Physical Sciences and Mathematics Commons^™

Bayesian Analysis Of Single Molecule Fluorescence Microscopy Data, Mohamadreza Fazel

Physics & Astronomy ETDs

The diffraction limit can be circumvent by creating and exploiting independent behaviors of the sample at lengths scale below the diffraction limit. In fluorescence microscopy, the independence arises from individual fluorescent labels switching between dark and fluorescence states. The fluorophores can then be localized employing the generated sparse image frames. Finally, the resulting list of coordinates is utilized to generate high resolution images or to gain quantitative insight into the underlying biological structures. Therefore image processing and post-processing are essential stages of SMLM techniques.

In this dissertation, Reversible Jump Markov Chain Monte Carlo was employed to implement Bayesian analysis of …

Methods Of Uncertainty Quantification For Physical Parameters, Kellin Rumsey

Mathematics & Statistics ETDs

Uncertainty Quantification (UQ) is an umbrella term referring to a broad class of methods which typically involve the combination of computational modeling, experimental data and expert knowledge to study a physical system. A parameter, in the usual statistical sense, is said to be physical if it has a meaningful interpretation with respect to the physical system. Physical parameters can be viewed as inherent properties of a physical process and have a corresponding true value. Statistical inference for physical parameters is a challenging problem in UQ due to the inadequacy of the computer model. In this thesis, we provide a comprehensive …