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Relevant bibliographies by topics / Spatial analysis (Statistics) Regression analysis. Bayesian statistical decision theory / Dissertations / Theses

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Dissertations / Theses on the topic 'Spatial analysis (Statistics) Regression analysis. Bayesian statistical decision theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Wheeler, David C. "Diagnostic tools and remedial methods for collinearity in linear regression models with spatially varying coefficients." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1155413322.

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2

Oleson, Jacob J. "Bayesian spatial models for small area estimation /." free to MU campus, to others for purchase, 2002. http://wwwlib.umi.com/cr/mo/fullcit?p3052203.

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3

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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4

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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5

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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6

Sun, Xiaoqian. "Bayesian spatial data analysis with application to the Missouri Ozark forest ecosystem project." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4477.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2006.
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 (May 1, 2007) Vita. Includes bibliographical references.

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7

Higdon, David. "Spatial applications of Markov chain Monte Carlo for Bayesian inference /." Thesis, Connect to this title online; UW restricted, 1994. http://hdl.handle.net/1773/8942.

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8

Miyamoto, Kazutoshi Seaman John Weldon. "Bayesian and maximum likelihood methods for some two-segment generalized linear models." Waco, Tex. : Baylor University, 2008. http://hdl.handle.net/2104/5233.

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9

Powers, Stephanie L. Stamey James D. "Bayesian approach to inference and variable selection for misclassified and under-reported response models." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5355.

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10

Byers, Simon. "Bayesian modeling of highly structured systems using Markov chain Monte Carlo /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/8980.

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11

Johnson, Edward P. "Applying Bayesian Ordinal Regression to ICAP Maladaptive Behavior Subscales." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2121.pdf.

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12

Michell, Justin Walter. "A review of generalized linear models for count data with emphasis on current geospatial procedures." Thesis, Rhodes University, 2016. http://hdl.handle.net/10962/d1019989.

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Analytical problems caused by over-fitting, confounding and non-independence in the data is a major challenge for variable selection. As more variables are tested against a certain data set, there is a greater risk that some will explain the data merely by chance, but will fail to explain new data. The main aim of this study is to employ a systematic and practicable variable selection process for the spatial analysis and mapping of historical malaria risk in Botswana using data collected from the MARA (Mapping Malaria Risk in Africa) project and environmental and climatic datasets from various sources. Details of how a spatial database is compiled for a statistical analysis to proceed is provided. The automation of the entire process is also explored. The final bayesian spatial model derived from the non-spatial variable selection procedure using Markov Chain Monte Carlo simulation was fitted to the data. Winter temperature had the greatest effect of malaria prevalence in Botswana. Summer rainfall, maximum temperature of the warmest month, annual range of temperature, altitude and distance to closest water source were also significantly associated with malaria prevalence in the final spatial model after accounting for spatial correlation. Using this spatial model malaria prevalence at unobserved locations was predicted, producing a smooth risk map covering Botswana. The automation of both compiling the spatial database and the variable selection procedure proved challenging and could only be achieved in parts of the process. The non-spatial selection procedure proved practical and was able to identify stable explanatory variables and provide an objective means for selecting one variable over another, however ultimately it was not entirely successful due to the fact that a unique set of spatial variables could not be selected.

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13

Moretti, Antonio Khalil. "Variational Bayesian Methods for Inferring Spatial Statistics and Nonlinear Dynamics." Thesis, 2021. https://doi.org/10.7916/d8-tk49-d623.

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This thesis discusses four novel statistical methods and approximate inference techniques for analyzing structured neural and molecular sequence data. The main contributions are new algorithms for approximate inference and learning in Bayesian latent variable models involving spatial statistics and nonlinear dynamics. First, we propose an amortized variational inference method to separate a set of overlapping signals into spatially localized source functions without knowledge of the original signals or the mixing process. In the second part of this dissertation, we discuss two approaches for uncovering nonlinear, smooth latent dynamics from sequential data. Both algorithms construct variational families on extensions of nonlinear state space models where the underlying systems are described by hidden stochastic differential equations. The first method proposes a structured approximate posterior describing spatially-dependent linear dynamics, as well as an algorithm that relies on the fixed-point iteration method to achieve convergence. The second method proposes a variational backward simulation technique from an unbiased estimate of the marginal likelihood defined through a subsampling process. In the final chapter, we develop connections between discrete and continuous variational sequential search for Bayesian phylogenetic inference. We propose a technique that uses sequential search to construct a variational objective defined on the composite space of non-clock phylogenetic trees. Each of these techniques are motivated by real problems within computational biology and applied to provide insights into the underlying structure of complex data.

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14

Rahman, Husneara. "A comparison of Bayesian variable selection approaches for linear models." 2014. http://liblink.bsu.edu/uhtbin/catkey/1749597.

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Bayesian variable selection approaches are more powerful in discriminating among models regardless of whether these models under investigation are hierarchical or not. Although Bayesian approaches require complex computation, use of theMarkov Chain Monte Carlo (MCMC) methods, such as, Gibbs sampler and Metropolis-Hastings algorithm make computations easier. In this study we investigated the e↵ectiveness of Bayesian variable selection approaches in comparison to other non-Bayesian or classical approaches. For this purpose, we compared the performance of Bayesian versus non-Bayesian variable selection approaches for linear models. Among these approaches, we studied Conditional Predictive Ordinate (CPO) and Bayes factor. Among the non-Bayesian or classical approaches, we implemented adjusted R-square, Akaike Information Criterion (AIC) and Bayes Information Criterion (BIC) for model selection. We performed a simulation study to examine how Bayesian and non- Bayesian approaches perform in selecting variables. We also applied these methods to real data and compared their performances. We observed that for linear models, Bayesian variable selection approaches perform consistently as that of non-Bayesian approaches.
Bayesian inference -- Bayesian inference for normally distributed likekilhood -- Model adequacy -- Simulation approach -- Application to wage data.
Department of Mathematical Sciences

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15

Che, Xuan. "Spatial graphical models with discrete and continuous components." Thesis, 2012. http://hdl.handle.net/1957/33644.

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Graphical models use Markov properties to establish associations among dependent variables. To estimate spatial correlation and other parameters in graphical models, the conditional independences and joint probability distribution of the graph need to be specified. We can rely on Gaussian multivariate models to derive the joint distribution when all the nodes of the graph are assumed to be normally distributed. However, when some of the nodes are discrete, the Gaussian model no longer affords an appropriate joint distribution function. We develop methods specifying the joint distribution of a chain graph with both discrete and continuous components, with spatial dependencies assumed among all variables on the graph. We propose a new group of chain graphs known as the generalized tree networks. Constructing the chain graph as a generalized tree network, we partition its joint distributions according to the maximal cliques. Copula models help us to model correlation among discrete variables in the cliques. We examine the method by analyzing datasets with simulated Gaussian and Bernoulli Markov random fields, as well as with a real dataset involving household income and election results. Estimates from the graphical models are compared with those from spatial random effects models and multivariate regression models.
Graduation date: 2013

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16

Fang, Yan. "Extensions to Gaussian copula models." Thesis, 2012. http://hdl.handle.net/1957/29482.

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A copula is the representation of a multivariate distribution. Copulas are used to model multivariate data in many fields. Recent developments include copula models for spatial data and for discrete marginals. We will present a new methodological approach for modeling discrete spatial processes and for predicting the process at unobserved locations. We employ Bayesian methodology for both estimation and prediction. Comparisons between the new method and Generalized Additive Model (GAM) are done to test the performance of the prediction. Although there exists a large variety of copula functions, only a few are practically manageable and in certain problems one would like to choose the Gaussian copula to model the dependence. Furthermore, most copulas are exchangeable, thus implying symmetric dependence. However, none of them is flexible enough to catch the tailed (upper tailed or lower tailed) distribution as well as elliptical distributions. An elliptical copula is the copula corresponding to an elliptical distribution by Sklar's theorem, so it can be used appropriately and effectively only to fit elliptical distributions. While in reality, data may be better described by a "fat-tailed" or "tailed" copula than by an elliptical copula. This dissertation proposes a novel pseudo-copula (the modified Gaussian pseudo-copula) based on the Gaussian copula to model dependencies in multivariate data. Our modified Gaussian pseudo-copula differs from the standard Gaussian copula in that it can model the tail dependence. The modified Gaussian pseudo-copula captures properties from both elliptical copulas and Archimedean copulas. The modified Gaussian pseudo-copula and its properties are described. We focus on issues related to the dependence of extreme values. We give our pseudo-copula characteristics in the bivariate case, which can be extended to multivariate cases easily. The proposed pseudo-copula is assessed by estimating the measure of association from two real data sets, one from finance and one from insurance. A simulation study is done to test the goodness-of-fit of this new model.
Graduation date: 2012

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