In this thesis, a mixture-model cluster analysis technique under different covariance structures of the component densities is developed and presented, to capture the compactness, orientation, shape, and the volume of component clusters in one expert system to handle Gaussian high dimensional heterogeneous data sets to achieve flexibility in currently practiced cluster analysis techniques. Two approaches to parameter estimation are considered and compared; one using the Expectation-Maximization (EM) algorithm and another following a Bayesian framework using the Gibbs sampler. We develop and score several forms of the ICOMP criterion of Bozdogan (1994, 2004) as our fitness function; to choose the number of component clusters, to choose the correct component covariance matrix structure among nine candidate covariance structures, and to select the optimal parameters and the best fitting mixture-model. We demonstrate our approach on simulated datasets and a real large data set, focusing on early detection of breast cancer. We show that our approach improves the probability of classification error over the existing methods.

In this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.

In this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.

Many prior distributions are suggested for variance parameters in the hierarchical model. The “Non-informative” interval of the conjugate inverse-gamma prior might cause problems. I consider three priors – conjugate inverse-gamma, log-normal and truncated normal for the variance parameters and do the numerical analysis on Gelman’s 8-schools data. Then with the posterior draws, I compare the Bayesian credible intervals of parameters using the three priors. I use predictive distributions to do predictions and then discuss the differences of the three priors suggested. / text

Time series involving count data are present in a wide variety of applications. In many applications, the observed counts are usually small and dependent. Failure to take these facts into account can lead to misleading inferences and may detect false relationships. To tackle such issues, a Poisson parameter-driven model is assumed for the time series at hand. This model can account for the time dependence between observations through introducing an autoregressive latent process. In this thesis, we consider Bayesian approaches for estimating the Poisson parameter-driven model. The main challenge is that the likelihood function for the observed counts involves a high dimensional integral after integrating out the latent variables. The main contributions of this thesis are threefold. First, I develop a new single-move (SM) Markov chain Monte Carlo (MCMC) method to sample the latent variables one by one. Second, I adopt the idea of the particle Gibbs sampler (PGS) method \citep{andrieu} into our model setting and compare its performance with the SM method. Third, I consider Bayesian composite likelihood methods and compare three different adjustment methods with the unadjusted method and the SM method. The comparisons provide a practical guide to what method to use. We conduct simulation studies to compare the latter two methods with the SM method. We conclude that the SM method outperforms the PGS method for small sample size, while they perform almost the same for large sample size. However, the SM method is much faster than the PGS method. The adjusted Bayesian composite methods provide closer results to the SM than the unadjusted one. The PGS and the selected adjustment method from simulation studies are compared with the SM method via a real data example. Similar results are obtained: first, the PGS method provides results very close to those of the SM method. Second, the adjusted composite likelihood methods provide closer results to the SM than the unadjusted one.

In this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.

In this thesis, we discuss some topics in random matrix theory which have applications to probability, statistics and quantum information theory. In Chapter 2, by relying on the spectral properties of an associated adjacency matrix, we find the distribution of the maximum of a Dyck path and show that it has the same distribution function as the unsigned Brownian excursion which was first derived in 1976 by Kennedy. We obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung, Kennedy and Khorunzhiy and Marckert. In Chapter 3, we discuss a method of sampling called the Gibbs-slice sampler. This method is based on Neal's slice sampling combined with Gibbs sampling. In Chapter 4, we discuss several examples which have applications in physics and quantum information theory.

One of the most significant changes in the evolution of modern business management is that organizations no longer compete as individual entities in the market, but as interlocking supply chains. Markets are no longer simply trading desks but dynamic ecosystems where people, organizations and the environment interact. Products and associated materials and resources are links that bridge supply chains from upstream (sourcing and manufacturing) to downstream (delivering and consuming). The lifecycle of a product plays a critical role in supply chains. Supply chains may be composed by, designed around, and modified for products. Product-related issues greatly impact supply chains. Existing studies have advanced product management and product lifecycle management literature through dimensions of product innovation, product growth, product line extensions, product efficiencies, and product acquisition. Product deletion, rationalization, or reduction research is limited but is a critical issue for many reasons. Sustainability is an important reason for this managerial decision. This study, grounded from multiple literature streams in both marketing and supply chain fields, identified relations and propositions to form a firm-level analysis on the role of supply chains in organizational product deletion decisions. Interviews, observational and archival data from international companies (i.e.: Australia, China, India, and Iran) contributed to the empirical support as case studies through a grounded theory approach. Bayesian analysis, an underused empirical analysis tool, was utilized to provide insights into this underdeveloped research stream; and its relationship to qualitative research enhances broader methodological understanding. Gibbs sampler and reversible jump Markov chain Monte Carlo (MCMC) simulation were used for Bayesian analysis based on collected data. The integrative findings are exploratory but provide insights for a number of research propositions.

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Over the past decade of accounting and finance research, the Ohlson (1995) model has been widely adopted as a framework for stock price prediction. While using the accounting data of 391 companies from SP500 in this paper, Bayesian statistical techniques are adopted to enhance both the estimative and predictive qualities of the Ohlson model comparing to the classical approaches. Specifically, the classical methods are used for the exploratory data analysis and then the Bayesian strategies are applied using Markov chain Monte Carlo method in three stages: individual analysis for each company, grouping analysis for each group and adaptive analysis by pooling information across companies. The base data, which consist of 20 quarters' observations starting from the first quarter of 1998, are used to make inferences for the regression coefficients (or parameters), evaluate the model adequacy and predict the stock price for the first quarter of 2004, when the real observations are set as the test data to evaluate the predictive ability of the Ohlson model. The results are averaged within each specified group categorized via the general industrial classification (GIC). The empirical results show that classical models result in larger stock price prediction errors, more positively-biased predictions and have much smaller explanatory powers than Bayesian models. A few transformations of both classical and Bayesian models are also performed in this paper, however, transformations of the classical models do not outweigh the usefulness of applying Bayesian statistics.