Ce mémoire traite de modèles d'arborescences en régression logistique 4-nomiale pour rendre compte du cas où les résultats proviennent de séquences d'expérience multinomiales consécutives ou parallèles. Dans le premier chapitre, nous rappelons le modèle général de régression logistique multinomiale et présentons une méthode d'estimation individuelle des paramètres. Le chapitre suivant rapporte les recherches de Rousseau et Sankoff sur les modèles d'arborescences en régression logistique et présente du même coup le cadre dans lequel la présente étude s'inscrit.. Le troisième chapitre porte sur différents résultats qui caractérisent les paramètres pour lesquels certaines structures d'arborescences sont équivalentes. Finalement, le dernier chapitre présente une étude de simulations Monte-Carlo effectuée pour comprendre et mettre en évidence les facteurs influençant l'ordre (selon le maximum de vraisemblance) dans lequel les arborescences sont sélectionnées. Ces simulations ont permis d'identifier certains principes auxquels cet ordre obéit, selon la forme du vecteur des paramètres et la grandeur de ces derniers. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Régression logistique, Arborescences, Modèles réduits.

Dans notre travail de mémoire, nous présentons l'approche bayésienne empirique dans l'inférence statistique. Les premiers articles dans ce domaine ont été publiés par Rabbins (1951, 1955, 1980). Robbins a utilisé une méthode non paramétrique (Maritz et Lwin (1989)) pour estimer la densité marginale. Plus tard, Morris (1983) a introduit l'approche paramétrique bayésienne empirique (voir aussi Efron et Morris (1973) (a), Casella (1985)). Nous décrivons les deux approches pour l'estimation de la moyenne de la loi gaussienne, de la loi de Poisson et de la loi exponentielle. Pour le cas gaussien, nous adaptons une méthodologie proposée par Angers (1992) pour l'estimation bayésienne hiérarchique à l'estimation bayésienne empirique dans le but d'obtenir des estimations plus robustes. Nous nous intéressons à l'estimation de la moyenne gaussienne et de la moyenne de la loi de Poisson quand les tailles des groupes sont inégales. Pour le cas gaussien, nous utilisons un estimateur du type James-Stein d'après Berger et Bock (1976) pour incorporer les tailles inégales. Dans le cas de la loi de Poisson, nous utilisons une méthode proposée par Maritz et Lwin (1989). Nous étudions également les estimateurs bayésiens empiriques pour estimer une moyenne exponentielle. Pour ce cas, nous avons introduit un nouvel estimateur bayésien empirique qui semble prometteur. Dans le cas gaussien, nous illustrons les approches en utilisant des banques de données pertinentes. Dans les autres cas, nous effectuons les études de simulation. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Analyse bayésienne, bayésien empirique, estimateur de stein, estimateur minimax, plans d'expérience non équilibrés.

A novel adaptive controller, suitable for linear and non-linear systems was developed. The controller is a discrete algorithm suitable for computer implementation and is based on gradient descent adaptation rules. Traditional recursive least squares based algorithms suffer from performance deterioration due to the continuous reduction of a covariance matrix used for adaptation. When this covariance matrix becomes too small, recursive least squares algorithms respond slow to changes in model parameters. Gradient descent adaptation was used to avoid the performance deterioration with time associated with regression based adaptation such as Recursive Least Squares methods. Stability was proven with Lyapunov stability theory, using an error filter designed to fulfill stability requirements. Similarities between the proposed controller with PI control have been found. A framework for on-line tuning was developed using the concept of estimation tracks. Estimation tracks allow the estimation gains to be selected from a finite set of possible values, while meeting Lyapunov stability requirements. The trade-off between sufficient excitation for learning and controller performance, typical for dual adaptive control techniques, are met by properly tuning the adaptation and filter gains to drive the rate of adaptation in response to a fixed excitation signal. Two methods for selecting the estimation track were developed. The first method uses simulations to predict the value of the bicriteria cost function that is a combination of prediction and feedback errors, to generate a performance score for each estimation track. The second method uses a linear matrix inequality formulation to find an upper bound on feedback error within the range of uncertainty of the plant parameters and acceptable reference signals. The linear matrix inequality approach was derived from a robust control approach. Numerical simulations were performed to systematically evaluate the performance and computational burden of configuration parameters, such as the number of estimation tracks used for tuning. Comparisons were performed for both tuning methods with an arbitrarily tuned adaptive controller, with arbitrarily selected tuning parameters as well as a common adaptive control algorithm.

Motor unit number estimation (MUNE) is an electrodiagnostic procedure used to estimate the number of MUs in a muscle. In this thesis, a new MUNE technique, called Automated MPS, has been developed to overcome the shortcomings of two current techniques, namely MPS and MUESA. This method can be summarized as follows. First, a muscle is stimulated with a train of constant intensity current pulses. Depending on various factors, one to three MUs activate probabilistically after each pulse, and several responses are collected. These collected responses should be divided into up to 2^n clusters, such that each cluster represents one possible combination of n Surface-detected Motor Unit Potentials (SMUPs). After clustering the collected responses, the average response of each cluster is calculated, the outliers are excluded, and similar groups are merged together. Then, depending on the number of response set groups, a decomposition technique is applied to the response clusters to obtain the $n$ constituent SMUPs. To estimate the number of MUs, the aforementioned process is repeated several times until enough SMUPs to calculate a reliable mean-SMUP are acquired. The number of MUs can then be determined by dividing the maximal compound muscle action potential (CMAP) size by the mean-SMUP size. The focus of this thesis was on using pattern recognition techniques to detect n SMUPs from a collected set of waveforms. Several experiments were performed using both simulated and real data to evaluate the ability of Automated MPS in finding the constituent SMUPs of a response set. Our experiments showed that performing Automated MPS needs less experience compared with MPS. Moreover, it can deal with more difficult situations and detect more accurate SMUPs compared with MUESA.

This dissertation deals with the channel estimation techniques for orthogonal frequency division multiplexing (OFDM) systems such as in IEEE 802.11. Although there has been a great amount of research in this area, characterization of typical wireless indoor environments and design of channel estimation schemes that are both robust and practical for such channel conditions have not been thoroughly investigated. It is well known that the minimum mean-square-error (MMSE) estimator provides the best mean-square-error (MSE) performance given a priori knowledge of channel statistics and operating signal-to-noise ratio (SNR). However, the channel statistics are usually unknown and the MMSE estimator has too much computational complexity to be realized in practical systems. In this work, we propose two simple channel estimation techniques: one that is based on modifying the channel correlation matrix from the MMSE estimator and the other one with averaging window based on the LS estimates. We also study the characteristics of several realistic indoor channel models that are of potential use for wireless local area networks (LANs). The first method, namely MMSE-exponential-Rhh, does not depend heavily on the channel statistics and yet offer performance improvement compared to that of the LS estimator. The simulation results also show that the second method, namely averaging window (AW) estimator, provides the best performance at moderate SNR range.

Reconstructing stature is at the core of providing information on unidentified human remains. This research shows that there are significant differences between modern populations and those used to create the most common stature estimation formulae. New formulae for the femur and fibula in males and females were created to provide accurate estimates for modern forensic cases. Additionally, a novel measurement of the femur is shown to be moderately correlated with stature and stature estimation formulae for this measurement are included.

In this thesis, we study certain aspects of signal source/target localization by sensory agents and their biomedical applications. We first focus on a generic distance measurement based problem: Estimation of the location of a signal source by a sensory agent equiped with a distance measurement unit or a team of such a sensory agent. This problem was addressed in some recent studies using a gradient based adaptive algorithm. In this study, we design a least-squares based adaptive algorithm with forgetting factor for the same task. Besides its mathematical background, we perform some simulations for both stationary and drifting target cases. The least-squares based algorithm we propose bears the same asymptotic stability and convergence properties as the gradient algorithm previously studied. It is further demonstrated via simulation studies that the proposed least-squares algorithm converges significantly faster to the resultant location estimates than the gradient algorithm for high values of the forgetting factor, and significantly reduces the noise effects for small values of the forgetting factor. We also focus on the problem of localizing a medical device/implant in human body by a mobile sensor unit (MSU) using distance measurements. As the particular distance measurement method, time of flight (TOF) based approach involving ultra wide-band signals is used, noting the important effects of the medium characteristics on this measurement method. Since human body consists of different organs and tissues, each with a different signal permittivity coefficient and hence a different signal propagation speed, one cannot assume a constant signal propagation speed environment for the aforementioned medical localization problem. Furthermore, the propagation speed is unknown. Considering all the above factors and utilizing a TOF based distance measurement mechanism, we use the proposed adaptive least-square algorithm to estimate the 3-D location of a medical device/implant in the human body. In the design of the adaptive algorithm, we first derive a linear parametric model with the unknown 3-D coordinates of the device/implant and the current signal propagation speed of the medium as its parameters. Then, based on this parametric model, we design the proposed adaptive algorithm, which uses the measured 3-D position of the MSU and the measured TOF as regressor signals. After providing a formal analysis of convergence properties of the proposed localization algorithm, we implement numerical tests to analyze the properties of the localization algorithm, considering two types of scenarios: (1) A priori information regarding the region, e.g quadrant (among upper-left, upper-right, lower-left, lower-right of the human body), of the implant location is available and (2) such a priori information is not available. In (1), assuming knowledge of fixed average relative permittivity for each region, we established that the proposed algorithm converges to an estimate with zero estimation error. Moreover, different white Gaussian noises are added to emulate the TOF measurement disturbances, and it is observed that the proposed algorithm is robust to such noises/disturbances. In (2), although perfect estimation is not achieved, the estimation error is at a low admissible level. In addition, for both cases (1) and (2), forgetting factor effects have been investigated and results show that use of small forgetting factor values reduces noise effects significantly, while use of high forgetting factor values speeds up convergence of the estimation.

Progressive developments in computing and sensor technologies during the past decades have enabled the formulation of increasingly advanced problems in statistical inference and signal processing. The thesis is concerned with statistical estimation methods, and is divided into three parts with focus on two different areas: sensor fusion and sparse signal processing. The first part introduces the well-established Bayesian, Fisherian and least-squares estimation frameworks, and derives new estimators. Specifically, the Bayesian framework is applied in two different classes of estimation problems: scenarios in which (i) the signal covariances themselves are subject to uncertainties, and (ii) distance bounds are used as side information. Applications include localization, tracking and channel estimation. The second part is concerned with the extraction of useful information from multiple sensors by exploiting their joint properties. Two sensor configurations are considered here: (i) a monocular camera and an inertial measurement unit, and (ii) an array of passive receivers. New estimators are developed with applications that include inertial navigation, source localization and multiple waveform estimation. The third part is concerned with signals that have sparse representations. Two problems are considered: (i) spectral estimation of signals with power concentrated to a small number of frequencies,and (ii) estimation of sparse signals that are observed by few samples, including scenarios in which they are linearly underdetermined. New estimators are developed with applications that include spectral analysis, magnetic resonance imaging and array processing. / <p>QC 20130426</p>

The classical parametric estimation approach, maximum likelihood, while providing maximally efficient estimators at the correct model, lacks robustness. As a modification of maximum likelihood, Huber (1964) introduced M-estimators, which are very general but often ad hoc. Basu et al. (1998) developed a family of density-based divergences, many of which exhibit robustness. It turns out that maximum likelihood is a special case of this general class of divergence functions, which are indexed by a parameter alpha. Basu noted that only values of alpha in the [0,1] range were of interest -- with alpha = 0 giving the maximum likelihood solution and alpha = 1 the L2E solution (Scott, 2001). As alpha increases, there is a clear tradeoff between increasing robustness and decreasing efficiency. This thesis develops a family of robust location and scale estimators by applying Basu's alpha-divergence function to a multivariate partial density component model (Scott, 2004). The usefulness of alpha values greater than 1 will be explored, and the new estimator will be applied to simulated cases and applications in parametric density estimation and regression.

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