See my Google Scholar page for a full list of publications.
Selected projects:
Spectral adjustment for spatial confounding Paper
Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the exposure to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matérn coherence function to more robust semiparametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets.
Computer Model Calibration based on Image Warping Metrics Paper
Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice fractures or leads in the ice. These simulated features can be partially misaligned or misshapen when compared to observational data. We develop a statistical emulation and calibration framework that accounts for feature misalignment and misshapenness. This involves optimally aligning model output with observed features using cutting edge image registration techniques.
Fine-Scale Spatiotemporal Air Pollution Analysis using Mobile Monitors on Google Street View Vehicles Paper
People are increasingly concerned with understanding their personal environment, including possible exposure to harmful air pollutants. In order to make informed decisions on their day-to-day activities, they are interested in real-time information on a localized scale. We analyze fine-scale, high-quality air pollution measurements acquired using mobile monitors and develop a computationally-efficient spatiotemporal model for these data to make high-resolution maps of current air pollution levels and short-term forecasts.
A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models Paper
Non-Gaussian spatial data arise in a number of disciplines such as species counts in ecology. A popular model for such data is the spatial generalized linear mixed models (SGLMMs), for which inference is computationally intensive when the data is large. Moreover, spatial confounding makes it difficult to interpret regression coefficients. We propose a novel approach to address both the computational and confounding issues for SGLMMs. We achieve these by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections.
Inferring Ice Thickness from a Glacier Dynamics Model and Multiple Surface Datasets Paper
The behavior of ice sheets, in particular their melting, can potentially have a significant impact on future climate. Information regarding properties of ice sheets is obtained from high-quality surface observations and an understanding of glacial physics. We develop a Bayesian hierarchical model that is flexible and capable of integrating a simple glacier dynamics model, multiple data sets and uncertainty sources to estimate the key parameter in the glacier dynamics model.