Sampling designs on stream networks using the pseudo-Bayesian approach

Falk, Matthew G., McGree, James, & Pettitt, Anthony N. (2014) Sampling designs on stream networks using the pseudo-Bayesian approach. Environmental and Ecological Statistics, 21(4), pp. 751-773.

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Abstract

Monitoring stream networks through time provides important ecological information. The sampling design problem is to choose locations where measurements are taken so as to maximise information gathered about physicochemical and biological variables on the stream network. This paper uses a pseudo-Bayesian approach, averaging a utility function over a prior distribution, in finding a design which maximizes the average utility. We use models for correlations of observations on the stream network that are based on stream network distances and described by moving average error models. Utility functions used reflect the needs of the experimenter, such as prediction of location values or estimation of parameters. We propose an algorithmic approach to design with the mean utility of a design estimated using Monte Carlo techniques and an exchange algorithm to search for optimal sampling designs. In particular we focus on the problem of finding an optimal design from a set of fixed designs and finding an optimal subset of a given set of sampling locations. As there are many different variables to measure, such as chemical, physical and biological measurements at each location, designs are derived from models based on different types of response variables: continuous, counts and proportions. We apply the methodology to a synthetic example and the Lake Eacham stream network on the Atherton Tablelands in Queensland, Australia. We show that the optimal designs depend very much on the choice of utility function, varying from space filling to clustered designs and mixtures of these, but given the utility function, designs are relatively robust to the type of response variable.

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ID Code: 66714
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Exchange Algorithm, Pseudo-Bayesian Design, Stream Network, Utility Function
DOI: 10.1007/s10651-014-0279-2
ISSN: 1352-8505
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Divisions: Current > Institutes > Institute for Future Environments
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Springer
Deposited On: 29 Jan 2014 02:28
Last Modified: 27 Dec 2014 05:42

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