# Browsing by Subject "Bayesian"

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Item Advanced methods for subsurface velocity estimation : trans-dimensional inversion and machine learning(2019-12) Biswas, Reetam; Sen, Mrinal K.; Arnulf, Adrien F.; Spikes, Kyle T.; Grand, Stephen P.; Bennett, NicholasShow more Inversion is a widely adopted tool to estimate the subsurface elastic properties of the Earth from seismic data. However, it faces several obstacles due to lack of adequate data coverage, and various assumptions made in forward modeling and inversion algorithms resulting often in sub-optimal results. One such assumption is the choice of parameterization of the model. In general, it is assumed to be known a priori and kept fixed. This can lead to either over or under parameterization, causing either overfitting or underfitting the data. In the first part of my thesis, I address the problem of model parameterization. Along with searching for models that fit the data, I also solve for the optimum number of model parameters required as dictated by the data. In a deterministic approach, I use the Basis Pursuit Inversion (BPI), which imposes sparsity in the model parameterization by adding a regularization term of L₁ norm of the model vector. The weight of the regularization term plays a dominant role, and I propose an approach for automatic calculation of this weighting factor. Alternately, I also develop a stochastic method, using Bayesian framework to solve my inverse problem in which the model parameters are treated as unknown. Unlike BPI, this method also provides us with estimates of uncertainty. Here, I make use of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) framework, which allows changing the number of model parameters. However, the conventional RJMCMC is generally very slow as it attempts to sample a variable dimensional model space. To address this, I propose a new method called the Reversible Jump Hamiltonian Monte Carlo (RJHMC), which improves the efficiency by combining RJMCMC with a gradient-based Hamiltonian Monte Carlo (HMC). The gradient-based steps ensure quick convergence by allowing the sampling to take large steps guided by the gradient instead of complete random steps. I represent my model space using a layer-based earth model for the 1D problem and using an adaptive ensemble of nuclei along with Voronoi partition for a 2D problem. Subsequently, I use the method to solve the deconvolution problem in 1D, and tomography and Full Waveform Inversion problems in a 2D setting. It also provides estimates of the elastic parameters and marginal distribution of the number of model parameters. I use the 1D RJHMC to estimate density, along with P- and Swave velocities from a pre-stack angle gather. The region contains paleo-residual gas (PRG), which shows same signature as that of normal gas saturation, and can be better differentiated using density. Additionally, I applied trans-dimensional tomography to invert for P-wave velocity structure at an Axial Seamount, which is one of the most volcanically active regions in northeastern Pacific. In addition to BPI and RJMHC, I develop workflows, which take advantage of the hybrid schemes and Machine Learning (ML) algorithms. Solving an elastic FWI problem can be challenging, as it is very computationally expensive in comparison to the more commonly used acoustic formulation. I propose a hybrid scheme, where the initial P-wave velocity result from an acoustic FWI can be used to perform less expensive pre-stack Amplitude vs. Angle (AVA) inversion. This provides us with all three elastic parameters: P-wave velocity, S-wave velocity, and Density. Several inverse problems can be mapped into a neural network architecture, which can be solved using the currently developed deep learning algorithms. The last part of my dissertation describes two machine learning (ML) algorithms that I have developed for seismic inversion. I use a Convolutional Neural Network (CNN) to perform seismic inversion, in which instead of using the traditional way of using input-output pairs to train the network, I use the physics of the forward wave-propagation to guide the training. It circumvents the need for providing the label data during training and makes it unsupervised. In addition to this, I propose to use a Recurrent Neural Network (RNN) to estimate NMO velocities, which is a basic seismic processing technique. Generally, the NMO velocity is hand-picked and requires a lot of human intervention and computation time. Using this workflow with only 10% of data used as training, the network estimates NMO velocities almost instantly for the rest of the datasetShow more Item Applied statistical modeling of three-dimensional natural scene data(2014-05) Su, Che-Chun; Bovik, Alan C. (Alan Conrad), 1958-; Cormack, Lawrence K.Show more 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.Show more Item Bayesian hierarchical linear modeling of NFL quarterback rating(2015-05) Hernandez, Steven V.; Walker, Stephen G., 1945-; Mahometa, Michael JShow more With 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.Show more Item Bayesian hierarchical parametric survival analysis for NBA career longevity(2012-05) Lakin, Richard Thomas; Scott, James (Statistician); Powers, DanielShow more In 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.Show more Item Bayesian inference for random partitions(2013-08) Sundar, Radhika; Müller, Peter, 1963 August 9-Show more 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.Show more Item Bayesian semiparametric inference of complex longitudinal and multiple time series systems(2023-04-17) Fan, Jingjing, Ph. D.; Sarkar, Abhra; Mueller, Peter; Carvalho, Carlos M; Chandrasekaran, BharathShow more Time series inference differs from traditional statistical analysis in that there is inherent dependence between observations in a time series. In the case of multiple time series, multivariate time series, or panel data, performing inference can become even more complex because of possible interactions between different subjects, variables, or both. We develop three new methodologies capable of performing inference on multiple time series, high dimensional multivariate time series, and panel data respectively. For multiple time series, we combine functional analysis with a Hidden Markov model to create a clustering algorithm that allows each time series to change its cluster membership over time. For high dimensional multivariate time series, we develop a tensor decomposition estimation method for the Vector Autoregressive (VAR) model which greatly reduces the parameter space without sacrificing accuracy. We extend the tensor decomposed VAR into a random effects model to allow for information sharing between subjects in multi-subject panels. For panels with many subjects, we employ a divide-and-conquer strategy with embarrassingly parallel samplers to lessen the computational burden on a single estimation process.Show more Item Camouflage detection & signal discrimination : theory, methods & experiments(2022-05-05) Das, Abhranil; Geisler, Wilson S.; Reichl, L. E.; Florin, Ernst-Ludwig; Marder, MichaelShow more Camouflage is an amazing feat of evolution, but also impressive is the ability of biological visual systems to detect them. They are the result of an evolutionary arms race that exposes many detection strategies and their limits. In this thesis, we investigate the principles of human detection of maximally-camouflaged objects, i.e. whose texture exactly mimics the background texture. Chapter 1 introduces and contextualizes the problem. In chapter 2, we develop a theory and model that extracts the relevant information in the image, and uses biologically plausible computations on them for detection. In chapter 3, we present a series of experiments which measured human camouflage detection ability along different dimensions of the task, such as across different textures and shapes. Chapter 5 is a reference on some methods and analysis used in the study. Chapter 6 describes mathematical methods and software on statistical signal discrimination that we developed to solve questions in visual detection, but with wider applications in other fields.Show more Item A collection of Bayesian models of stochastic failure processes(2013-05) Kirschenmann, Thomas Harold; Damien, Paul, 1960-; Press, William H.Show more 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.Show more Item Detecting calcium flux in T cells using a Bayesian model(2015-08) Hu, Zicheng; Müller, Peter, 1963 August 9-; Ehrlich, LaurenShow more Upon 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.Show more Item Modeling climate variables using Bayesian finite mixture models(2015-05) Cuthbertson, Thomas Edwin; Keitt, Timothy H.; Müller, PeterShow more This 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.Show more Item Modern analyses of complex datasets in plant ecology and conservation(2021-08-16) Northup, Alison Pechin; Keitt, Timothy H.; Farrior, Caroline E.; Jha, Shalene; Juenger, Thomas; Young, Kenneth RShow more Ecological data are often difficult to analyze, with complexity inherent in their real-world provenance, and with technological advancements and the passage of time resulting in publicly-available ecological datasets that are constantly growing in size. Timely ecological questions and large, complex datasets demand modern, innovative analytical approaches. This research comprises three cases where creative analytical approaches are used to tease out answers to questions about conservation and climate change impacts. The first case attempts to resolve a standing question: which of the two dominant tree species on the Edwards Plateau, TX, is more resistant to drought? Starting with an erratic sap flow dataset, environmental data are used to select the most relevant portions of the time series, and the application of a Bayesian model creates enough statistical power to suggest an answer to the question, helping resolve inconsistencies in prior literature. The second case makes use of herbarium sheet images and a spatially-explicit Bayesian model to explore continental-scale flowering phenology among a subfamily of trees in the New World Tropics, with surprising results. The third case uses environmental raster datasets and spatial optimization software to determine which areas within a region of West Texas are most vulnerable to future oil and gas development from a biodiversity and ecosystem services perspective. Together, these cases show the power that modern and creative analytical techniques can bring when applied to complex data sets.Show more Item A review on computation methods for Bayesian state-space model with case studies(2010-05) Yang, Mengta, 1979-; McCulloch, Robert E. (Robert Edward); Sager, Thomas W.Show more Sequential Monte Carlo (SMC) and Forward Filtering Backward Sampling (FFBS) are the two most often seen algorithms for Bayesian state space models analysis. Various results regarding the applicability has been either claimed or shown. It is said that SMC would excel under nonlinear, non-Gaussian situations, and less computationally expansive. On the other hand, it has been shown that with techniques such as Grid approximation (Hore et al. 2010), FFBS based methods would do no worse, though still can be computationally expansive, but provide more exact information. The purpose of this report to compare the two methods with simulated data sets, and further explore whether there exist some clear criteria that may be used to determine a priori which methods would suit the study better.Show more Item Sampling approaches in Bayesian computational statistics with R(2009-12) Sun, Wenwen; Sager, Thomas W.; Parker, MaryShow more Bayesian analysis is definitely different from the classic statistical methods. Although, both of them use subjective ideas, it is used in the selection of models in the classic statistical methods, rather than as an explicit part in Bayesian models, which allows the combination of subjective ideas with the data collected, update the prior information and improve inferences. Drastic growth of Bayesian applications indicates it becomes more and more popular, because the advent of computational methods (e.g., MCMC) renders sophisticated analysis. In Bayesian framework, the flexibility and generality allows it to cope with very complex problems. One big obstacle in earlier Bayesian analysis is how to sample from the usually complex posterior distribution. With modern techniques and fast-developed computation capacity, we now have tools to solve this problem. We discuss Acceptance-Rejection sampling, importance sampling and then the MCMC methods. Metropolis-Hasting algorithm, as a very versatile, efficient and powerful simulation technique to construct a Markov Chain, borrows the idea from the well-known acceptance-rejection sampling to generate candidates that are either accepted or rejected, but then retains the current values when rejection takes place (1). A special case of Metropolis-Hasting algorithm is Gibbs Sampler. When dealing with high dimensional problems, Gibbs Sampler doesn’t require a decent proposal distribution. It generates the Markov Chain through univariate conditional probability distribution, which greatly simplifies problems. We illustrate the use of those approaches with examples (with R codes) to provide a thorough review. Those basic methods have variants to deal with different situations. And they are building blocks for more advanced problems. This report is not a tutorial for statistics or the software R. The author assumes that readers are familiar with basic statistical concepts and common R statements. If needed, a detailed instruction of R programming can be found in the Comprehensive R Archive Network (CRAN): http://cran.R-project.orgShow more Item UTeach summer masters statistics course : a journey from traditional to Bayesian analysis(2010-08) Fitzpatrick, Daniel Lee; Armendáriz, Efraim P.; Daniels, Mark L.Show more This paper will outline some of the key parts of the Statistics course offered through the UTeach Summer Master’s Program as taught by Dr. Martha K. Smith. The paper begins with the introduction of the normal probability density function and is proven with calculus techniques and Euclidean geometry. Probability is discussed at great length in Smith’s course and the importance of understanding probability in statistical analysis is demonstrated through a reference to a study on how medical doctors confuse false positives in breast cancer testing. The frequentist perspective is concluded with a proof that the normal probability density function is zero. The shift from traditional to Bayesian inference begins with a brief introduction to the terminology involved, as well as an example with patient testing. The pros and cons of Bayesian inference are discussed and a proof is shown using the normal probability density function in finding a Bayes estimate for µ. It will be argued that a Statistics course moving from traditional to Bayesian analysis, such as that offered by the UTeach Summer Master’s Program and Smith, would supplement the traditional Statistics course offered at most universities. Such a course would be relevant for the mathematics major, mathematics educator, professionals in the medical industry, and individuals seeking to gain insights into how to understand data sets in new ways.Show more