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The discovery of the Standard Model (SM) Higgs boson by ATLAS and CMS at theLHC in 2012 marked a major milestone in particle physics. However, manyquestions remain unanswered, which has led to an active research program tosearch for either rare SM phenomena or Beyond Standard Model (BSM) physics thatinvolve the Higgs boson. In this dissertation, I present two example searchesinvolving the Higgs boson, using proton-proton ($pp$) collision data collectedby the ATLAS detector. The first search tackles the problem of how the SM Higgscouples to the second-generation fermions. It searches for the dimuon decay ofthe SM Higgs boson using data corresponding to an integrated luminosity of 139fb$^{-1}$ collected by the ATLAS detector in $pp$ collisions at $\sqrt{s} = 13\\mathrm{TeV}$ at the LHC. In the second search, we look for Dark Matterproduced in association with a Higgs boson decaying to $b$-quarks. This searchuses the same dataset as the $H\to\mu\mu$ search and targets events thatcontain large missing transverse momentum and either two $b$-taggedsmall-radius jets or a single large-radius jet associated with two $b$-taggedsubjets. In addition to the two physics analyses, unfolding is a key procedurein the high energy experiments, which corrects data for the detector effect. Ipresent a new unfolding method that allows to unfold data without having anyartificial binning and is also able to profile nuisance parameterssimultaneously. This new method provides much higher flexibility and increasesthe reusability for different downstream tasks compared to the traditionalapproach. It will benifit any future analyses including Higgs physics and DarkMatter searches.

Investigation of Higgs Boson Decaying to Di-muon, Dark Matter Produced  in Association with a Higgs Boson Decaying to $b$-quarks and Unbinned  Profiled Unfolding