Bioinformatics applications can address the transfer of information at several stages of the central dogma of molecular biology, including transcription and translation. This dissertation focuses on using Bayesian models to interpret biological data in bioinformatics, using Markov chain Monte Carlo (MCMC) for the inference method. First, we use our approach to interpret data at the transcription level. We propose a two-level hierarchical Bayesian model for variable selection on cDNA Microarray data. cDNA Microarray quantifies mRNA levels of a gene simultaneously so has thousands of genes in one sample. By observing the expression patterns of genes under various treatment conditions, important clues about gene function can be obtained. We consider a multivariate Bayesian regression model and assign priors that favor sparseness in terms of number of variables (genes) used. We introduce the use of different priors to promote different degrees of sparseness using a unified two-level hierarchical Bayesian model. Second, we apply our method to a problem related to the translation level. We develop hidden Markov models to model linker/non-linker sequence regions in a protein sequence. We use a linker index to exploit differences in amino acid composition between regions from sequence information alone. A goal of protein structure prediction is to take an amino acid sequence (represented as a sequence of letters) and predict its tertiary structure. The identification of linker regions in a protein sequence is valuable in predicting the three-dimensional structure. Because of the complexities of both models encountered in practice, we employ the Markov chain Monte Carlo method (MCMC), particularly Gibbs sampling (Gelfand and Smith, 1990) for the inference of the parameter estimation.

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This thesis studies realized volatility (RV), implied volatility (IV) and their applications in stochastic volatility models. The first essay uses both daytime and overnight high-frequency price data for equity index futures to estimate the RV of the S\&P500 and NASDAQ 100 indexes. Empirical results reveal strong inter-correlation between the regular-trading-time and after-hour RVs, as well as a significant predictive power of overnight RV on daytime RV and vice versa. We propose a new day-night realized stochastic volatility (DN-SV-RV) model, where the daytime and overnight returns are jointly modeled with their RVs, and their latent volatilities are correlated. The newly proposed DN-SV-RV model has the best out-of-sample return distribution forecasts among the models considered. The second essay extends the realized stochastic volatility model by jointly estimating return, RV and IV. We examine how RV and IV enhance the estimation of the latent volatility process for both the S\&P500 index and individual stocks. The third essay re-examines asymmetric stochastic volatility (ASV) models with different return-volatility correlation structures given RV and IV. We show by simulation that estimating the ASV models with return series alone may infer erroneous estimations of the correlation coefficients. The incorporation of volatility measures helps identify the true return-volatility correlation within the ASV framework. Empirical evidence on global equity market indices verifies that ASV models with additional volatility measures not only obtain significantly different estimations of the correlations compared to the benchmark ASV models, but also improve out-of-sample return forecasts. / Thesis / Doctor of Philosophy (PhD)

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific and time-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects. / Series: Working Papers in Regional Science

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects. / Series: Working Papers in Regional Science

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time invariant factors such as socio-cultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects. / Series: Working Papers in Regional Science

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The objective of this project is to fit a sequence of increasingly complex zero-inflated censored regression models to a known data set. It is quite common to find censored count data in statistical analyses of health-related data. Modeling such data while ignoring the censoring, zero-inflation, and overdispersion often results in biased parameter estimates. This project develops various regression models that can be used to predict a count response variable that is affected by various predictor variables. The regression parameters are estimated with Bayesian analysis using a Markov chain Monte Carlo (MCMC) algorithm. The tests for model adequacy are discussed and the models are applied to an observed data set.