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The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

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Disentangling mark/point interaction in marked-point processes

Renshaw, E. and Mateu, J. and Saura, F. (2007) Disentangling mark/point interaction in marked-point processes. Computational Statistics and Data Analysis, 51 (6). pp. 3123-3144. ISSN 0167-9473

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Abstract

In many spatial situations, not only do the point locations of mark variables (e.g. tree heights) play a key role in the underlying process generating mechanism, but there can be interdependence between the marks and points themselves. Although Monte Carlo frequency-domain analyses can separate mark and point structure, theoretical advances for marks have so far related to the conditional mark spectrum based on a given point structure. A 'discrepancy function' is therefore developed which isolates the spatial structure of the marks alone, and involves a harmonic decomposition of the mark frequencies. The concept is introduced via various simulated examples based on mark cosine waves and thinned point processes, with particular attention given to the construction of sequential and simultaneous search procedures for developing parameter estimates. The procedure is then applied to Spanish daily ozone data with missing values, a spatial growth-interaction process, and a classic longleaf pine data set from the Wade Tract in Georgia, USA.