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Articles 1 - 5 of 5
Full-Text Articles in Statistics and Probability
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 …
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 …
Wavelet-Based Functional Mixed Models To Characterize Population Heterogeneity In Accelerometer Profiles: A Case Study. , Jeffrey S. Morris, Cassandra Arroyo, Brent A. Coull, Louise M. Ryan, Steven L. Gortmaker
Wavelet-Based Functional Mixed Models To Characterize Population Heterogeneity In Accelerometer Profiles: A Case Study. , Jeffrey S. Morris, Cassandra Arroyo, Brent A. Coull, Louise M. Ryan, Steven L. Gortmaker
Jeffrey S. Morris
We present a case study illustrating the challenges of analyzing accelerometer data taken from a sample of children participating in an intervention study designed to increase physical activity. An accelerometer is a small device worn on the hip that records the minute-by-minute activity levels of the child throughout the day for each day it is worn. The resulting data are irregular functions characterized by many peaks representing short bursts of intense activity. We model these data using the wavelet-based functional mixed model. This approach incorporates multiple fixed effects and random effect functions of arbitrary form, the estimates of which are …
Wavelet-Based Functional Mixed Model Analysis: Computational Considerations, Richard C. Herrick, Jeffrey S. Morris
Wavelet-Based Functional Mixed Model Analysis: Computational Considerations, Richard C. Herrick, Jeffrey S. Morris
Jeffrey S. Morris
Wavelet-based Functional Mixed Models is a new Bayesian method extending mixed models to irregular functional data (Morris and Carroll, JRSS-B, 2006). These data sets are typically very large and can quickly run into memory and time constraints unless these issues are carefully dealt with in the software. We reduce runtime by 1.) identifying and optimizing hotspots, 2.) using wavelet compression to do less computation with minimal impact on results, and 3.) dividing the code into multiple executables to be run in parallel using a grid computing resource. We discuss rules of thumb for estimating memory requirements and computation times in …
Wavelet-Based Nonparametric Modeling Of Hierarchical Functions In Colon Carcinogenesis., Jeffrey S. Morris, Marina Vannucci, Philip J. Brown, Raymond J. Carroll
Wavelet-Based Nonparametric Modeling Of Hierarchical Functions In Colon Carcinogenesis., Jeffrey S. Morris, Marina Vannucci, Philip J. Brown, Raymond J. Carroll
Jeffrey S. Morris
In this article we develop new methods for analyzing the data from an experiment using rodent models to investigate the effect of type of dietary fat on O6-methylguanine-DNA-methyltransferase (MGMT), an important biomarker in early colon carcinogenesis. The data consist of observed profiles over a spatial variable contained within a two-stage hierarchy, a structure that we dub hierarchical functional data. We present a new method providing a unified framework for modeling these data, simultaneously yielding estimates and posterior samples for mean, individual, and subsample-level profiles, as well as covariance parameters at the various hierarchical levels. Our method is nonparametric in that …