissue remodeling processes in chronic obstructive pulmonary disease including emphysema. Pulmonary fibrosis has an aggressive course and is usually fatal within an average of 3 to 6 years after the onset of symptoms. Pulmonary fibrosis is associated with deposition of ECM components in the lung interstitium. The excessive airway remodeling as a result of an imbalance in the equilibrium of the normal processes of synthesis and degradation of ECM components could justify anti-protease treatments. Indeed, the correlation of the differences in hydroxyproline levels in the lungs of bleomycin-treated mice strongly suggests that a reduced molar pro-MMP-9/TIMP-1 ratio in bronchoalveolar lavage fluid is associated with collagen deposition, beginning as early as the inflammatory events at day 1 after bleomycin administration. Finally, these observations emphasize that effective treatment of these disorders must be started early during the natural history of the disease, prior to the development of extensive lung destruction and fibrosis.

Exercise sheet 8 pdf

Exercises and solutions in PDF

Exercise sheet 8

Exercises and solutions in LaTex

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.