Kaplan , Adam2021-05-172021-05-172021-02https://hdl.handle.net/11299/220118University of Minnesota Ph.D. dissertation. February 2021. Major: Biostatistics. Advisor: Eric Lock . 1 computer file (PDF); ix, 113 pages.Present research has gravitated towards making inferences from high-dimensional data, the scenario when we have considerably more variables than the number of observations we have to estimate their effects on a given outcome, and standard statistical methodology cannot be used here. Models assuming that a majority of these variables do not associate with the outcome, or shrinkage models, have been used for such situations. However, most standard shrinkage models tend to ignore the natural dependencies within high-dimensional data. For instance, geneticists have well understood that rare mutations along the chromosome are correlated, and this correlation decreases as the spatial distance between the mutations increases. As a result, treating these variants as independent from one another misses supplementing the estimation of their relationships with the outcome, with this contextual information. In this dissertation, instead, we present models assuming that the variables’ effects are dependent on each other which appends the shortage in observations. Specifically, we introduce this version of shrinkage models in the contexts of a clinical trial for optimizing a medical device for one patient and detecting genetic variants that are associated with a disease.enBayesian StatisticsCausal VariantsClinical TrialGeneticsNeurostimulationSingle Nucleotide PolymorphismsThesis or Dissertation