Statistical areas:
Primarily I am interested in models, methods, and computation in Bayesian analysis broadly with current focuses in time series analysis and dynamic models. Specifically this includes filtering and smoothing in state-space models using either Markov chain Monte Carlo for batch analysis or sequential Monte Carlo methods for real-time analysis.
Filtering
Filtering
occurs in dynamic
models, often referred to as state-space models, where the
objective is to determine the distribution of the latent state and
fixed parameters given all the data up to that time. I create
methodology for both analytical and simulated approximations to this
distribution for non-linear and non-Gaussian models. The picture plots
the 95% credible interval and median for three different
approximations to the filtered distribution for a fixed parameter.
Smoothing
Smoothing occurs in dynamic models where the objective is to
determine the distribution of the latent state and fixed parameters
given all the data (not just data up to a particular time). I create
approximations to this distribution for non-linear and non-Guassian
models. The picture plots the bivariate distribution between two
consecutive states. The high degree of multimodality depicted shows
the non-trivial nature of these problems.
Applied areas:
Dynamic models have wide application and here I describe a few applied areas of my research.Systems biology
Systems
biology studies the dynamics of cellular function. I build models
to represent the fluctuations of protein levels within cells. These
models are non-linear, multivariate processes that include both
intrinsic and extrinsic noise as well as measurement error. The
picture shows a snapshot of bacterial cells using fluorescence
microscopy, green brightness indicates the level of a particular
protein.
Syndromic surveillance
In syndromic surveillance the goal is to have an alert system that
quickly detects an outbreak of both known and unknown diseases. I
build models representing the baseline fluctuation as well as outbreak
profiles for a variety of diseases. The picture to the right shows a
reporting system with the observations as
points, outbreak period shown in red, and the blue line indicating the
alert system.
Drug abuse trends
The goal of this research was to build a system based on national
databases that could detect a change in opioid drug abuse rates. There
is known spatial hetergeneity that we accounted for using random
effects for states in a conditionally autoregressive model. The
picture shows a map of the posterior median for these random effects
where red indicates high abuse and blue indicates low abuse.