Date of Award


Document Type

Campus Access Thesis

Degree Name

Master of Science (MS)


Physics, Applied

First Advisor

Olga Goulko

Second Advisor

David Degras-Valabregue

Third Advisor

Maxim Olchanyi


The process of estimating the underlying probability density function that describes a sampled set of data is known as density estimation. The bin hierarchy method (BHM) is a density estimator that allows us to restore a smooth function from its underlying noisy integrals. It has been shown that the BHM computes the maximally smooth function using essentially all the information from the integrals in an efficient, automated, and minimally memory-intensive manner. The structure and mathematics for BHM have been presented in [9][10], with appropriate numerical tests having been conducted. This thesis reviews the BHM method and discusses potential generalizations for bivariate data, such as using bicubic splines or biquadratic histosplines as spline interpolants. Proposed applications on forms of joint probability density functions found within physics and other sciences are also discussed.


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