28053

Statistical Computing With Graphics Processing Units

Ruoyong Xu
Department of Department of Statistical Sciences, University of Toronto
University of Toronto, 2023

@phdthesis{xu2023statistical,

   title={Statistical Computing With Graphics Processing Units},

   author={Xu, Ruoyong},

   year={2023}

}

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This thesis consists of two main projects and a third project which is provided in the appendix. The contribution of the first project, is a tool set for parallel random number gen- eration on GPUs in R, namely, the clrng package. This package is currently the only R package that provides facilities for generating random numbers in parallel on a GPU. It enables reproducible research by setting random initial seeds for streams on GPU and CPU. The random number generator in clrng guarantees independent parallel samples even when R is used interactively in an ad-hoc manner, with sessions being interrupted and restored. This package can be easily incorporated in other R packages, allowing developers to develop other types of random number generators or accelerate suitable computations in statistical applications. The contribution of the second project, is a methodology and software for creating profile likelihoods for parameters in Gaussian spatial models with Mat ́ern family of correlation functions, including anisotropic models. This methodology adopts a novel reparametrization for generation of representative points, and is implemented in the software gpuLik, which uses GPUs for parallel profile likelihoods computation. Our work has shown how GPU’s enable likelihood-based inference for Gaussian spatial models without requiring approximations to the variance matrix, even for moderately large datasets. The third project provided in the Appendix is dedicated to evaluating the impact of the COVID-19 pandemic on online public interest in various cancers (breast, colon, lung, prostate, and thyroid). A cross-sectional retrospective study was conducted utilizing Google Trends aggregate anonymous online search data from Canada. Welch’s Two Sample t-tests were performed and Benjamini-Hochberg procedure was used to correct for multiple comparisons.
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