Pauline Coolen-Schrijner

Department of Mathematical Sciences

University of Durham

Pauline died on 23 April 2008

In due course, this webpage will be updated to present an overview of her career, with access to all her papers (conditional on agreement from publishers). For further information please contact Pauline's husband and colleague, Frank Coolen).

Good news: I have been promoted to Reader per 1 October 2007.

About me:

I was born in Arnhem, a nice place in The Netherlands. I did my M.Sc. in Econometrics (main subjects: stochastic processes, operations research and statistics) at the Catholic University of Brabant. After that I continued my university life as a Ph.D. student at the University of Twente, The Netherlands. Under supervision of Erik A. van Doorn I worked on the thesis "Quasi-stationarity of discrete-time Markov chain". After being a lecturer for one year at the University of Newcastle I took up my TMR grant of the European Community and joined the University of Durham as a senior research associate. In 1998, Frank (picture / homepage) and I married in the Catholic Church St. Cuthbert in Durham. In October 1999 I became a lecturer at Durham. My job consisted of two components: lecturing (half time) and working for the Statistics and Mathematics Consultancy Unit (half time), mainly on applications of statistical and operational research methods for industrial, commercial, academic and institutional clients. In February 2004 I left the Statistics and Mathematics Consultancy Unit as I wanted more time for my own research. So I started working as a lecturer on a 60% basis which gives me the perfect combination of lecturing and research, while the rest of the time I can concentrate on fighting my pulmonary fibrosis and improving my condition. Since 2005 I'm a member of the editorial board of Journal of Risk and Reliability. I have accepted an invitation by Prof Zacks (Binghampton, US) to write an entry on "Bayesian reliability demonstration" for the Wiley Encyclopedia of Statistics in Quality and Reliability (scheduled to appear in 2007), jointly with Prof. Frank Coolen.

Research interests:


Click on publications for an overview. If you would like to receive reprints, please contact me.

Research interests ... further explained:

Stochastic processes, in particular Markov chains, are widely used for modelling real-world phenomena. Some of these processes seem to settle down to an equilibrium after a relatively short time, only to reach their real equilibrium after a much longer time. This phenomenon is called quasi-stationary behaviour and can be described by means of quasi-stationary and limiting conditional distributions. One category of Markov chains that may display quasi-stationary behaviour are chains with an absorbing state. This kind of quasi-stationary behaviour has its applications in, for example, biology and chemistry. Another category of Markov chains that may display quasi-stationary behaviour are chains with a reflecting boundary. Sometimes, multi-access communication protocols where a single channel is shared by a number of communicating devices display such behaviour. During my Ph.D. I started this research for discrete-time birth-death processes, also called random walks. Here, orthogonal polynomials play an important role in the analysis. Also, a relation between the limiting conditional distributions for absorbing Markov chains and chains with drift to infinity has been established.

A slotted ALOHA protocol is an example of a multi-access communication protocol where a single channel is shared by a number of communicating devices and which can be modelled by a skip-free to the left Markov chain with positive drift. It also has certain monotonicity properties. Research is in progress to prove or disprove the R-positivity of such a protocol which is a sufficient condition for the existence of a limiting conditional distribution.

Together with Erik A. van Doorn, I did some research on the convergence to stationarity of birth-death processes and on the deviation matrix of continuous-time Markov chains. Research on asymptotic aperiodicity and the strong ratio limit property for Markov chains is going on. We also studied discrete-time and continuous-time birth-death processes with killing. Under which conditions does there exist a similar honest birth-death process? When does there exist a family of quasi-stationary distributions?

In addition to the above, I'm also working on some stochastic operations research problems tackled with Hill's assumption A(n), which is joint work with F.P.A. Coolen. In the first place we have worked on the nonparametric low structure analysis for queues. We have achieved guiding lines on which queue to join, via predictive probability results for the waiting time for customers in a queue, based on observed serving times for other customers in the same queue and a minimum of additional structural assumptions (e.g. Hill's assumption A(n)). Besides that we are dealing with the following important question in reliability theory "When do we need to replace a unit: wait until the unit fails or perform a preventive replacement?" In a paper on condition monitoring, the condition of a technical unit is measured continuously, with the measurement indicating in which of k>1 states the unit is. A new unit is in state 1, and failure occurs the moment a unit leaves state k. A unit will only go from a state j to state j+1, and these immediately noticed transitions occur at random moments. At such transition moments a decision is required on preventive replacement of the unit, which would require preparation time. Such a decision needs to be based on infereces about the total residual time till failure. This work can be seen as a first step towards adaptive replacement and maintenance strategies based on nonparametric predictive inference, the subject of my awarded EPSRC grant.

Together with Frank Coolen I worked on nonparametric predictive reliability demonstration for failure-free periods while we, together with our Ph.D. student, Maha Rahrouh, studied Bayesian reliability demonstration for failure-free periods.

As the result of some consultancy work concerning the estimation of the survival probabilities of Curlews, I became interested in Bayesian analysis, MCMC and the software programs WinBugs and Hugin. See my posterpresentation for the "Mathematical Methods in Reliability 2002" conference, Trondheim (Norway).


EPSRC grant: Adaptive replacement and maintenance strategies based on nonparametric predictive inference

Nonparametric predictive inference (NPI) is a recently developed statistical approach using few structural assumptions in addition to data. Application of such inferential methods for lifetimes of units enables fully adaptive strategies for replacement and maintenance. With my EPSRC grant "Adaptive replacement and maintenance strategies based on nonparametric predictive inference", we have started with the developing and analysing of NPI-based strategies for age replacement. This requires new theory on combining classical stochastic processes with NPI, the use of NPI with right-censored data, and further development of NPI including simulation methods. Together with Frank Coolen I worked on adaptive age replacement strategies with nonparametric predictive inference and also with my Postdoc, Simon Shaw, we worked on Nonparametric predictive adaptive opportunity-based age replacement strategies based on both the renewal reward theory and a one-cycle criterion. The latter one justified the adaptive behaviour better than the renewal reward theory. Computations for the nonparametric predictive methods for (opportunity-based) age replacement, as presented in these papers, were performed in R. Please contact me if you wish to have the algorithms. The following papers are a result of this EPSRC grant.

More information about nonparametric predictive inference can be found on the Nonparametric Predictive Inference webpage .

Ph.D./MSc. student:


Administrative duties:

"Breathing is not something we can take for granted".