This thesis considers likelihood inferences for generalized linear models with additional random effects. The likelihood function involved ordinarily cannot be evaluated in closed form and numerical integration is needed. The theme of the thesis is a closed-form approximation based on Laplace's method. We first consider a special yet important case of the above general setting -- the Mantel-Haenszel-type model with overdispersion. It is seen that the Laplace approximation is very accurate for likelihood inferences in that setting. The approach and results on accuracy apply directly to the more general setting involving multiple parameters and covariates. Attention is then given to how to maximize out nuisance parameters to obtain the profile likelihood function for parameters of interest. In evaluating the accuracy of the Laplace approximation, we utilized Gauss-Hermite quadrature. Although this is commonly used, it was found that in practice inadequate thought has been given to the implementation. A systematic method is proposed for transforming the variable of integration to ensure that the Gauss-Hermite quadrature is effective. We found that under this approach the Laplace approximation is a special case of the Gauss-Hermite quadrature. / Graduation date: 1994

In the application of cycle-to-cycle control to manufacturing processes, the model of the process reduces to a gain matrix and a pure delay. For a general multiple input – multiple output process, this matrix shows the degree of influence each input has on each output. For a system of high order, determining this gain matrix requires excessive numbers of experiments to be performed, and thus a simplified, but non-ideal form for the gain matrix must be developed. In this paper, the model takes the form of a Gaussian distribution with experimentally determined standard deviation and scaling coefficients. Discrete die sheet metal forming, a multiple input-multiple output process with high dimensionality, is chosen as a test application. Results of the prediction capabilities of the Gaussian model, as well as those of two previously existing models, are presented. It is shown that the Gaussian distribution model does the best job of predicting the output for a given input. The model’s invariance over a set of different formed parts is also presented. However, as shown in the companion paper on cycle-to-cycle control, the errors inherent in this model will cause non-ideal performance of the resulting control system. However, this model appears to be the best form for this problem, given the limit of minimal experimentation. / Singapore-MIT Alliance (SMA)

Julian J. Bussgang. / "March 26, 1952." / Bibliography: p. 14. / Army Signal Corps Contract DA36-039 sc-100, Project no. 8-102B-0. Dept. of the Army Project no. 3-99-10-022.

This paper discusses the relationship between the shape of the shading, the surface whose depth at each point equals the brightness in the image, and the shape of the original surface. I suggest the shading as an initial local approximation to shape, and discuss the scope of this approximation and what it may be good for. In particular, qualitative surface features, such as the sign of the Gaussian curvature, can be computed in some cases directly from the shading. Finally, a method to compute the direction of the illuminant (assuming a single point light source) from shading on occluding contours is shown.

Local descriptors are increasingly used for the task of object recognition because of their perceived robustness with respect to occlusions and to global geometrical deformations. We propose a performance criterion for a local descriptor based on the tradeoff between selectivity and invariance. In this paper, we evaluate several local descriptors with respect to selectivity and invariance. The descriptors that we evaluated are Gaussian derivatives up to the third order, gray image patches, and Laplacian-based descriptors with either three scales or one scale filters. We compare selectivity and invariance to several affine changes such as rotation, scale, brightness, and viewpoint. Comparisons have been made keeping the dimensionality of the descriptors roughly constant. The overall results indicate a good performance by the descriptor based on a set of oriented Gaussian filters. It is interesting that oriented receptive fields similar to the Gaussian derivatives as well as receptive fields similar to the Laplacian are found in primate visual cortex.

L'objectif de ce travail de recherche est l'étude des posibilités offertes par une nouvelle approche de l'information quantique basée sur des variables quantiques continues. Lorsque ces variables continues sont portées par le champs éléctromagnétique, un grand nombre de protocoles d'information quantique peuvent être implémentés à l'aide de lasers et d'éléments d'optique linéaire standards. Cette simplicité expérimentale rend cette approche très intéressantes d'un point de vue pratique, en particulier pour le développement des futurs réseaux de communications quantiques. Le travail peut se diviser en deux parties complémentaires. Dans la première partie, plus fondamentale, la relation complexe qui existe entre l'intrication et la nonlocalité de la mécanique quantique est étudiée sur base des variables optiques continues. Ces deux ressources étant essentielles pour l'information quantique, il est nécessaire de bien les comprendre et de bien les caractériser. Dans la seconde partie, orientée vers des applications concrètes, le problème de la correction d'erreur à variables continues est étudié. Pouvoir transmettre et manipuler l'information sans erreurs est nécessaire au bon développemnent de l'information quantique, mais, en pratique, les erreurs sont inévitables. Les codes correcteurs d'erreurs permettent de détecter et corriger ces erreures de manière efficace.

In this report we describe simulation of the surface current density on a PEC cylinder and the diffracted field for a line source above a finite PEC ground plane as a means to verify the Nero2D program. The results are compared with the exact solution and give acceptable errors. A terrain model for a communication link is studied in the report and we simulate the wave propagation for terrain with irregular shapes and different materials. The Nero2D program is based on the fast multipole method (FMM) to reduce computation time and memory. Gaussian sources are also studied to make the terrain model more realistic

We propose Bayesian methods for estimating the precision matrix in Gaussian graphical models. The methods lead to sparse and adaptively shrunk estimators of the precision matrix, and thus conduct model selection and estimation simultaneously. Our methods are based on selection and shrinkage priors leading to parsimonious parameterization of the precision (inverse covariance) matrix, which is essential in several applications in learning relationships among the variables. In Chapter I, we employ the Laplace prior on the off-diagonal element of the precision matrix, which is similar to the lasso model in a regression context. This type of prior encourages sparsity while providing shrinkage estimates. Secondly we introduce a novel type of selection prior that develops a sparse structure of the precision matrix by making most of the elements exactly zero, ensuring positive-definiteness. In Chapter II we extend the above methods to perform classification. Reverse-phase protein array (RPPA) analysis is a powerful, relatively new platform that allows for high-throughput, quantitative analysis of protein networks. One of the challenges that currently limits the potential of this technology is the lack of methods that allows for accurate data modeling and identification of related networks and samples. Such models may improve the accuracy of biological sample classification based on patterns of protein network activation, and provide insight into the distinct biological relationships underlying different cancers. We propose a Bayesian sparse graphical modeling approach motivated by RPPA data using selection priors on the conditional relationships in the presence of class information. We apply our methodology to an RPPA data set generated from panels of human breast cancer and ovarian cancer cell lines. We demonstrate that the model is able to distinguish the different cancer cell types more accurately than several existing models and to identify differential regulation of components of a critical signaling network (the PI3K-AKT pathway) between these cancers. This approach represents a powerful new tool that can be used to improve our understanding of protein networks in cancer. In Chapter III we extend these methods to mixtures of Gaussian graphical models for clustered data, with each mixture component being assumed Gaussian with an adaptive covariance structure. We model the data using Dirichlet processes and finite mixture models and discuss appropriate posterior simulation schemes to implement posterior inference in the proposed models, including the evaluation of normalizing constants that are functions of parameters of interest which are a result of the restrictions on the correlation matrix. We evaluate the operating characteristics of our method via simulations, as well as discuss examples based on several real data sets.

Livestock odour has been an obstacle for the development of livestock industry. Air dispersion models have been applied to predict odour concentrations downwind from the livestock operations. However, most of the air dispersion models were designed for industry pollutants and can only predict hourly average concentrations of pollutants. Currently, a livestock odour dispersion model that can consider the difference between livestock odour and traditional air pollutants and can account for the short time fluctuations is not available. Therefore, the objective of this research was to develop a dispersion model that is designed specifically for livestock odour and is able to consider the short time odour concentration fluctuations. A livestock odour dispersion model (LODM) was developed based on Gaussian fluctuating plume theory to account for odour instantaneous fluctuations. The model has the capability to predict mean odour concentration, instantaneous odour concentration, peak odour concentration and the frequency of odour concentration that is equal to or above a certain level with the input of hourly routine meteorological data.<p> LODM predicts odour frequency by a weighted odour exceeding half width method. A simple and effective method is created to estimate the odour frequency from multiple sources. Both Pasquill-Gifford and Hogstr¨¯m dispersion coefficients are applied in this model. The atmospheric condition is characterized by some derived parameters including friction velocity, sensible heat flux, M-O length, and mixing height. An advanced method adapted from AERMOD model is applied to derive these parameters. An easy to use procedure is generated and utilized to deal with the typical meteorological data input as ISC met file. LODM accepts and only requires routine meteorological data. It has the ability to process individual or multiple sources which could be elevated point sources, ground level sources, livestock buildings, manure storages, and manure land applications. It can also deal with constant and varied emission rates. Moreover, the model considers the relationships between odour intensity and odour concentrations in the model. Finally, the model is very easy to use with a friendly interface.<p> Model evaluations and validations against field plume measurement data and ISCST3 and CALPUFF models indicate that LODM can achieve fairly good odour concentration and odour frequency predictions. The sensitivity analyses demonstrate a medium sensitivity of LODM to the controllable odour source parameters, such as stack height, diameter, exit velocity, exit temperature, and emission rate. This shows that the model has a great potential for application on resolving odour issues from livestock operations. From that perspective, the most effective way to reduce odour problems from livestock buildings is to lessen the odour emission rate (e.g. biofiltration of exhaust air, diet changes).

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