This thesis is concerned with graphical Gaussian models with equality constraints on the concentration or partial correlation matrix introduced by Højsgaard and Lauritzen (2008) as RCON and RCOR models. The models can be represented by vertex and edge coloured graphs G = (V,ε), where parameters associated with equally coloured vertices or edges are restricted to being identical. In the first part of this thesis we study the problem of estimability of a non-zero model mean μ if the covariance structure Σ is restricted to satisfy the constraints of an RCON or RCOR model but is otherwise unknown. Exploiting results in Kruskal (1968), we obtain a characterisation of suitable linear spaces Ω such that if Σ is restricted as above, the maximum likelihood estimator μ(with circumflex) and the least squares estimator μ* of μ coincide for μ ∈ Ω, thus allowing μ and Σ to be estimated independently. For the special case of Ω being specified by equality relations among the entries of μ according to a partition M of the model variables V, our characterisation translates into a necessary and sufficient regularity condition on M and (V,ε). In the second part we address model selection of RCON and RCOR models. Due to the large number of models, we study the structure of four model classes lying strictly within the sets of RCON and RCOR models, each of which is defined by desirable statistical properties corresponding to colouring regularity conditions. Two of these appear in Højsgaard and Lauritzen (2008), while the other two arise from the regularity condition ensuring equality of estimators μ(with circumflex) = μ* we find in the first part. We show each of the colouring classes to form complete lattices, which qualifies the corresponding model spaces for an Edwards-Havránek model selection procedure (Edwards and Havránek, 1987). We develop a coresponding algorithm for one of the model classes and give an algorithm for a systematic search in accordance with the Edwards-Havránek principles for a second class. Both are applied to data sets previously analysed in the literature, with very encouraging performances.

Salient contour detection is an important lowlevel visual process in the human visual system, and has significance towards understanding higher visual and cognitive processes. Salience detection can be investigated by examining the visual cortical response to visual input. Visual response activity in the early stages of visual processing can be approximated by a sequence of convolutions of the input scene with the difference-of-Gaussian (DoG) and the oriented Gabor filters. The filtered responses are unusually high for prominent edge locations in the image, and are uniformly similar across different natural image inputs. Furthermore, such a response follows a power law distribution. The aim of this thesis is to examine how these response properties could be utilized to the problem of salience detection. First, I identify a method to find the best threshold on the response activity (orientation energy) toward the detection of salient contours: compare the response distribution to a Gaussian distribution of equal variance. Second, I justify this comparison by providing an explanation under the framework of Suspicious Coincidence proposed by Barlow [1]. A connection is provided between perceived salience of contours and the neuronal goal of detecting suspiciousness, where salient contours are seen as affording suspicious coincidences by the visual system. Finally, the neural plausibility of such a salience detection mechanism is investigated, and the representational effciency is shown which could potentially explain why the human visual system can effortlessly detect salience.

Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.

Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.

Salient contour detection is an important lowlevel visual process in the human visual system, and has significance towards understanding higher visual and cognitive processes. Salience detection can be investigated by examining the visual cortical response to visual input. Visual response activity in the early stages of visual processing can be approximated by a sequence of convolutions of the input scene with the difference-of-Gaussian (DoG) and the oriented Gabor filters. The filtered responses are unusually high for prominent edge locations in the image, and are uniformly similar across different natural image inputs. Furthermore, such a response follows a power law distribution. The aim of this thesis is to examine how these response properties could be utilized to the problem of salience detection. First, I identify a method to find the best threshold on the response activity (orientation energy) toward the detection of salient contours: compare the response distribution to a Gaussian distribution of equal variance. Second, I justify this comparison by providing an explanation under the framework of Suspicious Coincidence proposed by Barlow [1]. A connection is provided between perceived salience of contours and the neuronal goal of detecting suspiciousness, where salient contours are seen as affording suspicious coincidences by the visual system. Finally, the neural plausibility of such a salience detection mechanism is investigated, and the representational effciency is shown which could potentially explain why the human visual system can effortlessly detect salience.

This thesis investigates the design and implementation strategies for a Taiwanese speech recognition system. It adopts a 4 plus 1¡]five times¡^recording strategy, where the 1st four recordings are used for speech feature training and the last recording for speech recognition simulation. Mel-frequency cepstrum coefficients and hidden Markov model are used as the feature model and the recognition model respectively. Under the Intel Celeron 2.4 GHz personal computer and Red Hat Linux 9.0 operating system environment, a correct phrase recognition rate of 90% can be reached for a 4200 Taiwanese phrase database.

Tez (Yüksek Lisans) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, Fizik Anabilim Dalı, 2008. / Kaynakça var.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Also issued in print. Includes bibliographical references (leaves 81-84). Available via ProQuest Digital Dissertations.

Problem of the dissertation. The Gaussian random values are very common in practice, because if a random value depends on many additive factors, according to the Central Limit Theorem (if particular conditions are satisfied), the sum is approximately from Gaussian distribution. If the observed random value belongs to one of the several classes, it is from the Gaussian distribution mixture model. The mixtures of the Gaussian distributions are common in various fields: biology, medicine, astronomy, military science and many others. The most important statistical problems are problems of mixture identification and data clustering. In case of high data dimension, these tasks are not completely solved. The new parameter estimation of the multivariate Gaussian distribution mixture model and data clustering methods are proposed and analysed in the dissertation. Since it is much easier to solve these problems in univariate case, the projection-based approach is used. The aim of the dissertation. The aim of this work is the development of constructive algorithms for distribution analysis and clustering of data from the mixture model of the Gaussian distributions.

Problem of the dissertation. The Gaussian random values are very common in practice, because if a random value depends on many additive factors, according to the Central Limit Theorem (if particular conditions are satisfied), the sum is approximately from Gaussian distribution. If the observed random value belongs to one of the several classes, it is from the Gaussian distribution mixture model. The mixtures of the Gaussian distributions are common in various fields: biology, medicine, astronomy, military science and many others. The most important statistical problems are problems of mixture identification and data clustering. In case of high data dimension, these tasks are not completely solved. The new parameter estimation of the multivariate Gaussian distribution mixture model and data clustering methods are proposed and analysed in the dissertation. Since it is much easier to solve these problems in univariate case, the projection-based approach is used. The aim of the dissertation. The aim of this work is the development of constructive algorithms for distribution analysis and clustering of data from the mixture model of the Gaussian distributions.