Information for

Park Reilly

Distinguished Professor Emeritus

Park ReillyDegrees

  • BASc, University of Toronto
  • Diploma of the Imperial College (DIC), University of London
  • PhD, University of London

Research interest

Applied statistics in chemical engineering.

  • Mathematical modelling of scientific systems including plants and processes, physical & chemical processes, and stochastic simulation studies. Regression, error-in-variables models, multivariate analysis, model discrimination, design and analysis of experiments.
  • My research involves the development and application of statistical methods for scientific studies, particularly those in the field of chemical engineering. Experimentation is of fundamental importance in all science and statistical methods are essential to its successful planning and interpretation.
  • An important emphasis in my research has been on the Error-in Variables model. It describes a special case of the experimental estimation of the values of unknown constants (parameters) in mathematical models of physical and chemical systems. Ordinary least squares is a simple approach to this problem but it has the severe limitation that it allows uncertainty in the measurements of only one variable, the dependent one, while realistically there is more or less uncertainty in all measured quantities. The Error-in-Variables model addresses this problem. Some of my students and I have developed mathematical solutions for most practical applications of the model, and we are continuing research into further applications and also such aspects as the Design of Experiments which will be subject to Error-in-Variables interpretation. Computer software which will handle very general cases of the Error-in-Variables model are under development and will soon be published.
  • Multivariate statistical procedures such as Factor Analysis have long been used as essential tools in the social sciences. Such usages are characterised by large masses of data and lack of a mechanistic mathematical model. Since the advent of computerised data logging in complex chemical plants, situations similar to that in the social sciences often arise in a chemical engineering context, with the result that interesting opportunities present themselves to develop and extend multivariate methods for chemical process investigation.
  • Besides those mentioned above, there is an endless supply of fascinating statistical problems in chemical engineering.

Selected references

  • "A Microcomputer Program for Estimation of Copolymer Reactivity Ratios", M. Dubé, R. Amin Sanayei, A. Penlidis, K.F. O'Driscoll, and P.M. Reilly, J. Poly. Sci., Poly. Chem. (accepted 1990).
  • "Estimation of Parameters in Monte Carlo Modelling", T.A. Duever and P.M. Reilly, C.J.Ch.E., (Accepted 1990).
  • "The Error-in-Variables Model Applied to Parameter Estimation when the Error Covariance Matrix is Unknown", by S.E. Keeler and P.M. Reilly, C.J.Ch.E., (Accepted 1990).
  • "Monte Carlo Estimation of Kinetic Parameters in Polymerization Reactions", by T.A. Duever, K.F. O'Driscoll and P.M. Reilly, J. Poly. Sci. Poly. Chem., 26, p 965 (1988).
  • "An Application of the Error-in-Variables Model - Parameter Estimation from Van Ness-Type Vapour-Liquid Equilibrium Experiments", by T.A. Duever, S.E. Keeler, P.M. Reilly, J.H. Vera, and P.A. Williams, Chem. Eng. Sci. 42, p 403 (1987)
  • "A Bayesian Study of the Error-in-Variables Model", by P.M. Reilly and H. Patino-Leal, Technometrics, 23, p 221 (1981).
University of Waterloo