Expectations of linear functions with respect to truncated multinormal distributions - With applications for uncertainty analysis in environmental modelling

Authors:
J. J. Sharples;J. C. V. Pezzey
Affiliations:
School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Room 128, Canberra, ACT 2600, Australia;Centre for Resource and Environmental Studies, Australian National University, Australia
Venue:
Environmental Modelling & Software
Year:
2007

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Abstract

This paper discusses results concerning multivariate normal distributions that are subject to truncation by a hyperplane and how such results can be applied to uncertainty analysis in the environmental sciences. We present a suite of results concerning truncated multivariate normal distributions, some of which already appear in the mathematical literature. The focus here is to make these types of results more accessible to the environmental science community and to this end we include a conceptually simple alternative derivation of an important result. We illustrate how the theory of truncated multivariate normal distributions can be employed in the environmental sciences by means of an example from the economics of climate change control.