If it has cool math and an impactful question, I am interested. Based on my combined medical and statistical training, I tend to gravitate to problems in the analysis of biomedical data; especially, genomics and electronic health data. However, my research interests are varied and include both theoretical and applied aspects of mathematics and statistics.
Electronic Health / Personalized Medicine
- Statistical and machine learning methods for interpreting imperfect diagnostic tests
- Syndromic surveillance for emerging infectious diseases
- How can we infer changes in patient care seeking behavior during a pandemic?
- Statistical methods for the analysis of sequence count data (e.g., 16S microbiome surveys, bulk RNA-seq, and single-cell RNA-seq)
- Differential expression and correlation analysis when working with count compositional data. What kinds of assumptions allow these problems to be identifiable?
- What do zeros in sequence count data represent and how do we deal with them?
- Batch effects and PCR amplification bias
Statistics and Machine Learning
- Efficient and accurate methods for inferring high-dimensional Bayesian models
- Non-Gaussian, non-linear time-series analysis
- Compositional time-series
- Bayesian analysis of partially identified models
- Bayesian decision theory
- Optimal control and sequential and active learning
- Can symmetries in probabilistic models be found computationally and exploited for faster inference?
- When is there a closed form transformation between two families of probability distributions?
- How can you find a transformation that maps one family of probability models into another family (assuming the two families are topologically equivalent)?
- Gaussian process with asymmetric kernels
- How can you identify families of probability models with identical marginal distributions.
- Statistical Methods for Party Planning