Evaluation of integrals from sparse and noisy data in ecological applications

Natalia Petrovskaya (University of Birmingham)

Thursday 12th October, 2017 14:00-15:00 311B Mathematics and Statistics Building


(Lunch with the speaker will be at One A The Square, leaving from the school front foyer at 12.45.)

Accurate evaluation of the average population density or the total population size is an important requirement in many ecological problems. From a mathematical viewpoint the problem is to evaluate a certain integral where the evaluation procedure is based on discrete data available as a result of monitoring and sample collection. The data used for evaluation are often sparse due to financial, labour, and other restrictions on the sampling routine. The same sparse data can also be noisy because of the inherent nature of the ecological problem. It will be shown in our talk how insufficient data collected on a coarse sampling grid affect the accuracy of evaluation. The insufficient information is collected because of inadequate spatial resolution of the population density on coarse grids and this is especially true when a heterogeneous spatial population density is sampled. It will be argued in the talk that the evaluation error is a random variable on coarse sampling grids because of the uncertainty in sampling spatial data and a probabilistic approach should be employed in the evaluation procedure. We will also discuss how to quantify the effect of noise in data used for evaluation. It will be demonstrated in the talk that noise is a negligible factor in comparison with the uncertainty of evaluation arising as a result of poor sampling.


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