List of Publications

My research interests include a wide range of topics in probability and statistics and their applications in natural sciences.

My main interests are in studying the convergence and efficiency of various Markov chain Monte Carlo (MCMC) algorithms in high dimensions with the aid of extensive and computationally intensive simulation studies, as well as the applications of theses algorithms. Over the last 15 years, MCMC algorithms are widely used, largely due to their general applicability to Bayesian inference problems. Therefore, monitoring the convergence of these algorithms has become an important topic. I am also interested in the applications of MCMC in natural sciences. In particular, I am working on the reptation quantum Monte Carlo algorithm in quantum chemistry. The objective is to consider various adjustments to improve the efficiency in practical applications to more complex quantum systems. My other interests include implementations and applications of optimal robust designs, and density estimations based on level crossing methods.

Currently, I am working on the following problems:
  1. Bounding and optimizing the convergence rates. I generalize and combine available techniques through the application of decomposition theorems, from discrete state spaces, to general state spaces. I am also working on optimizing the scaling of the proposal distribution, when the dimension of the target density approaches infinity. My focus is on local MCMC algorithms, loosely referring to methods which have increment distributions centered at (or close to) the current state, and on proving weak convergence results for a wider class of target and proposal distributions.
  2. Applications of reptation quantum Monte Carlo algorithms in quantum chemistry. 
  3. Suggesting modifications and study practical implementation issues on some existing sampling algorithms (e.g. MCMC, adaptive MCMC, etc.) widely used in the scientific literature. This includes stabilities of adaptations, convergence and efficiencies of these algorithms, and other problems motivated by practitioners.
  4. Implementions and applications of optimal robust designs. 
  5. Density estimations based on level crossing methods.
My research is currently being funded by NSERC from 2007 to 2012.

REFEREED JOURNAL PUBLICATIONS
1)    M. L. Huang, W. K. Yuen and M. Zhang (2011), “Efficient methods on confidence intervals for prediction intervals,” submitted to J. Appl. Stat., 23 pages.
2)    P. Neal, G. O. Roberts and W. K. Yuen (2011), "Optimal scaling of Metropolis algorithms for discontinuous densities," to appear in Ann. Appl. Probab., 50 pages.
3)    W. K. Yuen and S. M. Rothstein (2011). “A note on the convergence of reptation quantum Monte Carlo algorithm,” submitted to J. Phys. A: Math. Theor., 6 pages.
4)    X. Xu and W. K. Yuen (2011), “Applications and implementations of continuous robust designs,” Comm. Statist. Theory Methods 40: 969-988.
5)    D. G. Oblinsky, W. K. Yuen, and S. M. Rothstein (2010), “Ground-state properties of the water molecule by reptation quantum Monte Carlo,” J. Mol. Struct. (Theochem) 961: 29-34.
6)    M. L. Huang and W. K. Yuen (2010), “A bivariate density estimation method based on level crossings,” Statistics 44: 31–55.
7)    W. K. Yuen, D. G. Oblinsky, R. D. Giacometti, and S. M. Rothstein (2009), "Improving reptation quantum Monte Carlo," Internat. J. Quantum Chem. 109: 3229-3234.
8)    W. K. Yuen and M. L. Huang (2009), "A weighted multivariate density estimation method," Adv. Appl. Stat. 13: 181-191.
9)    N. Madras and W. K. Yuen (2009), "Countable decomposition and spectral gaps of Metropolis chains," Far East J. Theor. Stat. 27: 157-191.
10)    W. K. Yuen, T. J. Farrar and S. M. Rothstein (2007), “No-compromise reptation quantum Monte Carlo,” J. Phys. A: Math. Theor. 40: F639-F646.
11)    M. L. Huang, M. Pollanen and W. K. Yuen (2007), “An efficient randomized quasi-Monte Carlo algorithm for the Pareto distribution,” Monte Carlo Methods Appl. 13 (1): 1-20.
12)    S. F. Jarner and W. K. Yuen (2004), “Conductance bounds on the L2 convergence rate of Metropolis algorithms on unbounded state spaces,” Adv. Appl. Prob. 37 (1): 243-266.
13)    W. K. Yuen (2002), “Generalization of discrete-time geometric bounds to the convergence rate of Markov processes on Rn,” Stoch. Models 18 (2), 301-331.
14)    W. K. Yuen (2000), “Applications of geometric bounds to the convergence rate of Markov chains on Rn,” Stoch. Proc. Appl. 87: 1-23.

OTHER REFEREED CONTRIBUTIONS
1)    W. K. Yuen and S.M. Rothstein (2011), “A Survey on Reptation Quantum Monte Carlo,” in P.E. Hoggan, E.J. Brndas, J. Maruani, P. Piecuch, and G. Delgado-Barrio, editors, Advances in the Theory of Quantum Systems in Chemistry and Physics, 327-342 (Book chapter).

PUBLISHED CONFERENCE PROCEEDINGS
1)    W. K. Yuen and S.M. Rothstein (2009), “On reptation quantum Monte Carlo algorithm,” in Yahya Abu Hasan et al.(eds) 5th Asian Mathematical Conference Proceedings (Volume II), June 2009, pp 280 - 287. ISBN: 978-967-5417-54-2.
2)    X. Xu and W. K. Yuen (2007), “Implementation schemes for continuous designs under Kolmogorov-Smirnov criterion,” Proceedings of the 9th Islamic Countries Conference on Statistical Sciences 2007, 775-785.

CONTRIBUTION RESULTING FROM PARTICIPATION IN INDUSTRIALLY RELEVANT RESEARCH AND DEVELOPMENT ACTIVITIES
1)    W. L. Pushka and W. K. Yuen (2000), “ALIgn System, Ver. 1.1, main model and source code, confidential document – internal use only,” First Paladin Research.