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Research Interests:
My research interests are mainly in probabilities, stochastic systems, statistics, and chaos and dynamical systems; and currently focused on hidden Markov Models (HMM). HMMs are the topic of my Ph.D. dissertation and also of my current works.
An HMM is of considerable interest for science and for various practical uses. It consists of a state sequence, a Markov chain sequence, which is "hidden," and an emission sequence, which can be observed. Both the state and observation space could be either discrete or continuous. Among the algorithms used for the parameter estimate of HMMs, those used to find the maximum likelihood estimate (MLE) are the most popular. However, while these algorithms have some known problems, the MLE itself has its own problem: it tends to be very unstable when the data set is small. On the other hand, the Bayes' estimate (or Bayesian posterior mean estimate) is stable regardless of the data size, but is often disregarded due to the computational complexity that, with a naïve implementation, grows exponentially with respect to the data size. However, this complexity becomes polynomial, for certain types of discrete HMMs, using an innovative algorithm that is introduced in my dissertation, making the Bayes' estimate quite feasible for various applications.
At the moment, I am also working on a new algorithm for the same parameter estimate but with a totally different approach. My current plan is to apply this new algorithm to earthquake data, while fully utilizing various kinds of software such as C++ (for quick simulations, etc.), Matlab, Maple, and R. However, I am very much interested in doing researches on any applications that involve HMMs through interdisciplinary collaboration.
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