Inferences on Growth in Biological Populations Via Distributed Parameters

• Published in: IFAC Proceedings Volumes Vol. 21; no. 1; pp. 281 - 286
• Main Authors: Read, K.L. Q., Berry, P.J. B.
• Format: Journal Article
• Language: English
• Published: 01.04.1988
• Subjects: Biology; Distributed Parameters; Maximum Likelihood; Statistics; Biology; Models; Statistics; Maximum Likelihood; Distributed Parameters
• ISSN: 1474-6670
• DOI: 10.1016/S1474-6670(17)57568-0

A flexible system of nonlinear statistical models based on Gamma distributions of integer order has been developed to describe aspects of animal growth and development in quantitative terms, Models from this system have been applied to data concerning the generation and growth of ovarian follicles in infant Wistar rats and shown to fit for a range of animals aged 8–24 days. The problem discussed here is how to combine the data from different animals to provide inferences on the parameters describing the population from which the experimental animals are assumed to be a random sample. This work is of methodological interest, since the information matrices of the estimates specific to individual animals vary depending on age and/or biological development. However, insofar as the underlying form of model is deemed adequate, the specific parameters may be regarded as randomly distributed about global population values which are fixed throughout time. On the standard asymptotic theory, estimates of parameters for individual animals are taken as Normally distributed, with dispersion matrices estimated in the usual way, and animals are considered to be independent. It is natural to assume that the animal-specific parameters are themselves Normal, and the main work of this paper is to discuss the estimation of this global distribution. The effects of parametric redundancies and other computational issues are assessed in the context of the results obtained for the Wistar rat data. Clearly, the theory discussed here is applicable generally to the estimation of population or reference values for developmental or growth parameters in humans or other animals.