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The validity and validation of mathematical models: Methodological, theoretical, and practical studies with emphasis on the modelling of complex biological systems

Leaning, M. S. (1980). The validity and validation of mathematical models: Methodological, theoretical, and practical studies with emphasis on the modelling of complex biological systems. (Unpublished Doctoral thesis, The City University)

Abstract

In recent years there has been a tremendous growth in the development and application of mathematical models in all areas of science and engineering. Aided by the advances and availability of computers, models have been used in many new areas, such as biology and the social sciences, and applied to increasingly complex systems. At the same time, model validity and validation have become correspondingly more problematic yet received little attention. The aims of this thesis are to clarify the meaning of model validity, to develop a range of procedures for model validation, and to consider in depth the validity of a number of specific models. The main focus is the use of models in systems science and in biology and medicine.

A review of the scientific literature of model validity and validation is made which reveals many techniques for empirical validation, but exposes the lack of a consistent conceptual approach towards model validity. In reviewing the philosophy of science with reference to validity and validation, the importance of regarding models and validation as part of an evolving research programme and of heuristic considerations in assessing model validity are emphasised.

A new and innovative theory of model validity is proposed which explicates model validity as a multidimensional concept closely related to modelling objectives. The different modelling objectives and types of data are classified and the various concepts of validity are expressed as validity criteria. The general relationship between modelling objectives, data, and validity criteria is explained. The theory is then used to devise a range of validation methodologies suitable for models in research areas at different stages of development.

Models of the human cardiovascular, renal, and respiratory systems are used as case studies for validation. Extensive use is made of the conceptual framework of the theory of model validity and the validation methodologies. The results are a precise delimiting of the validity of the models, the areas of uncertainty, and the potential for future development. This indicates the critical value of the theory and the appropriateness of the methodologies to complex biological models. Further support for the theory and its wide applicability is obtained in using it to consider aspects of validity and validation of models in the social sciences.

Finally, the implications of the work for modelling and validation in systems science and in biology and medicine are examined. In both areas it is shown that the theory of model validity leads to an improved understanding of the nature of modelling and validity, and that the validation methodologies are suitable for the critical and effective validation of a wide range of models. In biology and medicine specific recommendations are made for the types of model appropriate to different modelling objectives and for suitable techniques and methodologies for validation.

This thesis contributes to an improved understanding of the concept of model validity and offers a repertoire of validation methodologies. On another level, it is a broad methodological study of the kind urgently required in systems science. More practically, however, much of the thesis is concerned with the detailed validation of three specific biological models.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Departments: Doctoral Theses
Doctoral Theses > School of Mathematics, Computer Science and Engineering Doctoral Theses
School of Mathematics, Computer Science & Engineering
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