Date of Award

1-1-2012

Language

English

Document Type

Master's Thesis

Degree Name

Master of Science (MS)

College/School/Department

Department of Physics

Content Description

1 online resource (iv, 104 pages) : illustrations (some color)

Dissertation/Thesis Chair

Keith A Earle

Committee Members

Kevin Knuth, Carolyn MacDonald

Keywords

Data Analysis, Information Physics, Lineshape analysis, Magnetic Resonance Spectroscopy, Nuclear magnetic resonance spectroscopy, Information theory in physics

Subject Categories

Physics

Abstract

Magnetic resonance absorption lineshapes can be difficult to calculate but there are simple model systems for which analytical expressions are available which makes model exploration much easier. One goal of this work is to quantify how well model parameters may be inferred from a signal using tools from information theory. Another goal is to equip ourselves with tools to assess the importance of missing parameters in our model. We do this by monitoring the partition function determined from a suitably defined probability mass function for various parameter values. The optimum parameter set makes the partition function a maximum which gives us a criterion for determining the best model parameter set. In this work, we observe that at sufficiently low signal to noise ratio, the entropy landscape has no clear maximum, while the Fisher information always has a clear minimum at the optimum parameter set. The qualitative information we are able to gather from the entropy landscapes is also difficult to assess when the parameters are far from their actual values, at least for the model system studied here.

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