- Thesis:
- Bachelor in Mathematics
- Author:
- Ilia Kats
- Title:
- The horseshoe+ distribution and its application to modeling spatial cell state gradients in single-cell transcriptomics data
- Supervisors:
- Stefan Richter (Universität Heidelberg)
- Jan JOHANNES
- Abstract:
- In supervised regression models, often only a small subset of predictors is informative. The Bayesian gold standard for detecting and estimating the informative predictors is the so-called two-groups model, a mixture of a Dirac delta distribution at 0 and a Normal distribution. While theoretically appealing, in practice it incurs substantial computational cost as datasets get larger. Therefore a number of more tractable approximations have been developed, ranging from the venerable Ridge and Lasso regression models to newer approaches like global-local shrinkage priors on the regression coefficients. These priors achieve substantial shrinkage of the regression coefficients towards 0, while still allowing individual coefficients related to informative predictors to escape shrinkage. One popular global-local shrinkage prior is the horseshoe distribution, which tends to either shrink coefficients strongly or not at all, achieving a good approximation to the two-groups model. In the first part of this thesis, the horseshoe+ distribution, an improved variant of the horseshoe, is described and its error bounds are de- rived. The second part of this thesis uses the horseshoe+ distribution as part of a hierarchical Bayesian model to detect spatial cell state gradients in single-cell transcriptomics data.
References:- A. Bhadra, J. Datta, N.G. Polson and B. Willard. The Horseshoe+ estimator of ultra-sparse signals, Bayesian Analysis 12:1105–1131, 2017.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |