Project title: Bayesian multivariate mixed models in high-dimensional settings
Supervisors: Zhi Zhao, Manuela Zucknick
Background
With the development of high-throughput technologies in molecular biology, the large-scale molecular characterization of biological samples has become available, for example by genome-wide measurement of gene expression, single nucleotide polymorphisms or CpG methylation status. Other complex phenotypes, for example, pharmacological profiling from large-scale cancer drug screens, are also measured in order to guide personalized cancer therapies. The analysis of joint associations between multiple correlated phenotypes and high-dimensional molecular features is challenging.
Outline of the Work
The thesis will compare different high-dimensional multivariate regressions in the Bayesian framework with respect to their variable selection/structure recovery and prediction performance. Sample heterogeneity is common-place in many biomedical applications, so that mixed models will be exploited in this thesis. Existing data sets, such as the Genomics of Drug Sensitivity in Cancer data, can be analyzed to compare the performance of different Bayesian multivariate models. Depending on interest and progress, we may develop novel Bayesian machine learning methods based on our previous work in Zhao et al. (2021a, 2021b), with the aim to improve the model performance with respect to both variable selection and response predictions.
Learning Outcome
You will become familiar with (i) high-dimensional multivariate regressions, (ii) Bayesian machine learning, and (iii) applications in genomic research.
Prerequisites
To start the project, you should be familiar with (i) statistical learning methods and (ii) Bayesian statistics. Prior exposure to sparse Bayesian models may be helpful, but is not required.
References
Zhao Z, Banterle M, Bottolo L, Richardson S, Lewin A, Zucknick M (2021a). BayesSUR: An R package for high-dimensional multivariate Bayesian variable and covariance selection in linear regression. Journal of Statistical Software, 100 (11), 1-32.
Zhao Z, Banterle M, Lewin A, Zucknick M (2021b). Structured Bayesian variable selection for multiple correlated response variables and high-dimensional predictors. arXiv: 2101.05899.