A Large Deviations Result for Aggregation of Independent Noisy Observations

Sensing and aggregation of noisy observations should not be considered as separate issues. The quality of collective estimation involves a difficult tradeoff between sensing quality which increases by increasing the number of sensors, and aggregation quality which typically decreases if the number of sensors is too large. We examine a strategy for optimal aggregation for an ensemble of independent sensors with constrained system capacity. We show that in the large capacity limit larger scale aggregation always outperforms smaller scale aggregation at higher noise levels, while below a critical value of noise, there exist moderate scale aggregation levels at which optimal estimation is realized.