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Full-Text Articles in Statistics and Probability
Online Variational Bayes Inference For High-Dimensional Correlated Data, Sylvie T. Kabisa, Jeffrey S. Morris, David Dunson
Online Variational Bayes Inference For High-Dimensional Correlated Data, Sylvie T. Kabisa, Jeffrey S. Morris, David Dunson
Jeffrey S. Morris
High-dimensional data with hundreds of thousands of observations are becoming commonplace in many disciplines. The analysis of such data poses many computational challenges, especially when the observations are correlated over time and/or across space. In this paper we propose exible hierarchical regression models for analyzing such data that accommodate serial and/or spatial correlation. We address the computational challenges involved in fitting these models by adopting an approximate inference framework. We develop an online variational Bayes algorithm that works by incrementally reading the data into memory one portion at a time. The performance of the method is assessed through simulation studies. …
Functional Car Models For Spatially Correlated Functional Datasets, Lin Zhang, Veerabhadran Baladandayuthapani, Hongxiao Zhu, Keith A. Baggerly, Tadeusz Majewski, Bogdan Czerniak, Jeffrey S. Morris
Functional Car Models For Spatially Correlated Functional Datasets, Lin Zhang, Veerabhadran Baladandayuthapani, Hongxiao Zhu, Keith A. Baggerly, Tadeusz Majewski, Bogdan Czerniak, Jeffrey S. Morris
Jeffrey S. Morris
We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on …
Functional Regression, Jeffrey S. Morris
Functional Regression, Jeffrey S. Morris
Jeffrey S. Morris
Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and …
Ordinal Probit Wavelet-Based Functional Models For Eqtl Analysis, Mark J. Meyer, Jeffrey S. Morris, Craig P. Hersh, Jarret D. Morrow, Christoph Lange, Brent A. Coull
Ordinal Probit Wavelet-Based Functional Models For Eqtl Analysis, Mark J. Meyer, Jeffrey S. Morris, Craig P. Hersh, Jarret D. Morrow, Christoph Lange, Brent A. Coull
Jeffrey S. Morris
Current methods for conducting expression Quantitative Trait Loci (eQTL) analysis are limited in scope to a pairwise association testing between a single nucleotide polymorphism (SNPs) and expression probe set in a region around a gene of interest, thus ignoring the inherent between-SNP correlation. To determine association, p-values are then typically adjusted using Plug-in False Discovery Rate. As many SNPs are interrogated in the region and multiple probe-sets taken, the current approach requires the fitting of a large number of models. We propose to remedy this by introducing a flexible function-on-scalar regression that models the genome as a functional outcome. The …
Interpretation And Prediction Of A Logistic Model, Joseph M. Hilbe
Interpretation And Prediction Of A Logistic Model, Joseph M. Hilbe
Joseph M Hilbe
A basic overview of how to model and interpret a logistic regression model, as well as how to obtain the predicted probability or fit of the model and calculate its confidence intervals. R code used for all examples; some Stata is provided as a contrast.
Beta Binomial Regression, Joseph M. Hilbe
Beta Binomial Regression, Joseph M. Hilbe
Joseph M Hilbe
Monograph on how to construct, interpret and evaluate beta, beta binomial, and zero inflated beta-binomial regression models. Stata and R code used for examples.
Statistical Methods For Proteomic Biomarker Discovery Based On Feature Extraction Or Functional Modeling Approaches, Jeffrey S. Morris
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
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 …
Generalized Linear Models: Software Implementation And The Structure Of A General Power-Link Based Glm Algorithm, Joseph Hilbe
Generalized Linear Models: Software Implementation And The Structure Of A General Power-Link Based Glm Algorithm, Joseph Hilbe
Joseph M Hilbe
Generalized linear modeling (GLM) is currently undergoing a renaissance. The number of software packages offering GLM capability grows each year and as a partial consequence one finds an increased number of research endeavors being modeled using GLM methodology. On the other hand, there have likewise been an increasing number of requests to vendors by users of statistical packages to include GLM facilities amid other offerings. The overall effect has been a near 300 percent increase in GLM programs over the past four years.
I shall discuss the nature of generalized linear models followed by an examination of how they have …