40 research outputs found

    Relations among partitions

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    Combinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.PostprintPeer reviewe

    A holistic evaluation concept for long-term structural health monitoring

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    Ultrasound shear wave imaging for diagnosis of nonalcoholic fatty liver disease

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    Pour le diagnostic et la stratification de la fibrose hépatique, la rigidité du foie est un biomarqueur quantitatif estimé par des méthodes d'élastographie. L'élastographie par ondes de cisaillement (« shear wave », SW) utilise des ultrasons médicaux non invasifs pour évaluer les propriétés mécaniques du foie sur la base des propriétés de propagation des ondes de cisaillement. La vitesse des ondes de cisaillement (« shear wave speed », SWS) et l'atténuation des ondes de cisaillement (« shear wave attenuation », SWA) peuvent fournir une estimation de la viscoélasticité des tissus. Les tissus biologiques sont intrinsèquement viscoélastiques et un modèle mathématique complexe est généralement nécessaire pour calculer la viscoélasticité en imagerie SW. Le calcul précis de l'atténuation est essentiel, en particulier pour une estimation précise du module de perte et de la viscosité. Des études récentes ont tenté d'augmenter la précision de l'estimation du SWA, mais elles présentent encore certaines limites. Comme premier objectif de cette thèse, une méthode de décalage de fréquence revisitée a été développée pour améliorer les estimations fournies par la méthode originale de décalage en fréquence [Bernard et al 2017]. Dans la nouvelle méthode, l'hypothèse d'un paramètre de forme décrivant les caractéristiques spectrales des ondes de cisaillement, et assumé initialement constant pour tous les emplacements latéraux, a été abandonnée permettant un meilleur ajustement de la fonction gamma du spectre d'amplitude. En second lieu, un algorithme de consensus d'échantillons aléatoires adaptatifs (« adaptive random sample consensus », A-RANSAC) a été mis en œuvre pour estimer la pente du paramètre de taux variable de la distribution gamma afin d’améliorer la précision de la méthode. Pour valider ces changements algorithmiques, la méthode proposée a été comparée à trois méthodes récentes permettant d’estimer également l’atténuation des ondes de cisaillements (méthodes de décalage en fréquence, de décalage en fréquence en deux points et une méthode ayant comme acronyme anglophone AMUSE) à l'aide de données de simulations ou fantômes numériques. Également, des fantômes de gels homogènes in vitro et des données in vivo acquises sur le foie de canards ont été traités. Comme deuxième objectif, cette thèse porte également sur le diagnostic précoce de la stéatose hépatique non alcoolique (NAFLD) qui est nécessaire pour prévenir sa progression et réduire la mortalité globale. À cet effet, la méthode de décalage en fréquence revisitée a été testée sur des foies humains in vivo. La performance diagnostique de la nouvelle méthode a été étudiée sur des foies humains sains et atteints de la maladie du foie gras non alcoolique. Pour minimiser les sources de variabilité, une méthode d'analyse automatisée faisant la moyenne des mesures prises sous plusieurs angles a été mise au point. Les résultats de cette méthode ont été comparés à la fraction de graisse à densité de protons obtenue de l'imagerie par résonance magnétique (« magnetic resonance imaging proton density fat fraction », MRI-PDFF) et à la biopsie du foie. En outre, l’imagerie SWA a été utilisée pour classer la stéatose et des seuils de décision ont été établis pour la dichotomisation des différents grades de stéatose. Finalement, le dernier objectif de la thèse consiste en une étude de reproductibilité de six paramètres basés sur la technologie SW (vitesse, atténuation, dispersion, module de Young, viscosité et module de cisaillement). Cette étude a été réalisée chez des volontaires sains et des patients atteints de NAFLD à partir de données acquises lors de deux visites distinctes. En conclusion, une méthode robuste de calcul du SWA du foie a été développée et validée pour fournir une méthode de diagnostic de la NAFLD.For diagnosis and staging of liver fibrosis, liver stiffness is a quantitative biomarker estimated by elastography methods. Ultrasound shear wave (SW) elastography utilizes noninvasive medical ultrasound to assess the mechanical properties of the liver based on the monitoring of the SW propagation. SW speed (SWS) and SW attenuation (SWA) can provide an estimation of tissue viscoelasticity. Biological tissues are inherently viscoelastic in nature and a complex mathematical model is usually required to compute viscoelasticity in SW imaging. Accurate computation of attenuation is critical, especially for accurate loss modulus and viscosity estimation. Recent studies have made attempts to increase the precision of SWA estimation, but they still face some limitations. As a first objective of this thesis, a revisited frequency-shift method was developed to improve the estimates provided by the original implementation of the frequency-shift method [Bernard et al 2017]. In the new method, the assumption of a constant shape parameter of the gamma function describing the SW magnitude spectrum has been dropped for all lateral locations, allowing a better gamma fitting. Secondly, an adaptive random sample consensus algorithm (A-RANSAC) was implemented to estimate the slope of the varying rate parameter of the gamma distribution to improve the accuracy of the method. For the validation of these algorithmic changes, the proposed method was compared with three recent methods proposed to estimate SWA (frequency-shift, two-point frequency-shift and AMUSE methods) using simulation data or numerical phantoms. In addition, in vitro homogenous gel phantoms and in vivo animal (duck) liver data were processed. As a second objective, this thesis also aimed at improving the early diagnosis of nonalcoholic fatty liver disease (NAFLD), which is necessary to prevent its progression and decrease the overall mortality. For this purpose, the revisited frequency-shift method was tested on in vivo human livers. The new method's diagnosis performance was investigated with healthy and NAFLD human livers. To minimize sources of variability, an automated analysis method averaging measurements from several angles has been developed. The results of this method were compared to the magnetic resonance imaging proton density fat fraction (MRI-PDFF) and to liver biopsy. SWA imaging was used for grading steatosis and cut-off decision thresholds were established for dichotomization of different steatosis grades. As a third objective, this thesis is proposing a reproducibility study of six SW-based parameters (speed, attenuation, dispersion, Young’s modulus, viscosity and shear modulus). The assessment was performed in healthy volunteers and NAFLD patients using data acquired at two separate visits. In conclusion, a robust method for computing the liver’s SWA was developed and validated to provide a diagnostic method for NAFLD

    Optimized automated survey design in wildlife population assessment

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    Increased pressure on the environment has placed numerous ecological populations under threat of extinction. Management schemes dedicated to the future conservation of wildlife populations rely on effective monitoring of the size of those populations. This requires that accurate and precise abundance estimates are obtained for the purposes of wildlife population assessment. The accuracy and precision of estimates are determined to a large extent by the survey design used to obtain population samples. Methods for optimizing the survey design process are detailed, with a particular- focus on automating the sui-vey designs using computer software. The technique of automated survey design is a simulation-based tool, which provides the means to assess the properties of any type of survey design, permits the evaluation of abundance estimates over sui-vey regions with assumed population densities, and from a practical standpoint facilitates the creation of a survey plan that can be implemented in the field. Survey design properties include the probability of a particular location being included in the sample, the spatial distribution of the sampling locations within the survey region, and the distances covered by observers to obtain the sample data. The design properties are directly linked to the accuracy and precision of estimates, as well as the efficiency, achieved by a type of design. A comparative study of a number of different survey designs that can be broadly classified as systematic or non-systematic is presented. The simulation results show their performance with regard to the above-mentioned properties and the abundance estimates obtained if the designs are applied to some known population densities. Due to the more even spatial distribution of the systematic designs the estimates they produce are potentially more precise and the distances covered by observers less variable as well. It is also shown how biased estimates can result if the probability of a particular location being included in the sample is assumed to be even over the entire survey region when it is not. The problems associated with surveying along the boundary of a survey region and within non-convex regions are addressed. The methods are illustrated with a number of survey design examples

    A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

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    When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

    A Statistical Approach to the Alignment of fMRI Data

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    Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

    Experimental uncertainty estimation and statistics for data having interval uncertainty.

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    Uncertainty Estimation for Target Detection System Discrimination and Confidence Performance Metrics

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    This research uses a Bayesian framework to develop probability densities for target detection system performance metrics. The metrics include the receiver operating characteristic (ROC) curve and the confidence error generation (CEG) curve. The ROC curve is a discrimination metric that quantifies how well a detection system separates targets and non-targets, and the CEG curve indicates how well the detection system estimates its own confidence. The degree of uncertainty in these metrics is a concern that previous research has not adequately addressed. This research formulates probability densities of the metrics and characterizes their uncertainty using confidence bands. Additional statistics are obtained that verify the accuracy of the confidence bands. Methods for the generation and characterization of the probability densities of the metrics are specified and demonstrated, where the initial analysis employs beta densities to model target and non-target samples of detection system output. For given target and non-target data, given functional forms of the data densities (such as beta density forms), and given prior densities of the form parameters, the methods developed here provide exact performance metric probability densities. Computational results compare favorably with existing approaches in cases where they can be applied; in other cases the methods developed here produce results that existing approaches cannot address
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