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?

Genomics

• 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

Other

• 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