- Spatial Statistics:
A bonus of working with spatial data is that you get to create and present awesome maps.
We have developed computationally efficient approaches for massive spatial
datasets with millions of observations.
I have also been working
on spatial disease mapping using area level aggregated data, and multivariate spatial interpolation that preserve the dependency
between multiple spatial outcomes.
Much of my work on large spaial and spatio-temporal data has been based on Gaussian Processes which has persuaded me in exploring its use in other
contexts like non-parametric regression and computer model emulation.
My main areas of application have been air pollution, forestry, ecology. I'm also interested in exploring spatial models for neuroimaging,
Earth system models and exposure-risk models for assesing environmental impact of health outcomes.
- High-dimensional data:
My work in this area have focussed on high-dimensional
regression in settings where some commonly used assumptions are violated in the data. We have developed a method
for model selection and regression for high dimensional
data with measurement error in the covariates. We have established asymptotic and finite sample properties of our estimator and have developed a convex
algorithm that leverages existing softwares. In another project, we have developed
a Bayesian high dimensional piece-wise linear regression for analyzing datasets with
change points. Our method can be applied to a wide variety of high-dimensional time series data and has been used to identify the changing relationship
between house prices and stock prices in Minnesota before and after the recession in 2008.
- Small area estimation: Even in this age of big data, we often encounter small datasets and analyzing them remains a challenge.
I'm currently working on estimating size of key populations relevant to infectious diseases. In another project, that recently got funded, I'll be
calibrating verbal autopsy data to improve cause of death determination.
Bayesian hierarchical models are often a convenient choice for such problems as it provides a unified platform to incorporate all available information that can potentially help
in finding the answers we seek.