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
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
applications of optimal robust designs, and density estimations based
on level crossing methods.
Currently, I am working on the following problems:
My research is currently being funded by NSERC from 2007 to 2012.
- 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.
- Applications of reptation quantum Monte Carlo algorithms in
- Suggesting modifications and study practical implementation
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.
- Implementions and applications of optimal robust
- Density estimations based on level crossing methods.
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
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:
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
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.