Statistical Models Commons^™

Identifying The Spatial Distribution Of Three Plethodontid Salamanders In Great Smoky Mountains National Park Using Two Habitat Modeling Methods, Matthew Stephen Kookogey

Masters Theses

The main objective was to create habitat models of three plethodontid salamander species (Desmognathus conanti, D. ocoee, and Plethodon jordani) in GSMNP. To investigate the relationships between salamanders and their habitats, I used three models—logistic regression with use-availability sampling, logistic regression with case-control sampling, and Mahalanobis distance (D²)—for each species to gain a robust view of the relationships. The secondary objective was to compare the different modeling methods within and across the three species. Elevation was the dominant variable for all three species.

D² for D. conanti predicted low elevations, close proximity …

Differential Patterns Of Interaction And Gaussian Graphical Models, Masanao Yajima, Donatello Telesca, Yuan Ji, Peter Muller

COBRA Preprint Series

We propose a methodological framework to assess heterogeneous patterns of association amongst components of a random vector expressed as a Gaussian directed acyclic graph. The proposed framework is likely to be useful when primary interest focuses on potential contrasts characterizing the association structure between known subgroups of a given sample. We provide inferential frameworks as well as an efficient computational algorithm to fit such a model and illustrate its validity through a simulation. We apply the model to Reverse Phase Protein Array data on Acute Myeloid Leukemia patients to show the contrast of association structure between refractory patients and relapsed …

Spatial And Temporal Correlations Of Freeway Link Speeds: An Empirical Study, Piotr J. Rachtan

Masters Theses 1911 - February 2014

Congestion on roadways and high level of uncertainty of traffic conditions are major considerations for trip planning. The purpose of this research is to investigate the characteristics and patterns of spatial and temporal correlations and also to detect other variables that affect correlation in a freeway setting. 5-minute speed aggregates from the Performance Measurement System (PeMS) database are obtained for two directions of an urban freeway – I-10 between Santa Monica and Los Angeles, California. Observations are for all non-holiday weekdays between January 1st and June 30th, 2010. Other variables include traffic flow, ramp locations, number of lanes and the …

Statistical Methods For Proteomic Biomarker Discovery Based On Feature Extraction Or Functional Modeling Approaches, Jeffrey S. Morris

Jeffrey S. Morris

In recent years, developments in molecular biotechnology have led to the increased promise of detecting and validating biomarkers, or molecular markers that relate to various biological or medical outcomes. Proteomics, the direct study of proteins in biological samples, plays an important role in the biomarker discovery process. These technologies produce complex, high dimensional functional and image data that present many analytical challenges that must be addressed properly for effective comparative proteomics studies that can yield potential biomarkers. Specific challenges include experimental design, preprocessing, feature extraction, and statistical analysis accounting for the inherent multiple testing issues. This paper reviews various computational …

Integrative Bayesian Analysis Of High-Dimensional Multi-Platform Genomics Data, Wenting Wang, Veerabhadran Baladandayuthapani, Jeffrey S. Morris, Bradley M. Broom, Ganiraju C. Manyam, Kim-Anh Do

Jeffrey S. Morris

Motivation: Analyzing data from multi-platform genomics experiments combined with patients’ clinical outcomes helps us understand the complex biological processes that characterize a disease, as well as how these processes relate to the development of the disease. Current integration approaches that treat the data are limited in that they do not consider the fundamental biological relationships that exist among the data from platforms.

Statistical Model: We propose an integrative Bayesian analysis of genomics data (iBAG) framework for identifying important genes/biomarkers that are associated with clinical outcome. This framework uses a hierarchical modeling technique to combine the data obtained from multiple platforms …

Modeling Dependence Using Skew T Copulas: Bayesian Inference And Applications, Michael S. Smith, Quan Gan, Robert Kohn

Michael Stanley Smith

[THIS IS AN AUGUST 2010 REVISION THAT REPLACES ALL PREVIOUS VERSIONS.]

We construct a copula from the skew t distribution of Sahu, Dey & Branco (2003). This copula can capture asymmetric and extreme dependence between variables, and is one of the few copulas that can do so and still be used in high dimensions effectively. However, it is difficult to estimate the copula model by maximum likelihood when the multivariate dimension is high, or when some or all of the marginal distributions are discrete-valued, or when the parameters in the marginal distributions and copula are estimated jointly. We therefore propose …

Estimation Of Copula Models With Discrete Margins Via Bayesian Data Augmentation, Michael S. Smith, Mohamad A. Khaled

Michael Stanley Smith

Estimation of copula models with discrete margins is known to be difficult beyond the bivariate case. We show how this can be achieved by augmenting the likelihood with latent variables, and computing inference using the resulting augmented posterior. To evaluate this we propose two efficient Markov chain Monte Carlo sampling schemes. One generates the latent variables as a block using a Metropolis-Hasting step with a proposal that is close to its target distribution, the other generates them one at a time. Our method applies to all parametric copulas where the conditional copula functions can be evaluated, not just elliptical copulas …