The main objective of our study is to employ copula methodology to develop Bayesian
hierarchical models to study the dependencies exhibited by temporal, spatial and
spatio-temporal processes. We develop hierarchical models for both discrete and
continuous outcomes. In doing so we expect to address the dearth of copula based
Bayesian hierarchical models to study hydro-meteorological events and other physical
processes yielding discrete responses.
First, we present Bayesian methods of analysis for longitudinal binary outcomes using
Generalized Linear Mixed models (GLMM). We allow flexible marginal association
among the repeated outcomes from different time-points. An unique property of this
copula-based GLMM is that if the marginal link function is integrated over the distribution
of the random effects, its form remains same as that of the conditional link
function. This unique property enables us to retain the physical interpretation of the
fixed effects under conditional and marginal model and yield proper posterior distribution.
We illustrate the performance of the posited model using real life AIDS data
and demonstrate its superiority over the traditional Gaussian random effects model.
We develop a semiparametric extension of our GLMM and re-analyze the data from
the AIDS study.
Next, we propose a general class of models to handle non-Gaussian spatial data. The proposed model can deal with geostatistical data that can accommodate skewness,
tail-heaviness, multimodality. We fix the distribution of the marginal processes and
induce dependence via copulas. We illustrate the superior predictive performance
of our approach in modeling precipitation data as compared to other kriging variants.
Thereafter, we employ mixture kernels as the copula function to accommodate
non-stationary data. We demonstrate the adequacy of this non-stationary model by
analyzing permeability data. In both cases we perform extensive simulation studies
to investigate the performances of the posited models under misspecification.
Finally, we take up the important problem of modeling multivariate extreme values
with copulas. We describe, in detail, how dependences can be induced in the
block maxima approach and peak over threshold approach by an extreme value copula.
We prove the ability of the posited model to handle both strong and weak extremal
dependence and derive the conditions for posterior propriety. We analyze the extreme
precipitation events in the continental United States for the past 98 years and come
up with a suite of predictive maps.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-08-7160 |
| Date | 2009 August 1900 |
| Creators | Ghosh, Souparno |
| Contributors | Mallick, Bani K. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | application/pdf |
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