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Markov Chain Monte Carlo on the GPU

Michael D. Dumont
Rochester Institute of Technology, Rochester, New York
Rochester Institute of Technology, 2011

@phdthesis{dumont2011markov,

   title={Markov Chain Monte Carlo on the GPU},

   author={Dumont, M.D.},

   year={2011},

   school={Rochester Institute of Technology}

}

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Markov chains are a useful tool in statistics that allow us to sample and model a large population of individuals. We can extend this idea to the challenge of sampling solutions to problems. Using Markov chain Monte Carlo (MCMC) techniques we can also attempt to approximate the number of solutions with a certain confidence based on the number of samples we use to compute our estimate. Even though this approximation works very well for getting accurate results for very large problems, it is still computationally intensive. Many of the current algorithms use parallel implementations to improve their performance. Modern day graphics processing units (GPU’s) have been increasing in computational power very rapidly over the past few years. Due to their inherently parallel nature and increased flexibility for general purpose computation, they lend themselves very well to building a framework for general purpose Markov chain simulation and evaluation. In addition, the majority of mid- to high-range workstations have graphics cards capable of supporting modern day general purpose GPU (GPGPU) frameworks such as OpenCL, CUDA, or DirectCompute. This thesis presents work done to create a general purpose framework for Markov chain simulations and Markov chain Monte Carlo techniques on the GPU using the OpenCL toolkit. OpenCL is a GPGPU framework that is platform and hardware independent, which will further increase the accessibility of the software. Due to the increasing power, flexibility, and prevalence of GPUs, a wider range of developers and researchers will be able to take advantage of a high performing general purpose framework in their research. A number of experiments are also conducted to demonstrate the benefits and feasibility of using the power of the GPU to solve Markov chain Monte Carlo problems.
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