To develop a spectrum of computationally efficient state of the art conditional
probability density and parameter estimation algorithms that collectively
solve the gamut of real time detection, tracking, path-space filtering,
prediction,and image processing problems based upon possibly incompletely
determined predictive models.
To advance the art of predictive modeling through increased realism, mathematical
complexity, and efficient computer tractable approximations.
To analyze, compare, and evaluate our algorithms and models on prototype
problems suggested by our corporate sponsors or with real world applications.
To promote the use of sophisticated mathematics in industry.
To determine the additional skills necessary for graduates of the mathematical
sciences to be sought by industry. Subsequently,
to train students accordingly.
To develop a set of course materials to help train graduate students in
applications of stochastic analysis.
Develop and advance efficient, computer workable filtering algorithms;
Develop combined parameter and state estimation algorithms for tracking,
prediction and image processing;
Create computer workable nonlinear filtering and estimation algorithms
using our SERP, REST, IDEX and combined
parameter-state estimation methods as well as other particle filter, convolutional,
chaos, or Markov chain techniques. Compare methods empirically on
Prove consistency and rates of convergence for the algorithms in 1) and
Develop prediction systems to control lighting, microphones, etc. for live
theatre performers. (Acoustic Positioning Research problem);
Improve model approximation and robustness;
Generate filters for signals in random environments;
Further basic filtering theory including uniqueness, particle representation,
existence, and the innovations theorem.