Russell Cheng's Home Page
[Last update:Aug 2006: This is
index06.html]
Contact Information
Faculty of Mathematical Studies,
Tel: +44 (0)23 8059 4550 (direct), 8059
5155 (OR secretaries)
Fax: +44 (0)23 8059 5147
email: rchc@maths.soton.ac.uk
Brief CV
Russell C.H. Cheng is Professor of Operational Research in the
Faculty of Mathematical Studies,
He has an M.A. and the Diploma in
Mathematical Statistics from
Research Interests
I have divided my Publication List into the six main areas that I have been interested in. My main current areas of interest are 2. Design and Analysis of Computer Simulation Experiments, and 4. Estimation in Non-Regular Problems
Here is a brief description of each.
Click on linked items to jump straight to them in the list.
Commentary on
Publication list:
1. Computer Generation of Random Variables
From 1976 to 1984 there was considerable
interest in the development of computer methods of generating random variables
from various probability distributions, notably the so-called gamma and beta
distributions. The better current implementations date from that time, but be
warned there are still books being written, and implementations using outmoded,
demonstrably inferior, methods from before then. If you want something neat and
simple then [A1,A2] and those [A3,A4] with Feast ( a research assistant
at the time) are methods that I am most pleased with.
If you want cookbook recipes then try my
Chapter on Random Variate Generation. This appears in A7 Handbook of Simulation, edited by Jerry Banks and published by Wiley in
1998.
2. Design and Analysis of Computer Simulation Experiments
I have several current research interests
in this area: optimal design, selection of input models, validation and
sensitivity analysis.
The papers [B2, B3] jointly with Feast were the first
to investigate the use of control variables under normality assumptions. This
is a common assumption nowadays.
The method of antithetic variates is well
known in theory, but is not so easy to apply in practice. The papers [b1,b2 B4,B5]
develop a practical methodology for its application from a novel viewpoint.
Paper [b3],
is expository, but suggests a structure for the methodology of variance
reduction. The conference paper [a1][, gives an implementation of quasi-random generators.
The papers [A5, A6], though concerned with variate
generation, would find application in variance reduction In particular [A5]
contains a result concerning the decomposition of inverse Gaussian variates.
Paper [b4], is concerned with some unusual ways of doing stratified
sampling.
Paper [B6] with
Most recently I have worked with a
research student, Traylor, and a colleague,
I have also been working on sensitivity
issues with Prof Jack Kleijnen (
3. Construction of Confidence Bands
The basic idea of constructing confidence
bands dates back to the work of Working and Hotelling in 1927. However the idea
can be extended non-trivially. Paper [C2] with Iles gives convenient closed form formulas
for a problem a number of well known distributions. Papers [C3,C5,c1,c2] describe some of the work done for the MoD in
this area, as well as applications to materials handling. The methodology
developed in paper [C3] is capable of wide application.
4. Estimation in Non-Regular Problems
This is technically the most demanding
area that I have worked on. It concerns a number of problems in which the
well-known and the normally powerful method of maximum likelihood can fail to
provide estimators with good properties. The papers [D1,D2,D3,D4,D5,D6] address a notorious outstanding problem where
the likelihood blows up and such estimators are inconsistent. The joint paper
[D2] with Amin (a research student at the time) gives what I consider to be a
natural and practical solution using spacings that is demonstrably superior to
previous suggestions. The joint paper [D4] to some extent gives a unifying
explanation of why certain methods work and why others do not for such
problems. Paper [D6] proves a remarkable property of the spacings method that
has uses in goodness-of-fit testing. The joint papers [D7,D8] tackle a second problem of non-regularity that
occurs in estimation and in curve fitting respectively. Each paper gives a new
characterization of the difficulty, and each shows how the problem can be fully
solved. This work lead to the a read paper to the Royal Statistical Society [D10].
Papers [D9, D11] is recent work on this with Steve Liu from
5. Optimal Control of Jump Processes
The papers [E1,E2],[e1] and those [E3,E4] jointly with Jones (then a part-time student)
attempt to model the operation and control of large scale chemical plants using
Markov Decision Processes. The purpose is to develop a practical solution to a
problem of industrial interest which is analytically intractable except in
simplistic rather trivial cases. Paper [E2] establishes, in fair theoretical
detail, conditions under which the technique can be expected to work. As [E3]
and [E4] go on to show, the practical results agree with the theory. The topic
has been relatively unexplored, with what published work being dispersed.
Relatively recently I returned to the
problem and [E5]
contains a detailed theoretical analysis using the theory of maximal
differential equations.
6. Computer Generated Imagery Techniques and Marine Simulation
I have developed a number of computer
algorithms over several years in my consultancy work on applications of
computer generated imagery in marine simulation. These have had real and I held
two Teaching Company Grants from the EPSRC in this field; each Scheme included
a specific research component in addition to the usual commercial ones. Some
results of this work are reported in [f2, f3, f4].
Perhaps more interesting are the papers [F1,
F2]. Paper [F1], though short,
gives a new rendering method that is demonstrably two to three times faster
than previously suggested methods. Paper [F2] gives a comprehensive solution to
the problem of fast anti-aliasing. Both methods have been used in several
extremely successful commercial systems.
Some Teaching Materials
NATCORSimulationCourse This has been updated since the course was given in June 2009 (4th July 2009).
Site Construction: Box-Jenkins Method for ARIMA Models Using X12 from Excel.
