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Bayesian Analysis and Monte Carlo Sampling in the Study of Cryo-Electron Microscopy

Posted on:2017-01-11Degree:Ph.DType:Dissertation
University:New York UniversityCandidate:Lewis, MichaelFull Text:PDF
GTID:1460390014473026Subject:Mathematics
Abstract/Summary:
Cryo Electron Microscopy is a useful tool in studying the geometry of macromolecular assemblies. This method deduces the underlying density of the structure by inference from a multitude of blurry projections of the density. Consequently, the results can be framed as an inverse problem with noisy data. We formulate a posterior distribution for the system using Bayesian analysis and deduce meaningful aspects of the maximum likelihood solution. We also construct novel ways to sample this distribution via Markov chain Monte Carlo methods. We test and analyze our numerical results from our simulations, and propose future enhancements.
Keywords/Search Tags:Monte carlo, Bayesian analysis
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