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Bayesian functional concurrent logis...

Jiang, Qi.

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Bayesian functional concurrent logistic models for spatial categorical data.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bayesian functional concurrent logistic models for spatial categorical data./
作者:	Jiang, Qi.
面頁冊數:	152 p.
附註:	Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.
Contained By:	Dissertation Abstracts International77-10B(E).
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10111268
ISBN:	9781339744773

Bayesian functional concurrent logistic models for spatial categorical data.
Jiang, Qi.

Bayesian functional concurrent logistic models for spatial categorical data. - 152 p.

Source: Dissertation Abstracts International, Volume: 77-10(E), Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2016.

My thesis focuses primarily on developing statistical methods for analyzing spatial categorical data and for relating such data to spatial covariates. In Chapter 1, we proposed an approximate method to model spatial binary images by first transforming spatial binary images into roughly continuous images and then using the approach of Shang and Clayton (2011). In Chapter 2, we proposed a new functional concurrent logistic model for analyzing spatial binary data based on the development of Zhang et al. (2011) and Shang and Clayton (2012). To estimate this model, we employed a Polya-Gamma data augmentation strategy proposed by Polson et al. (2013) for simple and effective posterior inferences. This new data-augmentation framework uses a new class of Polya-Gamma distributions to help derive exact posterior distributions for a Gibbs sampler. In Chapter 3, we further extended the functional concurrent logistic model to address spatial multinomial data and proposed a Gibbs sampling algorithm for making statistical inferences.

ISBN: 9781339744773Subjects--Topical Terms:

517247
Statistics.

Bayesian functional concurrent logistic models for spatial categorical data.
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500 $a Adviser: Murray Clayton.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2016.
520 $a My thesis focuses primarily on developing statistical methods for analyzing spatial categorical data and for relating such data to spatial covariates. In Chapter 1, we proposed an approximate method to model spatial binary images by first transforming spatial binary images into roughly continuous images and then using the approach of Shang and Clayton (2011). In Chapter 2, we proposed a new functional concurrent logistic model for analyzing spatial binary data based on the development of Zhang et al. (2011) and Shang and Clayton (2012). To estimate this model, we employed a Polya-Gamma data augmentation strategy proposed by Polson et al. (2013) for simple and effective posterior inferences. This new data-augmentation framework uses a new class of Polya-Gamma distributions to help derive exact posterior distributions for a Gibbs sampler. In Chapter 3, we further extended the functional concurrent logistic model to address spatial multinomial data and proposed a Gibbs sampling algorithm for making statistical inferences.
520 $a We examined our methods developed in Chapter 2 and 3 with simulated spatial binary and multinomial datasets under various circumstances. Both visual checks and quantitative measures from the simulation studies provided evidence that our methods are able to detect the relationship between the response and covariate and to recover parameter surfaces in all simulation settings. Moreover, our methods give near optimal prediction accuracy using the ideal predictors as benchmarks.
520 $a We also applied our methods to real datasets obtained from the Midwest Tension Zone project to better understand the relationship between spatial variation in tree species and environmental factors. Our results show that there does exist relationships between the occurrence of various land covers and water content in the soil. We also discussed several challenges that come with our methods. First, we discussed the computational challenge when dealing with large scale images; one of our approaches to improve computational speed is a two-stage prefiltering method which filters out unnecessary wavelet bases for fine details during the preparation stage and then runs our methods only with selected wavelet bases. Second, we discussed ways of selecting the most important explanatory covariates. To achieve this, we proposed two schemes of model selection which allow simultaneous model selection and estimation. Simulation results provide evidence that our methods are capable of selecting the correct covariates, although with some occasional failures to exclude unimportant covariates. Finally, we addressed the analysis of spatial images when missing data occur. Our findings show that our missing data handling mechanism can help to impute missing pixels in the response image.
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