Browsing by Subject "Bayesian"
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Item A Production Characterization of the Eagle Ford Shale, Texas - A Bayesian Analysis Approach(2015-01-29) Moridis, Nefeli GWe begin this research by asking "can we better estimate reserves in unconventional reservoirs using Bayes' theorem?" To attempt to answer this question, we obtained data for 68 wells in the Greater Core of the Eagle Ford Shale, Texas. As process, we eliminated the wells that did not have enough data, that did not show a production decline and/or wells that had too much data noise (this left us with 8 wells for analysis). We next performed decline curve analysis (DCA) using the Modified Hyperbolic (MH) and Power-Law Exponential (PLE) models (the two most common DCA models), consisting in user-guided analysis software. Then, the Bayesian paradigm was implemented to calibrate the same two models on the same set of wells. The primary focus of the research was the implementation of the Bayesian paradigm on the 8 well data set. We first performed a "best fit" parameter estimation using least squares optimization, which provided an optimized set of parameters for the two decline curve models. This was followed by using the Markov Chain Monte Carlo (MCMC) integration of the Bayesian posterior function for each model, which provided a full probabilistic description of its parameters. This allowed for the simulation of a number of likely realizations of the decline curves, from which first order statistics were computed to provide a confidence metric on the calibration of each model as applied to the production data of each well. Results showed variation on the calibration of the MH and PLE models. The forward models (MH and PLE) either over- or underestimate the reserves compared with the Bayesian calibrations, proving that the Bayesian paradigm was able to capture a more accurate trend of the data and thus able to determine more accurate estimates of reserves. In industry, the same decline curve models are used for unconventional wells as for conventional wells, even though we know that the same models may not apply. Based on the proposed results, we believe that Bayesian inference yields more accurate estimates of reserves for unconventional reservoirs than deterministic DCA methods. Moreover, it provides a measure of confidence on the prediction of production as as function of varying data and varying decline curve models.Item An efficient Bayesian formulation for production data integration into reservoir models(Texas A&M University, 2005-02-17) Leonardo, Vega VelasquezCurrent techniques for production data integration into reservoir models can be broadly grouped into two categories: deterministic and Bayesian. The deterministic approach relies on imposing parameter smoothness constraints using spatial derivatives to ensure large-scale changes consistent with the low resolution of the production data. The Bayesian approach is based on prior estimates of model statistics such as parameter covariance and data errors and attempts to generate posterior models consistent with the static and dynamic data. Both approaches have been successful for field-scale applications although the computational costs associated with the two methods can vary widely. This is particularly the case for the Bayesian approach that utilizes a prior covariance matrix that can be large and full. To date, no systematic study has been carried out to examine the scaling properties and relative merits of the methods. The main purpose of this work is twofold. First, we systematically investigate the scaling of the computational costs for the deterministic and the Bayesian approaches for realistic field-scale applications. Our results indicate that the deterministic approach exhibits a linear increase in the CPU time with model size compared to a quadratic increase for the Bayesian approach. Second, we propose a fast and robust adaptation of the Bayesian formulation that preserves the statistical foundation of the Bayesian method and at the same time has a scaling property similar to that of the deterministic approach. This can lead to orders of magnitude savings in computation time for model sizes greater than 100,000 grid blocks. We demonstrate the power and utility of our proposed method using synthetic examples and a field example from the Goldsmith field, a carbonate reservoir in west Texas. The use of the new efficient Bayesian formulation along with the Randomized Maximum Likelihood method allows straightforward assessment of uncertainty. The former provides computational efficiency and the latter avoids rejection of expensive conditioned realizations.Item Applied statistical modeling of three-dimensional natural scene data(2014-05) Su, Che-Chun; Bovik, Alan C. (Alan Conrad), 1958-; Cormack, Lawrence K.Natural scene statistics (NSS) have played an increasingly important role in both our understanding of the function and evolution of the human vision system, and in the development of modern image processing applications. Because depth/range, i.e., egocentric distance, is arguably the most important thing a visual system must compute (from an evolutionary perspective), the joint statistics between natural image and depth/range information are of particular interest. However, while there exist regular and reliable statistical models of two-dimensional (2D) natural images, there has been little work done on statistical modeling of natural luminance/chrominance and depth/disparity, and of their mutual relationships. One major reason is the dearth of high-quality three-dimensional (3D) image and depth/range database. To facilitate research progress on 3D natural scene statistics, this dissertation first presents a high-quality database of color images and accurately co-registered depth/range maps using an advanced laser range scanner mounted with a high-end digital single-lens reflex camera. By utilizing this high-resolution, high-quality database, this dissertation performs reliable and robust statistical modeling of natural image and depth/disparity information, including new bivariate and spatial oriented correlation models. In particular, these new statistical models capture higher-order dependencies embedded in spatially adjacent bandpass responses projected from natural environments, which have not yet been well understood or explored in literature. To demonstrate the efficacy and effectiveness of the advanced NSS models, this dissertation addresses two challenging, yet very important problems, depth estimation from monocular images and no-reference stereoscopic/3D (S3D) image quality assessment. A Bayesian depth estimation framework is proposed to consider the canonical depth/range patterns in natural scenes, and it forms priors and likelihoods using both univariate and bivariate NSS features. The no-reference S3D image quality index proposed in this dissertation exploits new bivariate and correlation NSS features to quantify different types of stereoscopic distortions. Experimental results show that the proposed framework and index achieve superior performance to state-of-the-art algorithms in both disciplines.Item Assessment of Eagle Ford Shale Oil and Gas Resources(2013-07-30) Gong, XinglaiThe Eagle Ford play in south Texas is currently one of the hottest plays in the United States. In 2012, the average Eagle Ford rig count (269 rigs) was 15% of the total US rig count. Assessment of the oil and gas resources and their associated uncertainties in the early stages is critical for optimal development. The objectives of my research were to develop a probabilistic methodology that can reliably quantify the reserves and resources uncertainties in unconventional oil and gas plays, and to assess Eagle Ford shale oil and gas reserves, contingent resources, and prospective resources. I first developed a Bayesian methodology to generate probabilistic decline curves using Markov Chain Monte Carlo (MCMC) that can quantify the reserves and resources uncertainties in unconventional oil and gas plays. I then divided the Eagle Ford play from the Sligo Shelf Margin to the San Macros Arch into 8 different production regions based on fluid type, performance and geology. I used a combination of the Duong model switching to the Arps model with b = 0.3 at the minimum decline rate to model the linear flow to boundary-dominated flow behavior often observed in shale plays. Cumulative production after 20 years predicted from Monte Carlo simulation combined with reservoir simulation was used as prior information in the Bayesian decline-curve methodology. Probabilistic type decline curves for oil and gas were then generated for all production regions. The wells were aggregated probabilistically within each production region and arithmetically between production regions. The total oil reserves and resources range from a P_(90) of 5.3 to P_(10) of 28.7 billion barrels of oil (BBO), with a P_(50) of 11.7 BBO; the total gas reserves and resources range from a P_(90) of 53.4 to P_(10) of 313.5 trillion cubic feet (TCF), with a P_(50) of 121.7 TCF. These reserves and resources estimates are much higher than the U.S. Energy Information Administration?s 2011 recoverable resource estimates of 3.35 BBO and 21 TCF. The results of this study provide a critical update on the reserves and resources estimates and their associated uncertainties for the Eagle Ford shale formation of South Texas.Item Automatic history matching in Bayesian framework for field-scale applications(Texas A&M University, 2006-04-12) Mohamed Ibrahim Daoud, AhmedConditioning geologic models to production data and assessment of uncertainty is generally done in a Bayesian framework. The current Bayesian approach suffers from three major limitations that make it impractical for field-scale applications. These are: first, the CPU time scaling behavior of the Bayesian inverse problem using the modified Gauss-Newton algorithm with full covariance as regularization behaves quadratically with increasing model size; second, the sensitivity calculation using finite difference as the forward model depends upon the number of model parameters or the number of data points; and third, the high CPU time and memory required for covariance matrix calculation. Different attempts were used to alleviate the third limitation by using analytically-derived stencil, but these are limited to the exponential models only. We propose a fast and robust adaptation of the Bayesian formulation for inverse modeling that overcomes many of the current limitations. First, we use a commercial finite difference simulator, ECLIPSE, as a forward model, which is general and can account for complex physical behavior that dominates most field applications. Second, the production data misfit is represented by a single generalized travel time misfit per well, thus effectively reducing the number of data points into one per well and ensuring the matching of the entire production history. Third, we use both the adjoint method and streamline-based sensitivity method for sensitivity calculations. The adjoint method depends on the number of wells integrated, and generally is of an order of magnitude less than the number of data points or the model parameters. The streamline method is more efficient and faster as it requires only one simulation run per iteration regardless of the number of model parameters or the data points. Fourth, for solving the inverse problem, we utilize an iterative sparse matrix solver, LSQR, along with an approximation of the square root of the inverse of the covariance calculated using a numerically-derived stencil, which is broadly applicable to a wide class of covariance models. Our proposed approach is computationally efficient and, more importantly, the CPU time scales linearly with respect to model size. This makes automatic history matching and uncertainty assessment using a Bayesian framework more feasible for large-scale applications. We demonstrate the power and utility of our approach using synthetic cases and a field example. The field example is from Goldsmith San Andres Unit in West Texas, where we matched 20 years of production history and generated multiple realizations using the Randomized Maximum Likelihood method for uncertainty assessment. Both the adjoint method and the streamline-based sensitivity method are used to illustrate the broad applicability of our approach.Item Bayesian Gaussian Graphical models using sparse selection priors and their mixtures(2012-10-19) Talluri, RajeshWe 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.Item Bayesian hierarchical linear modeling of NFL quarterback rating(2015-05) Hernandez, Steven V.; Walker, Stephen G., 1945-; Mahometa, Michael JWith endless amounts of statistics in American football, there are numerous ways to evaluate quarterback performance in the National Football League. Owners, general managers, and coaches are always looking for ways to improve quarterback play to increase overall team performance. In doing so, one may ask: Does the performance in the first quarter have any effect on the fourth quarter performance? This paper will investigate the linear dependence of the first quarter NFL QB rating on the fourth quarter NFL QB rating for 17 NFL starting quarterbacks from the 2014-2015 season. The aim is to use Bayesian hierarchical linear modeling to attain slope and intercept estimates for each quarterback in the study and attempt to determine what is causing the dependence, if any. Then, if a linear dependence is detected, investigating whether or not the statistic used is a viable measure of performance.Item Bayesian hierarchical parametric survival analysis for NBA career longevity(2012-05) Lakin, Richard Thomas; Scott, James Gordon; Powers, DanielIn evaluating a prospective NBA player, one might consider past performance in the player’s previous years of competition. In doing so, a general manager may ask the following questions: Do certain characteristics of a player’s past statistics play a role in how long a player will last in the NBA? In this study, we examine the data from players who entered in the NBA in a five-‐year period (1997-‐1998 through 2001-‐2002 season) by looking at their attributes from their collegiate career to see if they have any effect on their career longevity. We will look at basic statistics take for each of these players, such as field goal percentage, points per game, rebounds per game and assists per game. We aim to use Bayesian survival methods to model these event times, while exploiting the hierarchical nature of the data. We will look at two types of models and perform model diagnostics to determine which of the two we prefer.Item Bayesian inference for random partitions(2013-08) Sundar, Radhika; Müller, Peter, 1963 August 9-I consider statistical inference for clustering, that is the arrangement of experimental units in homogeneous groups. In particular, I discuss clustering for multivariate binary outcomes. Binary data is not very informative, making it less meaningful to proceed with traditional (deterministic) clustering methods. Meaningful inference needs to account for and report the considerable uncertainty related with any reported cluster arrangement. I review and implement an approach that was proposed in the recent literature.Item Bayesian learning in bioinformatics(2009-05-15) Gold, David L.Life sciences research is advancing in breadth and scope, affecting many areas of life including medical care and government policy. The field of Bioinformatics, in particular, is growing very rapidly with the help of computer science, statistics, applied mathematics, and engineering. New high-throughput technologies are making it possible to measure genomic variation across phenotypes in organisms at costs that were once inconceivable. In conjunction, and partly as a consequence, massive amounts of information about the genomes of many organisms are becoming accessible in the public domain. Some of the important and exciting questions in the post-genomics era are how to integrate all of the information available from diverse sources. Learning in complex systems biology requires that information be shared in a natural and interpretable way, to integrate knowledge and data. The statistical sciences can support the advancement of learning in Bioinformatics in many ways, not the least of which is by developing methodologies that can support the synchronization of efforts across sciences, offering real-time learning tools that can be shared across many fields from basic science to the clinical applications. This research is an introduction to several current research problems in Bioinformatics that addresses integration of information, and discusses statistical methodologies from the Bayesian school of thought that may be applied. Bayesian statistical methodologies are proposed to integrate biological knowledge and improve statistical inference for three relevant Bioinformatics applications: gene expression arrays, BAC and aCGH arrays, and real-time gene expression experiments. A unified Bayesian model is proposed to perform detection of genes and gene classes, defined from historical pathways, with gene expression arrays. A novel Bayesian statistical method is proposed to infer chromosomal copy number aberrations in clinical populations with BAC or aCGH experiments. A theoretical model is proposed, motivated from historical work in mathematical biology, for inference with real-time gene expression experiments, and fit with Bayesian methods. Simulation and case studies show that Bayesian methodologies show great promise to improve the way we learn with high-throughput Bioinformatics experiments.Item Bayesian methods for hurdle models.(2015-02-09) Cheng, Joyce H., 1986-; Kahle, David J.; Seaman, John Weldon, 1956-Hurdle models are often presented as an alternative to zero-inflated models for count data with excess zeros. They consist of two parts: a binary model indicating a positive response (the “hurdle”) and a zero-truncated count model. One or both parts of the model can depend on covariates, which may or may not coincide. In this dissertation, we explore the Bayesian approach to these models in detail, focusing on prior structures. Many of the Bayesian hurdle models encountered in the literature fail to incorporate expert opinion into the prior structure. We consider how prior information can be elicited from experts and incorporated into the prior structure of a hurdle model with shared covariates through the use of conditional means priors. More specifically, we propose a prior structure that assumes an inherent functional relationship between the two parts of the model. Through simulations, we explore the potential gains, as well as the shortcomings, of the approach. We also consider a simulation algorithm for Bayesian sample size determination for such models. We illustrate the use of the new methods on data from a hypothetical sleep disorder study.Item Bayesian network analysis of nuclear acquisitions(2009-05-15) Freeman, Corey RossNuclear weapons proliferation produces a vehement global safety and security concern. Perhaps most threatening is the scenario of a rogue nation or a terrorist organization acquiring nuclear weapons where the conventional ideas of nuclear deterrence may not apply. To combat this threat, innovative tools are needed that will help to improve understanding of the pathways an organization will take in attempting to obtain nuclear weapons and in predicting those pathways based on existing evidence. In this work, a methodology was developed for predicting these pathways. This methodology uses a Bayesian network. An organization?s motivations and key resources are evaluated to produce the prior probability distributions for various pathways. These probability distributions are updated as evidence is added. The methodology is implemented through the use of the commercially available Bayesian network software package, Netica. A few simple scenarios are considered to show that the model?s predictions agree with intuition. These scenarios are also used to explore the model?s strengths and limitations. The model provides a means to measure the relative threat that an organization poses to nuclear proliferation and can identify potential pathways that an organization will likely pursue. Thus, the model can serve to facilitate preventative efforts in nuclear proliferation. The model shows that an organization?s motivations biased the various pathways more than their resources; however, resources had a greater impact on an organization?s overall chance of success. Limitations of this model are that (1) it can not account for deception, (2) it can not account for parallel weapon programs, and (3) the accuracy of the output can only be as good as the user input. This work developed the first, published, quantitative methodology for predicting nuclear proliferation with consideration for how an organization?s motivations impact their pathway probabilities.Item Bayesian prediction of modulus of elasticity of self consolidated concrete(2009-05-15) Bhattacharjee, ChandanCurrent models of the modulus of elasticity, E , of concrete recommended by the American Concrete Institute (ACI) and the American Association of State Highway and Transportation Officials (AASHTO) are derived only for normally vibrated concrete (NVC). Because self consolidated concrete (SCC) mixtures used today differ from NVC in the quantities and types of constituent materials, mineral additives, and chemical admixtures, the current models may not take into consideration the complexity of SCC, and thus they may predict the E of SCC inaccurately. Although some authors recommend specific models to predict the E of SCC, they include only a single variable of assumed importance, namely the compressive strength of concrete, c f ? . However there are other parameters that may need to be accounted for while developing a prediction model for the E of SCC. In this research, a Bayesian variable selection method is implemented to identify the significant parameters in predicting the E of SCC and more accurate models for the E are generated using these variables. The models have a parsimonious parameterization for ease of use in practice and properly account for the prevailing uncertainties.Item Bayesian-lopa methodology for risk assessment of an LNG importation terminal(2009-05-15) Yun, Geun-WoongLNG (Liquefied Natural Gas) is one of the fastest growing energy sources in the U.S. to fulfill the increasing energy demands. In order to meet the LNG demand, many LNG facilities including LNG importation terminals are operating currently. Therefore, it is important to estimate the potential risks in LNG terminals to ensure their safety. One of the best ways to estimate the risk is LOPA (Layer of Protection Analysis) because it can provide quantified risk results with less time and efforts than other methods. For LOPA application, failure data are essential to compute risk frequencies. However, the failure data from the LNG industry are very sparse. Bayesian estimation is identified as one method to compensate for its weaknesses. It can update the generic data with plant specific data. Based on Bayesian estimation, the frequencies of initiating events were obtained using a conjugate gamma prior distribution such as OREDA (Offshore Reliability Data) database and Poisson likelihood distribution. If there is no prior information, Jeffreys noninformative prior may be used. The LNG plant failure database was used as plant specific likelihood information. The PFDs (Probability of Failure on Demand) of IPLs (Independent Protection Layers) were estimated with the conjugate beta prior such as EIReDA (European Industry Reliability Data Bank) database and binomial likelihood distribution. In some cases EIReDA did not provide failure data, so the newly developed Frequency-PFD conversion method was used instead. By the combination of Bayesian estimation and LOPA procedures, the Bayesian-LOPA methodology was developed and was applied to an LNG importation terminal. The found risk values were compared to the tolerable risk criteria to make risk decisions. Finally, the risk values of seven incident scenarios were compared to each other to make a risk ranking. In conclusion, the newly developed Bayesian-LOPA methodology really does work well in an LNG importation terminal and it can be applied in other industries including refineries and petrochemicals. Moreover, it can be used with other frequency analysis methods such as Fault Tree Analysis (FTA).Item Causal Network Methods for Integrated Project Portfolio Risk Analysis(2014-08-06) Govan, PaulCorporate portfolio risk analysis is of primary concern for many organizations, as the success of strategic objectives greatly depends on an accurate risk assessment. Current risk analysis methods typically involve statistical models of risk with varying levels of complexity. Though, as risk events are often rare, sufficient data is often not available for statistical models. Other methods are the so-called expert models, which involve subjective estimates of risk based on experience and intuition. However, experience and intuition are often insufficient for expert models as well. Furthermore, neither of these approaches reflects the general information available on projects, both expert opinions and the observed data. The goal of this dissertation is to develop a general corporate portfolio risk analysis methodology that identifies theoretical causal relationships and integrates expert opinions with the observed data. The proposed conceptual framework takes a resource-based view, where risk is identified and measured in terms of the uncertainty associated with project resources. The methodological framework utilizes causal networks to model risk and the associated consequences. This research contributes to the field of risk analysis in two primary ways. First, this research introduces a new general theory of corporate portfolio risk analysis. This theoretical framework supports risk-based decision making whether through a formal analysis or heuristic measures. Second, this research applies the causal network methodology to the problem of project risk analysis. This methodological framework provides the ability to model risk events throughout the project life-cycle. Furthermore, this framework identifies risk-based dependencies given varying levels of information, and promotes organizational learning by identifying which project information is more or less valuable to the organization.Item A collection of Bayesian models of stochastic failure processes(2013-05) Kirschenmann, Thomas Harold; Damien, Paul, 1960-; Press, William H.Risk managers currently seek new advances in statistical methodology to better forecast and quantify uncertainty. This thesis comprises a collection of new Bayesian models and computational methods which collectively aim to better estimate parameters and predict observables when data arise from stochastic failure processes. Such data commonly arise in reliability theory and survival analysis to predict failure times of mechanical devices, compare medical treatments, and to ultimately make well-informed risk management decisions. The collection of models proposed in this thesis advances the quality of those forecasts by providing computational modeling methodology to aid quantitative based decision makers. Through these models, a reliability expert will have the ability: to model how future decisions affect the process; to impose his prior beliefs on hazard rate shapes; to efficiently estimate parameters with MCMC methods; to incorporate exogenous information in the form of covariate data using Cox proportional hazard models; to utilize nonparametric priors for enhanced model flexibility. Managers are often forced to make decisions that affect the underlying distribution of a stochastic process. They regularly make these choices while lacking a mathematical model for how the process may itself depend significantly on their decisions. The first model proposed in this thesis provides a method to capture this decision dependency; this is used to make an optimal decision policy in the future, utilizing the interactions of the sequences of decisions. The model and method in this thesis is the first to directly estimate decision dependency in a stochastic process with the flexibility and power of the Bayesian formulation. The model parameters are estimated using an efficient Markov chain Monte Carlo technique, leading to predictive probability densities for the stochastic process. Using the posterior distributions of the random parameters in the model, a stochastic optimization program is solved to determine the sequence of decisions that minimise a cost-based objective function over a finite time horizon. The method is tested with artificial data and then used to model maintenance and failure time data from a condenser system at the South Texas Project Nuclear Operating Company (STPNOC). The second and third models proposed in this thesis offer a new way for survival analysts and reliability engineers to utilize their prior beliefs regarding the shape of hazard rate functions. Two generalizations of Weibull models have become popular recently, the exponentiated Weibull and the modified Weibull densities. The popularity of these models is largely due to the flexible hazard rate functions they can induce, such as bathtub, increasing, decreasing, and unimodal shaped hazard rates. These models are more complex than the standard Weibull, and without a Bayesian approach, one faces difficulties using traditional frequentist techniques to estimate the parameters. This thesis develops stylized families of prior distributions that should allow engineers to model their beliefs based on the context. Both models are first tested on artificial data and then compared when modeling a low pressure switch for a containment door at the STPNOC in Bay City, TX. Additionally, survival analysis is performed with these models using a famous collection of censored data about leukemia treatments. Two additional models are developed using the exponentiated and modified Weibull hazard functions as a baseline distribution to implement Cox proportional hazards models, allowing survival analysts to incorporate additional covariate information. Two nonparametric methods for estimating survival functions are compared using both simulated and real data from cancer treatment research. The quantile pyramid process is compared to Polya tree priors and is shown to have a distinct advantage due to the need for choosing a distribution upon which to center a Polya tree. The Polya tree and the quantile pyramid appear to have effectively the same accuracy when the Polya tree has a very well-informed choice of centering distribution. That is rarely the case, however, and one must conclude that the quantile pyramid process is at least as effective as Polya tree priors for modeling unknown situations.Item Convergence of Bayesian posterior distributions(2009-08) Gillies, Kendall; Martin, Clyde F.; Toda, Magdalena D.With comparing the model of determining the true price of a product to determining the proportion of black balls in a bottom less, rotating urn, it is seen that as long as the ratio of black balls converge to the true proportion, the Bayesian updating method for the rth moment will converge to the true proportion raised to the rth power. Thus the posterior distributions converge to unit mass at the true proportion. With the knowledge of convergence a theory for speeding up the convergence rate for the Bayesian updating method was tested.Item Detecting calcium flux in T cells using a Bayesian model(2015-08) Hu, Zicheng; Müller, Peter, 1963 August 9-; Ehrlich, LaurenUpon antigen recognition, T cells are activated to carry out its effector functions. A hallmark of T cell activation is the dramatic increase of the intracellular calcium concentration (calcium influx). Indo-1 is a calcium indicator dye widely used to detect T cell activation events in in vitro assays. The use of Indo-1 to detect T cell activation events in live tissues remains a challenge, due to the high noise to signal ratio data generated. Here, we developed a Bayesian probabilistic model to identify T cell activation events from noisy Indo-1 data. The model was able to detect T cell activation events accurately from simulated data, as well as real biological data in which the time of T cell activation events are known. We then used the model to detect OTII T cells that are activated by dendritic cells in thymic medulla in Rip-OVAhi transgenic mouse. We found that dendritic cells contribute 60% of all T cell activations in the mouse model.Item Integration and quantification of uncertainty of volumetric and material balance analyses using a Bayesian framework(Texas A&M University, 2005-11-01) Ogele, ChileEstimating original hydrocarbons in place (OHIP) in a reservoir is fundamentally important to estimating reserves and potential profitability. Quantifying the uncertainties in OHIP estimates can improve reservoir development and investment decision-making for individual reservoirs and can lead to improved portfolio performance. Two traditional methods for estimating OHIP are volumetric and material balance methods. Probabilistic estimates of OHIP are commonly generated prior to significant production from a reservoir by combining volumetric analysis with Monte Carlo methods. Material balance is routinely used to analyze reservoir performance and estimate OHIP. Although material balance has uncertainties due to errors in pressure and other parameters, probabilistic estimates are seldom done. In this thesis I use a Bayesian formulation to integrate volumetric and material balance analyses and to quantify uncertainty in the combined OHIP estimates. Specifically, I apply Bayes?? rule to the Havlena and Odeh material balance equation to estimate original oil in place, N, and relative gas-cap size, m, for a gas-cap drive oil reservoir. The paper considers uncertainty and correlation in the volumetric estimates of N and m (reflected in the prior probability distribution), as well as uncertainty in the pressure data (reflected in the likelihood distribution). Approximation of the covariance of the posterior distribution allows quantification of uncertainty in the estimates of N and m resulting from the combined volumetric and material balance analyses. Several example applications to illustrate the value of this integrated approach are presented. Material balance data reduce the uncertainty in the volumetric estimate, and the volumetric data reduce the considerable non-uniqueness of the material balance solution, resulting in more accurate OHIP estimates than from the separate analyses. One of the advantages over reservoir simulation is that, with the smaller number of parameters in this approach, we can easily sample the entire posterior distribution, resulting in more complete quantification of uncertainty. The approach can also detect underestimation of uncertainty in either volumetric data or material balance data, indicated by insufficient overlap of the prior and likelihood distributions. When this occurs, the volumetric and material balance analyses should be revisited and the uncertainties of each reevaluated.Item Modeling climate variables using Bayesian finite mixture models(2015-05) Cuthbertson, Thomas Edwin; Keitt, Timothy H.; Müller, PeterThis paper presents an alternative to point-based clustering models using a Bayesian finite mixture model. Using a simulation of soil moisture data in the Amazon region of South America, a Bayesian mixture of regressions is used to preserve periodic behavior within clusters. The mixture model provides a full probabilistic description of all uncertainties in the parameters that generated the data in addition to a clustering algorithm which better preserves the periodic nature of data at a particular pixel.