Sanders, Barry C.de Guise, HubertSalimi Moghadam, Mahkame2024-09-242024-09-242024-09-20Salimi Moghadam, M. (2024). Estimating imprecision lower bound in a neighbourhood of a known Cramér-Rao lower bound (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.https://hdl.handle.net/1880/119868The ultimate metrology limit, classical or quantum, for estimating an unknown parameter defining a distribution of measurement outcomes, is determined by the Cramér-Rao lower bound (CRLB). However, which distribution pertains to the measurement setup can itself fluctuate for running each trial of the experiment or even within one run, meaning that we are estimating the distribution parameter in the case that we have a distribution of distributions. Our aim is to estimate the imprecision CRLB for the parameter of a distribution but in a small neighbourhood of this distribution rather than precisely at this parameter. We determine this CRLB in a neighbourhood by calculating a Taylor expansion of the Fisher information for the distribution in a neighbourhood of its defining parameter, obtain the expression for the CRLB for each distribution in this neighbourhood and then calculate the average CRLB over this neighbourhood. We illustrate our result for the case of two-parameter estimation in SU(2) interferometry for which singularities of the CRLB arise, making this averaging not just illustrative but also needed to circumvent the singularity.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Fisher informationCramér-Rao lower boundMach–Zehnder interferometerSingular matricesQuantum metrologyParameter estimationPhysics--TheoryStatisticsmaster thesis