Browsing by Subject "Bayesian Inference"
Now showing 1 - 5 of 5
Results Per Page
Sort Options
Item Bayesian wavelet approaches for parameter estimation and change point detection in long memory processes(Texas A&M University, 2005-11-01) Ko, KyungdukThe main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.Item Comparative Deterministic and Probabilistic Modeling in Geotechnics: Applications to Stabilization of Organic Soils, Determination of Unknown Foundations for Bridge Scour, and One-Dimensional Diffusion Processes(2013-08-08) Yousefpour, NeginThis study presents different aspects on the use of deterministic methods including Artificial Neural Networks (ANNs), and linear and nonlinear regression, as well as probabilistic methods including Bayesian inference and Monte Carlo methods to develop reliable solutions for challenging problems in geotechnics. This study addresses the theoretical and computational advantages and limitations of these methods in application to: 1) prediction of the stiffness and strength of stabilized organic soils, 2) determination of unknown foundations for bridges vulnerable to scour, and 3) uncertainty quantification for one-dimensional diffusion processes. ANNs were successfully implemented in this study to develop nonlinear models for the mechanical properties of stabilized organic soils. ANN models were able to learn from the training examples and then generalize the trend to make predictions for the stiffness and strength of stabilized organic soils. A stepwise parameter selection and a sensitivity analysis method were implemented to identify the most relevant factors for the prediction of the stiffness and strength. Also, the variations of the stiffness and strength with respect to each factor were investigated. A deterministic and a probabilistic approach were proposed to evaluate the characteristics of unknown foundations of bridges subjected to scour. The proposed methods were successfully implemented and validated by collecting data for bridges in the Bryan District. ANN models were developed and trained using the database of bridges to predict the foundation type and embedment depth. The probabilistic Bayesian approach generated probability distributions for the foundation and soil characteristics and was able to capture the uncertainty in the predictions. The parametric and numerical uncertainties in the one-dimensional diffusion process were evaluated under varying observation conditions. The inverse problem was solved using Bayesian inference formulated by both the analytical and numerical solutions of the ordinary differential equation of diffusion. The numerical uncertainty was evaluated by comparing the mean and standard deviation of the posterior realizations of the process corresponding to the analytical and numerical solutions of the forward problem. It was shown that higher correlation in the structure of the observations increased both parametric and numerical uncertainties, whereas increasing the number of data dramatically decreased the uncertainties in the diffusion process.Item Estimation and Detection of Multivariate Gene Regulatory Relationships(2013-09-18) Chen, TingThe Coefficient of Determination (CoD) plays an important role in Genomics problems, for instance, in the inference of gene regulatory networks from gene- expression data. However, the inference theory about CoD has not been investigated systematically. In this dissertation, we study the inference of discrete CoD from both frequentist and Bayesian perspectives, with its applications to system identification problems in Genomics. From a frequentist viewpoint, we provide a theoretical framework for CoD estimation by introducing nonparametric CoD estimators and parametric maximum-likelihood (ML) CoD estimators based on static and dynamical Boolean models. Inference algorithms are developed to discover gene regulatory relationships, and numerical examples are provided to validate preferable performance of the ML approach with access to sufficient prior knowledge. To make the applications of the CoD independent of user-selectable thresholds, we describe rigorous multiple testing procedures to investigate significant regulatory relation- ships among genes using the discrete CoD, and to discover canalyzing genes using the intrinsically multivariate prediction (IMP) criterion. We develop practical statistic tools that are open to the scientific community. On the other hand, we propose a Bayesian framework for the inference of the CoD across a parametrized family of joint distributions between target and predictors. Examples of applications of the Bayesian approach are provided against those of nonparametric and parametric approaches by using synthetic data. We have found that, with applications to system identification problems in Genomics, both parametric and Bayesian CoD estimation approaches outperform the nonparametric approaches. Hence, we conclude that parametric and Bayesian estimation approaches are preferred when we have partial knowledge about gene regulation. On the other hand, we have shown that the two proposed statistical testing frameworks can detect well-known gene regulation and canalyzing genes like p53 and DUSP1 from real data sets, respectively. This indicates that our methodology could serve as a promising tool for the detection of potential gene regulatory relationships and canalyzing genes. In one word, this dissertation is intended to serve as foundation for a detailed study of applications of CoD estimation in Genomics and related fields.Item Investigation of Genomic Estimated Breeding Values and Association Methodologies using Bayesian Inference in a Nellore-Angus Crossbred Population for Two Traits(2013-05-15) Hulsman, Lauren LoreneThe objectives of this study were to 1) evaluate marker associations for genomic regions of interest and significant ontology terms, 2) evaluate and compare 4 models for their efficacy in predicting genetic merit, 3) evaluate and compare the impact of using breed-of-origin genotypes in a Bayesian prediction model, and 4) evaluate the effects of data partitioning using family structure on predictions. Nellore-Angus F2, F3 and half-sibling calves were used with records for overall temperament at weaning (OTW; a subjective scoring system; n = 769) and Warner-Bratzler shear force (WBSF; a measure of tenderness; n = 389). After filtering, 34,913 markers were available for use. Bayesian methods employed were BayesB (using ?) and BayesC (using ? = 0 and ?) in GenSel software, where, after estimation, ? ? = 0.995 or 0.997 for WBSF or OTW, respectively. No regions associated with either trait were found using ? ?, but when ? = 0 associated regions were identified (37 and 147 regions for OTW and WBSF, respectively). Comparison of genomic estimated breeding values from these 3 Bayesian models to an animal model showed that BayesC procedures (using ?) had the highest accuracy for both traits, but that BayesB had the lowest indication of bias in either case. Using a subset of the population (n = 440), genotypes based on the breed in which the alleles originated from (i.e., breed-of-origin genotypes) were assigned to markers mapped to autosomes (n = 34,449), and incorporated into prediction analyses using BayesB (? ? = 0.997) with or without nucleotide-based genotypes. In either case, there was an increase in accuracy when breed-of-origin genotypes were incorporated into prediction analyses. Data partitions based on family structure resulted in 13 distinct training and validations groups. Relationship of individuals in the training with validation individuals did have an impact in some cases, but not all. There was poor prediction of genomic estimated breeding values for individuals in the validation population using BayesB methods, but performed better in all cases than breeding values generated using an animal model. Future studies incorporating breed-of-origin genotypes are of interest to determine if accuracy is improved in these groups.