Dissertations / Theses: 'Hierarchal Bayesian statistics'

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Cheng, Si. "Hierarchical Nearest Neighbor Co-kriging Gaussian Process For Large And Multi-Fidelity Spatial Dataset." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613750570927821.

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Lawson, Elizabeth Anne. "Autologous Stem Cell Transplant: Factors Predicting the Yield of CD34+ Cells." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1144.pdf.

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Seat, Marlee Lyn. "Using LiDAR Data to Analyze Access Management Criteria in Utah." BYU ScholarsArchive, 2017. https://scholarsarchive.byu.edu/etd/6329.

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The Utah Department of Transportation (UDOT) has completed a Light Detection and Ranging (LiDAR) data inventory that includes access locations across the UDOT network. The new data are anticipated to be extremely useful in better defining safety and in completing a systemwide analysis of locations where safety could be improved, or where safety has been improved across the state. The Department of Civil and Environmental Engineering at Brigham Young University (BYU) has worked with the new data to perform a safety analysis of the state related to access management, particularly related to driveway spacing and raised medians. The primary objective of this research was to increase understanding of the safety impacts across the state related to access management. These objectives were accomplished by using the LiDAR database to evaluate driveway spacing and locations to aid in hot spot identification and to develop relationships between access design and location as a function of safety and access category (AC). Utah Administrative Rule R930-6 contains access management guidelines to balance the access found on a roadway with traffic and safety operations. These guidelines were used to find the maximum number of driveways recommended for a roadway. ArcMap 10.3 and Microsoft Excel were used to visualize the data and identify hot spot locations. An analysis conducted in this study compared current roadway characteristics to the R930-6 guidelines to find locations where differences occurred. This analysis does not indicate the current AC is incorrect; it simply means that the assigned AC does not meet current roadway characteristic based on the LiDAR data analysis. UDOT can decide what this roadway will become in the future and help shape each segment using the AC outlined in the R930-6. A hierarchal Bayesian statistical before-after model, created in previous BYU safety research, was used to analyze locations where raised medians have been installed. Twenty locations where raised medians were installed in Utah between 2002 to 2014 were used in this model. The model analyzed the raised medians by AC. Only three AC were represented in the data. Regression plots depicting a decrease in crashes before and after installation, posterior distribution plots showing the probability of a decrease in crashes after installation, and crash modification factor (CMF) plots presenting the CMF values estimated for different vehicle miles traveled (VMT) values were all created as output from the before-after model. Overall, installing a raised median gives an approximate reduction of 53 percent for all crashes. Individual AC analysis yielded results ranging from 32 to 44 percent for all severity groups except severity 4 and 5. When the model was only run for crash severity 4 and 5, a larger reduction of 57 to 58 percent was found.

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Woodard, Roger. "Bayesian hierarchical models for hunting success rates /." free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9951135.

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Brody-Moore, Peter. "Bayesian Hierarchical Meta-Analysis of Asymptomatic Ebola Seroprevalence." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2228.

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The continued study of asymptomatic Ebolavirus infection is necessary to develop a more complete understanding of Ebola transmission dynamics. This paper conducts a meta-analysis of eight studies that measure seroprevalence (the number of subjects that test positive for anti-Ebolavirus antibodies in their blood) in subjects with household exposure or known case-contact with Ebola, but that have shown no symptoms. In our two random effects Bayesian hierarchical models, we find estimated seroprevalences of 8.76% and 9.72%, significantly higher than the 3.3% found by a previous meta-analysis of these eight studies. We also produce a variation of this meta-analysis where we exclude two of the eight studies. In this model, we find an estimated seroprevalence of 4.4%, much lower than our first two Bayesian hierarchical models. We believe a random effects model more accurately reflects the heterogeneity between studies and thus asymptomatic Ebola is more seroprevalent than previously believed among subjects with household exposure or known case-contact. However, a strong conclusion cannot be reached on the seriousness of asymptomatic Ebola without an international testing standard and more data collection using this adopted standard.

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Southey, Richard. "Bayesian hierarchical modelling with application in spatial epidemiology." Thesis, Rhodes University, 2018. http://hdl.handle.net/10962/59489.

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Disease mapping and spatial statistics have become an important part of modern day statistics and have increased in popularity as the methods and techniques have evolved. The application of disease mapping is not only confined to the analysis of diseases as other applications of disease mapping can be found in Econometric and financial disciplines. This thesis will consider two data sets. These are the Georgia oral cancer 2004 data set and the South African acute pericarditis 2014 data set. The Georgia data set will be used to assess the hyperprior sensitivity of the precision for the uncorrelated heterogeneity and correlated heterogeneity components in a convolution model. The correlated heterogeneity will be modelled by a conditional autoregressive prior distribution and the uncorrelated heterogeneity will be modelled with a zero mean Gaussian prior distribution. The sensitivity analysis will be performed using three models with conjugate, Jeffreys' and a fixed parameter prior for the hyperprior distribution of the precision for the uncorrelated heterogeneity component. A simulation study will be done to compare four prior distributions which will be the conjugate, Jeffreys', probability matching and divergence priors. The three models will be fitted in WinBUGS® using a Bayesian approach. The results of the three models will be in the form of disease maps, figures and tables. The results show that the hyperprior of the precision for the uncorrelated heterogeneity and correlated heterogeneity components are sensitive to changes and will result in different results depending on the specification of the hyperprior distribution of the precision for the two components in the model. The South African data set will be used to examine whether there is a difference between the proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Two models will be fitted in WinBUGS® for this comparison. Both the hyperpriors of the precision for the uncorrelated heterogeneity and correlated heterogeneity components will be modelled using a Jeffreys' prior distribution. The results show that there is no significant difference between the results of the model with a proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the South African data, although there are a few disadvantages of using a proper conditional autoregressive prior for the correlated heterogeneity which will be stated in the conclusion.

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Bao, Haikun. "Bayesian hierarchical regression model to detect quantitative trait loci /." Electronic version (PDF), 2006. http://dl.uncw.edu/etd/2006/baoh/haikunbao.pdf.

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McBride, John Jacob Bratcher Thomas L. "Conjugate hierarchical models for spatial data an application on an optimal selection procedure /." Waco, Tex. : Baylor University, 2006. http://hdl.handle.net/2104/3955.

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Thomas, Zachary Micah. "Bayesian Hierarchical Space-Time Clustering Methods." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1435324379.

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George, Robert Emerson. "The role of hierarchical priors in robust Bayesian inference /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487847761308082.

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Page, Garritt L. "Using Box-Scores to Determine a Position's Contribution to Winning Basketball Games." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd998.pdf.

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Pflugeisen, Bethann Mangel. "Analysis of Otolith Microchemistry Using Bayesian Hierarchical Mixture Models." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1275059376.

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Zhang, Yanwei. "A hierarchical Bayesian approach to model spatially correlated binary data with applications to dental research." Diss., Connect to online resource - MSU authorized users, 2008.

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Fang, Qijun. "Hierarchical Bayesian Benchmark Dose Analysis." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/316773.

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An important objective in statistical risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs) that induce a pre-specified Benchmark Response (BMR) in a target population. Established inferential approaches for BMD analysis typically involve one-sided, frequentist confidence limits, leading in practice to what are called Benchmark Dose Lower Limits (BMDLs). Appeal to hierarchical Bayesian modeling and credible limits for building BMDLs is far less developed, however. Indeed, for the few existing forms of Bayesian BMDs, informative prior information is seldom incorporated. Here, a new method is developed by using reparameterized quantal-response models that explicitly describe the BMD as a target parameter. This potentially improves the BMD/BMDL estimation by combining elicited prior belief with the observed data in the Bayesian hierarchy. Besides this, the large variety of candidate quantal-response models available for applying these methods, however, lead to questions of model adequacy and uncertainty. Facing this issue, the Bayesian estimation technique here is further enhanced by applying Bayesian model averaging to produce point estimates and (lower) credible bounds. Implementation is facilitated via a Monte Carlo-based adaptive Metropolis (AM) algorithm to approximate the posterior distribution. Performance of the method is evaluated via a simulation study. An example from carcinogenicity testing illustrates the calculations.

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Zhang, Zuoshun. "Proper posterior distributions for some hierarchical models and roundoff effects in the Gibbs sampler /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Ho, Yu-Yun. "Diagnostics for hierarchical Bayesian regression models with application to repeated measures data /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487856906261615.

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Jaberansari, Negar. "Bayesian Hierarchical Models for Partially Observed Data." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1479818516727153.

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Tak, Hyung Suk. "Topics in Bayesian Hierarchical Modeling and its Monte Carlo Computations." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493573.

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The first chapter addresses a Beta-Binomial-Logit model that is a Beta-Binomial conjugate hierarchical model with covariate information incorporated via a logistic regression. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive data-dependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. Frequency coverage properties of several hyper-prior distributions are also investigated to see when and whether Bayesian interval estimates of random effects meet their nominal confidence levels. The second chapter deals with a time delay estimation problem in astrophysics. When the gravitational field of an intervening galaxy between a quasar and the Earth is strong enough to split light into two or more images, the time delay is defined as the difference between their travel times. The time delay can be used to constrain cosmological parameters and can be inferred from the time series of brightness data of each image. To estimate the time delay, we construct a Gaussian hierarchical model based on a state-space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian approach jointly infers model parameters via a Gibbs sampler. We also introduce a profile likelihood of the time delay as an approximation of its marginal posterior distribution. The last chapter specifies a repelling-attracting Metropolis algorithm, a new Markov chain Monte Carlo method to explore multi-modal distributions in a simple and fast manner. This algorithm is essentially a Metropolis-Hastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes repelling, followed by an uphill move in density that aims to make local modes attracting. The downhill move is achieved via a reciprocal Metropolis ratio so that the algorithm prefers downward movement. The uphill move does the opposite using the standard Metropolis ratio which prefers upward movement. This down-up movement in density increases the probability of a proposed move to a different mode.
Statistics

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Li, Yuan. "Hierarchical Bayesian Model for AK Composite Estimators in the Current Population Survey (CPS)." Thesis, The George Washington University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10748002.

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The Current Population Survey (CPS) is a multistage probability sample survey conducted by the U.S. Census Bureau and the Bureau of Labor Statistics (BLS). The 4-8-4 rotation design is applied to produce overlap in the sample across months. Several weighting steps are used to adjust the ultimate sample in each month to be representative of the population. In order to produce efficient estimates of labor force levels and month-to-month change, the so-called AK composite estimator combines current estimates from eight rotation panels and the previous month’s estimates to estimate current values. Values of coefficients A and K are chosen every decade or so for the nation. The Successive Difference Replicate (SDR) method and Balanced Repeated Replication (BRR) method are currently used by the CPS for estimating the variance of the AK Composite Estimates.

Instead of using constant CPS (A, K) values for AK Composite Estimator over time, one could find the monthly optimal coefficients ( A, K) that minimize the variance for measuring the monthly level of unemployment in the target population. The CPS (A, K) values are stable over time but can produce larger variance in some months, while the monthly optimal (A, K) values have lower variance within a month but high variability across months.

In order to make a compromise between the CPS (A, K) values and monthly optimal (A, K), a Hierarchical Bayesian method is proposed through modeling the obtained monthly optimal ( A, K)’s using a bivariate normal distribution. The parameters, including the mean vector and the variance-covariance matrix, are unknown in this distribution. In such case, a first step towards a more general model is to assume a conjugate prior distribution for the bivariate normal model. Computing the conditional posterior distribution can be approximated through simulation. In particular, it can be achieved by the Gibbs sampling algorithm with its sequential sampling. As the key to the success of this Hierarchical Bayesian method is that approximated distributions are improved as iteration goes on in the simulation, one needs to check the convergence of the simulated sequences. Then, the sample mean after a number of iterations in the simulation will serve as the Hierarchical Bayesian (HB) (A, K). The HB (A, K) estimates in effect produce a shrinkage between the CPS (A, K) values and the monthly optimal (A, K) values. The shrinkage of the estimates of the coefficients ( A, K) occurs by manipulating the certain hyperparameter in the model.

In this dissertation, detailed comparisons are made among the three estimators. The AK Estimator using the CPS (A, K) values, using the monthly optimal (A, K) values, and using the Hierarchical Bayesian (A,K) values are compared in terms of estimates produced, estimated variance, and estimated coefficients of variation. In each month of the data set, separate estimates using the three methods are produced.

In order to assess the performance of the proposed methods, a simulation study is implemented and summarized. In the CPS, eight rotating survey panels contribute to the overall estimate in each month. Each panel is measured in a month at one of its month-in- sample. The month-in- sample range from one to eight. In the simulation, month-in- sample values are generated as if replicate panels were available for estimation. These month-in-sample values are used as the original monthly panel estimates of unemployment to produce CPS-style (A, K) estimates, AK-estimates using monthly optimal ( A, K) values, and AK-estimates using Hierarchical Bayesian ( A, K) values. Performance of each method is evaluated on the simulated data by examining several criteria including bias, variance, and mean squared error.

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Davies, Vinny. "Sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution." Thesis, University of Glasgow, 2016. http://theses.gla.ac.uk/7808/.

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Understanding how virus strains offer protection against closely related emerging strains is vital for creating effective vaccines. For many viruses, including Foot-and-Mouth Disease Virus (FMDV) and the Influenza virus where multiple serotypes often co-circulate, in vitro testing of large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Vaccines will offer cross-protection against closely related strains, but not against those that are antigenically distinct. To be able to predict cross-protection we must understand the antigenic variability within a virus serotype, distinct lineages of a virus, and identify the antigenic residues and evolutionary changes that cause the variability. In this thesis we present a family of sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution (SABRE), as well as an extended version of the method, the extended SABRE (eSABRE) method, which better takes into account the data collection process. The SABRE methods are a family of sparse Bayesian hierarchical models that use spike and slab priors to identify sites in the viral protein which are important for the neutralisation of the virus. In this thesis we demonstrate how the SABRE methods can be used to identify antigenic residues within different serotypes and show how the SABRE method outperforms established methods, mixed-effects models based on forward variable selection or l1 regularisation, on both synthetic and viral datasets. In addition we also test a number of different versions of the SABRE method, compare conjugate and semi-conjugate prior specifications and an alternative to the spike and slab prior; the binary mask model. We also propose novel proposal mechanisms for the Markov chain Monte Carlo (MCMC) simulations, which improve mixing and convergence over that of the established component-wise Gibbs sampler. The SABRE method is then applied to datasets from FMDV and the Influenza virus in order to identify a number of known antigenic residue and to provide hypotheses of other potentially antigenic residues. We also demonstrate how the SABRE methods can be used to create accurate predictions of the important evolutionary changes of the FMDV serotypes. In this thesis we provide an extended version of the SABRE method, the eSABRE method, based on a latent variable model. The eSABRE method takes further into account the structure of the datasets for FMDV and the Influenza virus through the latent variable model and gives an improvement in the modelling of the error. We show how the eSABRE method outperforms the SABRE methods in simulation studies and propose a new information criterion for selecting the random effects factors that should be included in the eSABRE method; block integrated Widely Applicable Information Criterion (biWAIC). We demonstrate how biWAIC performs equally to two other methods for selecting the random effects factors and combine it with the eSABRE method to apply it to two large Influenza datasets. Inference in these large datasets is computationally infeasible with the SABRE methods, but as a result of the improved structure of the likelihood, we are able to show how the eSABRE method offers a computational improvement, leading it to be used on these datasets. The results of the eSABRE method show that we can use the method in a fully automatic manner to identify a large number of antigenic residues on a variety of the antigenic sites of two Influenza serotypes, as well as making predictions of a number of nearby sites that may also be antigenic and are worthy of further experiment investigation.

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Kim, Yong Ku. "Bayesian multiresolution dynamic models." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180465799.

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Butler, Allison M. "Hierarchical Probit Models for Ordinal Ratings Data." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2656.

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University students often complete evaluations of their courses and instructors. The evaluation tool typically contains questions about the course and the instructor on an ordinal Likert scale. We assess instructor effectiveness while adjusting for known confounders. We present a probit regression model with a latent variable to measure the instructor effectiveness accounting for student specific covariates, such as student grade in the course, high school and university GPA, and ACT score.

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Olsen, Andrew Nolan. "Hierarchical Bayesian Methods for Evaluation of Traffic Project Efficacy." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2922.

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A main objective of Departments of Transportation is to improve the safety of the roadways over which they have jurisdiction. Safety projects, such as cable barriers and raised medians, are utilized to reduce both crash frequency and crash severity. The efficacy of these projects must be evaluated in order to use resources in the best way possible. Five models are proposed for the evaluation of traffic projects: (1) a Bayesian Poisson regression model; (2) a hierarchical Poisson regression model building on model (1) by adding hyperpriors; (3) a similar model correcting for overdispersion; (4) a dynamic linear model; and (5) a traditional before-after study model. Evaluation of these models is discussed using various metrics including DIC. Using the models selected for analysis, it was determined that cable barriers are quite effective at reducing severe crashes and cross-median crashes on Utah highways. Raised medians are also largely effective at reducing severe crashes. The results of before and after analyses are highly valuable to Departments of Transportation in identifying effective projects and in determining which roadway segments will benefit most from their implementation.

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Lu, Jun. "Bayesian hierarchical models and applications in psychology research /." free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p3144437.

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Pearson, Caroline. "Analysis of a hierarchial Bayesian method for quantitative trait loci /." Electronic version (PDF), 2007. http://dl.uncw.edu/etd/2007-2/pearsonc/carolinepearson.pdf.

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Lin, Xiaoyan. "Bayesian hierarchical models for the recognition-memory experiments." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/6047.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 3, 2009) Vita. Includes bibliographical references.

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Monson, Rebecca Lee. "Modeling Transition Probabilities for Loan States Using a Bayesian Hierarchical Model." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2179.pdf.

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Liu, Yingying. "Bayesian hierarchical normal intrinsic conditional autoregressive model for stream networks." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6606.

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Water quality and river/stream ecosystems are important for all living creatures. To protect human health, aquatic life and the surrounding ecosystem, a considerable amount of time and money has been spent on sampling and monitoring streams and rivers. Water quality monitoring and analysis can help researchers predict and learn from natural processes in the environment and determine human impacts on an ecosystem. Measurements such as temperature, pH, nitrogen concentration, algae and fish count collected along the network are all important factors in water quality analysis. The main purposes of the statistical analysis in this thesis are (1) to assess the relationship between the variable measured in the water (response variable) and other variables that describe either the locations on/along the stream network or certain characteristics at each location (explanatory variable), and (2) to assess the degree of similarity between the response variable values measured at different locations of the stream, i.e. spatial dependence structure. It is commonly accepted that measurements taken at two locations close to each other should have more similarity than locations far away. However, this is not always true for observations from stream networks. Observations from two sites that do not share water flow could be independent of each other even if they are very close in terms of stream distance, especially those observations taken on objects that move passively with the water flow. To model stream network data correctly, it is important to quantify the strength of association between observations from sites that do not share water.

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Li, Qie. "A Bayesian Hierarchical Model for Multiple Comparisons in Mixed Models." Bowling Green State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1342530994.

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Woo, Bo-kei, and 胡寶琦. "A new hierarchical Bayesian approach to low-field magnetic resonance imaging." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31226917.

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Ulrich, Michael David. "Meta-Analysis Using Bayesian Hierarchical Models in Organizational Behavior." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2349.

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Meta-analysis is a tool used to combine the results from multiple studies into one comprehensive analysis. First developed in the 1970s, meta-analysis is a major statistical method in academic, medical, business, and industrial research. There are three traditional ways in which a meta-analysis is conducted: ﬁxed or random eﬀects, and using an empirical Bayesian approach. Derivations for conducting meta-analysis on correlations in the industrial psychology and organizational behavior (OB) discipline were reviewed by Hunter and Schmidt (2004). In this approach, Hunter and Schmidt propose an empirical Bayesian analysis where the results from previous studies are used as a prior. This approach is still widely used in OB despite recent advances in Bayesian methodology. This paper presents the results of a hierarchical Bayesian model for conducting meta-analysis of correlations and then compares these results to a traditional Hunter-Schmidt analysis conducted by Judge et al. (2001). In our approach we treat the correlations from previous studies as a likelihood, and present a prior distribution for correlations.

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Roualdes, Edward A. "New Results in ell_1 Penalized Regression." UKnowledge, 2015. http://uknowledge.uky.edu/statistics_etds/13.

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Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the frequentist formulation. We then introduce Bayesian trend filtering which exemplifies the benefits of our Bayesian version. Bayesian trend filtering is shown to be an empirically strong technique for fitting univariate, nonparametric regression. Through a simulation study, we show that Bayesian trend filtering reduces prediction error and attains more accurate coverage probabilities over the frequentist method. We then apply Bayesian trend filtering to real data sets, where our method is quite competitive against a number of other popular nonparametric methods.

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Ellis, Amanda R. "ACCOUNTING FOR MATCHING UNCERTAINTY IN PHOTOGRAPHIC IDENTIFICATION STUDIES OF WILD ANIMALS." UKnowledge, 2018. https://uknowledge.uky.edu/statistics_etds/31.

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I consider statistical modelling of data gathered by photographic identification in mark-recapture studies and propose a new method that incorporates the inherent uncertainty of photographic identification in the estimation of abundance, survival and recruitment. A hierarchical model is proposed which accepts scores assigned to pairs of photographs by pattern recognition algorithms as data and allows for uncertainty in matching photographs based on these scores. The new models incorporate latent capture histories that are treated as unknown random variables informed by the data, contrasting past models having the capture histories being fixed. The methods properly account for uncertainty in the matching process and avoid the need for researchers to confirm matches visually, which may be a time consuming and error prone process. Through simulation and application to data obtained from a photographic identification study of whale sharks I show that the proposed method produces estimates that are similar to when the true matching nature of the photographic pairs is known. I then extend the method to incorporate auxiliary information to predetermine matches and non-matches between pairs of photographs in order to reduce computation time when fitting the model. Additionally, methods previously applied to record linkage problems in survey statistics are borrowed to predetermine matches and non-matches based on scores that are deemed extreme. I fit the new models in the Bayesian paradigm via Markov Chain Monte Carlo and custom code that is available by request.

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Bai, Yan. "A Bayesian approach to detect the onset of activity limitation among adults in NHIS." Link to electronic thesis, 2005. http://www.wpi.edu/Pubs/ETD/Available/etd-050605-155002/.

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White, Staci A. "Quantifying Model Error in Bayesian Parameter Estimation." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433771825.

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Milo, Michael William. "Anomaly Detection in Heterogeneous Data Environments with Applications to Mechanical Engineering Signals & Systems." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/23962.

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Anomaly detection is a relevant problem in the field of Mechanical Engineering, because the analysis of mechanical systems often relies on identifying deviations from what is considered "normal". The mechanical sciences are represented by a heterogeneous collection of data types: some systems may be highly dimensional, may contain exclusively spatial or temporal data, may be spatiotemporally linked, or may be non-deterministic and best described probabilistically. Given the broad range of data types in this field, it is not possible to propose a single processing method that will be appropriate, or even usable, for all data types. This has led to human observation remaining a common, albeit costly and inefficient, approach to detecting anomalous signals or patterns in mechanical data. The advantages of automated anomaly detection in mechanical systems include reduced monitoring costs, increased reliability of fault detection, and improved safety for users and operators. This dissertation proposes a hierarchical framework for anomaly detection through machine learning, and applies it to three distinct and heterogeneous data types: state-based data, parameter-driven data, and spatiotemporal sensor network data. In time-series data, anomaly detection results were robust in synthetic data generated using multiple simulation algorithms, as well as experimental data from rolling element bearings, with highly accurate detection rates (>99% detection, <1% false alarm). Significant developments were shown in parameter-driven data by reducing the sample sizes necessary for analysis, as well as reducing the time required for computation. The event-space model extends previous work into a geospatial sensor network and demonstrates applications of this type of event modeling at various timescales, and compares the model to results obtained using other approaches. Each data type is processed in a unique way relative to the others, but all are fitted to the same hierarchical structure for system modeling. This hierarchical model is the key development proposed by this dissertation, and makes both novel and significant contributions to the fields of mechanical analysis and data processing. This work demonstrates the effectiveness of the developed approaches, details how they differ from other relevant industry standard methods, and concludes with a proposal for additional research into other data types.
Ph. D.

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Ross, Beth E. "Assessing Changes in the Abundance of the Continental Population of Scaup Using a Hierarchical Spatio-Temporal Model." DigitalCommons@USU, 2012. http://digitalcommons.usu.edu/etd/1147.

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In ecological studies, the goal is often to describe and gain further insight into ecological processes underlying the data collected during observational studies. Because of the nature of observational data, it can often be difficult to separate the variation in the data from the underlying process or `state dynamics.' In order to better address this issue, it is becoming increasingly common for researchers to use hierarchical models. Hierarchical spatial, temporal, and spatio-temporal models allow for the simultaneous modeling of both first and second order processes, thus accounting for underlying autocorrelation in the system while still providing insight into overall spatial and temporal pattern. In this particular study, I use two species of interest, the lesser and greater scaup (Aythya affnis and Aythya marila), as an example of how hierarchical models can be utilized in wildlife management studies. Scaup are the most abundant and widespread diving duck in North America, and are important game species. Since 1978, the continental population of scaup has declined to levels that are 16% below the 1955-2010 average and 34% below the North American Waterfowl Management Plan goal. The greatest decline in abundance of scaup appears to be occurring in the western boreal forest, where populations may have depressed rates of reproductive success, survival, or both. In order to better understand the causes of the decline, and better understand the biology of scaup in general, a level of high importance has been placed on retrospective analyses that determine the spatial and temporal changes in population abundance. In order to implement Bayesian hierarchical models, I used a method called Integrated Nested Laplace Approximation (INLA) to approximate the posterior marginal distribution of the parameters of interest, rather than the more common Markov Chain Monte Carlo (MCMC) approach. Based on preliminary analysis, the data appeared to be overdispersed, containing a disproportionately high number of zeros along with a high variance relative to the mean. Thus, I considered two potential data models, the negative binomial and the zero-inflated negative binomial. Of these models, the zero-inflated negative binomial had the lowest DIC, thus inference was based on this model. Results from this model indicated that a large proportion of the strata were not decreasing (i.e., the estimated slope of the parameter was not significantly different from zero). However, there were important exceptions with strata in the northwest boreal forest and southern prairie parkland habitats. Several strata in the boreal forest habitat had negative slope estimates, indicating a decrease in breeding pairs, while some of the strata in the prairie parkland habitat had positive slope estimates, indicating an increase in this region. Additionally, from looking at plots of individual strata, it seems that the strata experiencing increases in breeding pairs are experiencing dramatic increases. Overall, my results support previous work indicating a decline in population abundance in the northern boreal forest of Canada, and additionally indicate that the population of scaup has increased rapidly in the prairie pothole region since 1957. Yet, by accounting for spatial and temporal autocorrelation in the data, it appears that declines in abundance are not as widespread as previously reported.

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Zhuang, Lili. "Bayesian Dynamical Modeling of Count Data." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1315949027.

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Tunaru, Radu. "Statistical modelling of road accident data via graphical models and hierarchical Bayesian models." Thesis, Middlesex University, 1999. http://eprints.mdx.ac.uk/8030/.

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The objective of this thesis is to develop statistical models for multivariate road accident data. Two directions of research are followed: graphical modelling for contingency tables cross-classified by accident characteristics, and hierarchical Bayesian models for multiple accident frequencies of different types modelled jointly. Multi-dimensional tables are analysed and it is shown how to use collapsibility to reduce the dimensionality of the analysis without the problems of Simpson's paradox. It is revealed that accident severity and the number of casualties are associated, and that these variables are mainly influenced by the number of vehicles and speed limit. Graphical chain models allow causal hypotheses to be formulated and it is shown how they are valuable tools for empirical research about road accident characteristics. The hierarchical Bayesian models developed combine generalized linear models with random effects. The novelty of these models consists in the joint modelling of multiple response variables. The models account for overdispersion and they are used for accident prediction and for ranking hazardous sites. All models are fully Bayesian and are fitted using Markov Chain Monte Carlo methods. It is shown that multiple response variables models are superior to separate univariate response models. Some theoretical problems are examined regarding the maximum likelihood estimation process for the two parameters negative binomial distribution. A condition is given that is equivalent with unique maximum likelihood estimators. The two directions of research are connected by using graphs to describe the models. In addition, a new Bayesian model selection procedure for contingency tables is proposed. This is based on Gibbs sampling and avoids problems associated with asymptotic tests. The conclusions revealed here can help practitioners to design better safety policies and to spend money more wisely on sites that really are dangerous.

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Ren, Yan. "A Non-parametric Bayesian Method for Hierarchical Clustering of Longitudinal Data." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1337085531.

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Fawcett, Lee, Neil Thorpe, Joseph Matthews, and Karsten Kremer. "A novel Bayesian hierarchical model for road safety hotspot prediction." Elsevier, 2016. https://publish.fid-move.qucosa.de/id/qucosa%3A72268.

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In this paper, we propose a Bayesian hierarchical model for predicting accident counts in future years at sites within a pool of potential road safety hotspots. The aim is to inform road safety practitioners of the location of likely future hotspots to enable a proactive, rather than reactive, approach to road safety scheme implementation. A feature of our model is the ability to rank sites according to their potential to exceed, in some future time period, a threshold accident count which may be used as a criterion for scheme implementation. Our model specification enables the classical empirical Bayes formulation – commonly used in before-and-after studies, wherein accident counts from a single before period are used to estimate counterfactual counts in the after period – to be extended to incorporate counts from multiple time periods. This allows site-specific variations in historical accident counts (e.g. locally-observed trends) to offset estimates of safety generated by a global accident prediction model (APM), which itself is used to help account for the effects of global trend and regression-to-mean (RTM). The Bayesian posterior predictive distribution is exploited to formulate predictions and to properly quantify our uncertainty in these predictions. The main contributions of our model include (i) the ability to allow accident counts from multiple time-points to inform predictions, with counts in more recent years lending more weight to predictions than counts from time-points further in the past; (ii) where appropriate, the ability to offset global estimates of trend by variations in accident counts observed locally, at a site-specific level; and (iii) the ability to account for unknown/unobserved site-specific factors which may affect accident counts. We illustrate our model with an application to accident counts at 734 potential hotspots in the German city of Halle; we also propose some simple diagnostics to validate the predictive capability of our model. We conclude that our model accurately predicts future accident counts, with point estimates from the predictive distribution matching observed counts extremely well.

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Napier, Gary. "A Bayesian hierarchical model of compositional data with zeros : classification and evidence evaluation of forensic glass." Thesis, University of Glasgow, 2014. http://theses.gla.ac.uk/5793/.

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A Bayesian hierarchical model is proposed for modelling compositional data containing large concentrations of zeros. Two data transformations were used and compared: the commonly used additive log-ratio (alr) transformation for compositional data, and the square root of the compositional ratios. For this data the square root transformation was found to stabilise variability in the data better. The square root transformation also had no issues dealing with the large concentrations of zeros. To deal with the zeros, two different approaches have been implemented: the data augmentation approach and the composite model approach. The data augmentation approach treats any zero values as rounded zeros, i.e. traces of components below limits of detection, and updates those zero values with non-zero values. This is better than the simple approach of adding constant values to zeros as it reduces any artificial correlation produced by updating the zeros as part of the modelling procedure. However, due to the small detection limit it does not necessarily alleviate the problems of having a point mass very close to zero. The composite model approach treats any zero components as being absent from a composition. This is done by splitting the data into subsets according to the presence or absence of certain components to produce different data configurations that are then modelled separately. The models are applied to a database consisting of the elemental configurations of forensic glass fragments with many levels of variability and of various use types. The main purposes of the model are (i) to derive expressions for the posterior predictive probabilities of newly observed glass fragments to infer their use type (classification) and (ii) to compute the evidential value of glass fragments under two complementary propositions about their source (forensic evidence evaluation). Simulation studies using cross-validation are carried out to assess both model approaches, with both performing well at classifying glass fragments of use types bulb, headlamp and container, but less well so when classifying car and building windows. The composite model approach marginally outperforms the data augmentation approach at the classification task; both approaches have the edge over support vector machines (SVM). Both model approaches also perform well when evaluating the evidential value of glass fragments, with false negative and false positive error rates below 5%. The results from glass classification and evidence evaluation are an improvement over existing methods. Assessment of the models as part of the evidence evaluation simulation study also leads to a restriction being placed upon the reported strength of the value of this type of evidence. To prevent strong support in favour of the wrong proposition it is recommended that this glass evidence should provide, at most, moderately strong support in favour of a proposition. The classification and evidence evaluation procedures are implemented into an online web application, which outputs the corresponding results for a given set of elemental composition measurements. The web application contributes a quick and easy-to-use tool for forensic scientists that deal with this type of forensic evidence in real-life casework.

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Wang, Xiaohui. "Bayesian classification and survival analysis with curve predictors." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1205.

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Fang, Fang. "A simulation study for Bayesian hierarchical model selection methods." View electronic thesis (PDF), 2009. http://dl.uncw.edu/etd/2009-2/fangf/fangfang.pdf.

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Huddleston, Scott D. "Hitters vs. Pitchers: A Comparison of Fantasy Baseball Player Performances Using Hierarchical Bayesian Models." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3173.

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In recent years, fantasy baseball has seen an explosion in popularity. Major League Baseball, with its long, storied history and the enormous quantity of data available, naturally lends itself to the modern-day recreational activity known as fantasy baseball. Fantasy baseball is a game in which participants manage an imaginary roster of real players and compete against one another using those players' real-life statistics to score points. Early forms of fantasy baseball began in the early 1960s, but beginning in the 1990s, the sport was revolutionized due to the advent of powerful computers and the Internet. The data used in this project come from an actual fantasy baseball league which uses a head-to-head, points-based scoring system. The data consist of the weekly point totals that were accumulated over the first three-fourths of the 2011 regular season by the top 110 hitters and top 70 pitchers in Major League Baseball. The purpose of this project is analyze the relative value of pitchers versus hitters in this league using hierarchical Bayesian models. Three models will be compared, one which differentiates between hitters and pitchers, another which also differentiates between starting pitchers and relief pitchers, and a third which makes no distinction whatsoever between hitters and pitchers. The models will be compared using the deviance information criterion (DIC). The best model will then be used to predict weekly point totals for the last fourth of the 2011 season. Posterior predictive densities will be compared to actual weekly scores.

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Somal, Harsimran S. "Heterogeneous computing for the Bayesian hierarchical normal intrinsic conditional autoregressive model with incomplete data." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2145.

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A popular model for spatial association is the conditional autoregressive (CAR) model, and generalizations exist in the literature that utilize intrinsic CAR (ICAR) models within spatial hierarchical models. One generalization is the class of Bayesian hierarchical normal ICAR models, abbreviated HNICAR. The Bayesian HNICAR model can be used to smooth areal or lattice data, estimate the directional strength of spatio-temporal associations, and make posterior predictions at each point in space or time. Furthermore, the Bayesian HNICAR model allows for sample-based posterior inference about model parameters and predictions. R package CARrampsOcl enables fast, independent sampling-based inference for a Bayesian HNICAR model when data are complete and the spatial precision matrix is expressible as a Kronecker sum of lower order matrices. This thesis presents an independent sampling algorithm to accommodate incomplete data and arbitrary precision structures, a parallelized implementation of the algorithm that can be executed on a wide range of hardware, including NVIDIA and AMD graphical processing units (GPUs) and multicore Intel CPUs, analysis of the effects of missingness on the posterior distribution of model parameters and predictive densities, and a survey of model comparison methods for CAR models. The merits of the model and algorithm are demonstrated through both simulation and analysis of an environmental data set.

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Kim, Hoon. "Bayesian hierarchical spatio-temporal analysis of mortality rates with disease mapping /." free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9953872.

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Mitchell, Shira Arkin. "Capture-recapture Estimation for Conflict Data and Hierarchical Models for Program Impact Evaluation." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11586.

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A relatively recent increase in the popularity of evidence-based activism has created a higher demand for statisticians to work on human rights and economic development projects. The statistical challenges of revealing patterns of violence in armed conflict require efficient use of the data, and careful consideration of the implications of modeling decisions on estimates. Impact evaluation of a complex economic development project requires a careful consideration of causality and transparency to donors and beneficiaries. In this dissertation, I compare marginal and conditional models for capture recapture, and develop new hierarchical models that accommodate challenges in data from the armed conflict in Colombia, and more generally, in many other capture recapture settings. Additionally, I propose a study design for a non-randomized impact evaluation of the Millennium Villages Project (MVP), to be carried out during my postdoctoral fellowship. The design includes small area estimation of baseline variables, propensity score matching, and hierarchical models for causal inference.

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Brynjarsdóttir, Jenný. "Dimension Reduced Modeling of Spatio-Temporal Processes with Applications to Statistical Downscaling." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312935520.

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Olid, Pilar. "Making Models with Bayes." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/593.

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Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects the model. We will also make a comparison between the Bayesian approach and the traditional frequentist approach to data analyses.

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Dissertations / Theses on the topic 'Hierarchal Bayesian statistics'

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