Abstract
As plankton biologists ask more detailed questions of necessarily sparse and noisy spatial data, the need for well founded methods for statistical analysis of such data grows. This note examines the utility of constrained thin-plate smoothing splines as a tool for inferring underlying spatial distribution functions from sparse noisy data. Constrained thin-plate splines are described in a straightforward manner. An economical method of calculation is suggested, which sacrifices mathematical optimality for ease of computation. Using simulated data several methods for choosing the complexity of the inferred distribution function are compared and robustness to large amplitude noise is examined. Confidence intervals are calculated and tested. The method is applied to egg data from Dover sole (Solea solea) in the Bristol Channel.
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