According to a recent ScienceWatch.com
analysis, Professor Jesper Møller is a
Rising Star in the field of Mathematics, having
achieved the highest percent increase in total
citations in this field for the October 2007-December
2007 update period. His current record in this field,
according to Essential Science Indicators from
Reuters, includes 25 papers cited a total of 247
times between January 1, 1998 and February 29,
Professor Møller received his Ph.D. in 1988 from the University
of Aarhus, and his D.Sc. in 2000 from Aalborg University. He is currently a
Professor in the Department of Mathematical Sciences at Aalborg
In the interview below, he talks about his
highly cited work.
What do you consider the main focus of your
research, and what drew your interest to this particular area?
My main focus of research is in mathematical statistics and applied
probability, particularly in relation to spatial data sets and
computational problems as covered in the research areas known as spatial
statistics, stochastic geometry, simulation-based inference, Markov chain
Monte Carlo methods, and perfect simulation.
In my Ph.D. thesis and earlier in my career I worked mainly on problems
associated with stochastic geometry, where I contributed to the
mathematical theory on random tessellations (that is, random space filling
structures) with a monograph and various papers on Voronoi tessellations
and Johnson-Mehl tessellations, and also developed new models for spatial
point processes and random fields.
recent years, fast computers and
advances in computational
statistics, particularly Markov
chain Monte Carlo methods, have had
a major impact on the development
of statistics for spatial point
My later research contributions often still concern spatial processes but
more and more from a statistical and computational perspective. Most of my
recent books and papers deal with statistical inference and computational
methods for spatial and spatio-temporal point processes.
My research is motivated by problems in basic research as well as
applications in science, engineering, and medicine. For example, spatial
point pattern data occur frequently in a wide variety of scientific
disciplines, including seismology, ecology, forestry, geography, spatial
epidemiology, and material science.
Several of your highly cited papers deal with log
Gaussian Cox processes and the Markov chain Monte Carlo methods. Would
you walk our readers through these particular aspects of your research
and its applications?
My interest in spatial point processes have concentrated on the two main
classes of models, namely Markov (or Gibbs) point processes and Cox point
processes. They both apply to a range of applications in astronomy,
physics, ecology, epidemiology, etc. Markov point processes are models
where interaction between neighboring events is modeled explicitly. Cox
processes are constructed from models for "complete spatial randomness" by
adding additional variability.
This extra variability may be modeled by a shot-noise process or a log
Gaussian process, whereby shot-noise Cox processes and log Gaussian Cox
processes appear. In my research I have studied the many appealing
mathematical and statistical properties of these point process models. This
has furthermore been exploited in connection with developing new
statistical methodology and for performing simulation-based inference for
various application examples.
My research on Markov chain Monte Carlo (MCMC) methods has been much
related to random tessellations, spatial point processes, and Markov random
fields. In particular I have been interested in MCMC methods related to
simulation-based inference, since this enables us to analyze very
complicated stochastic systems for large data sets as appearing in modern
statistical applications, including spatial statistics.
research is motivated by problems
in basic research as well as
applications in science,
One of the most exciting recent developments in stochastic simulation is
perfect (or exact) simulation, which turns out to be particularly
applicable for most point process models and many Markov random field
models as demonstrated in my work. Recently, in connection to Bayesian
inference, the problem with unknown normalizing constants of the likelihood
term has been solved using an MCMC auxiliary variable method as introduced
in Møller et al. (J. Møller, A. N. Pettitt, K. K.
Berthelsen and R. W. Reeves, "An efficient MCMC method for distributions
with intractable normalising constants", Biometrika 93: 451-8,
2006). The method involves perfect simulations.
Would you talk a little about one of your more recent
papers, "Modern statistics for spatial point processes"
(Scandinavian Journal of Statistics 34: 643-711, 2007), and
its significance for your field?
The classical spatial point process textbooks usually dealt with relatively
small point patterns, where the assumption of stationarity is central and
non-parametric methods based on summary statistics played a major role. In
recent years, fast computers and advances in computational statistics,
particularly Markov chain Monte Carlo methods, have had a major impact on
the development of statistics for spatial point processes.
The focus has now changed to likelihood-based inference for flexible
parametric models, often depending on covariates, and liberated from
restrictive assumptions of stationarity. In short, "Modern statistics for
spatial point processes," which we also used as the title of this paper.
The paper is followed by various discussion contributions by the leading
experts in the field.
Are there other papers you have published that you feel
are key to your field, regardless of database restrictions?
The Biometrika paper from 2006 noted above is worth mentioning, as
is the rather recent research monograph, Statistical Inference and
Simulation for Spatial Point Processes, by J. Møller and R.P.
Waagepetersen. Published in 2004 by Chapman and Hall/CRC, it provides a
detailed account on the theory of spatial point process models and
simulation-based inference as well as various application
Jesper Møller, Professor, Ph.D., D.Sc.
Department of Mathematical Sciences
Keywords: mathematical statistics, applied probability, spatial
statistics, stochastic geometry, simulation-based inference, Markov
chain Monte Carlo methods, perfect simulation, Markov point processes,
Cox point processes, spatial point processes, log Gaussian Cox