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Random vs. systematic sampling J. Gallego, MARS AGRI4CAST

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Geographic systematic sampling Positive More efficient than random sampling if the spatial autocorrelation is a decreasing function of the distance More difficult to manipulate: it gives more confidence Important if the results are politically sensitive

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Geographic systematic sampling (2) Negative It may introduce a distortion in the variance if the landscape is repetitive Chess board effect if the size and orientation of the cells is the same as the sampling step This can be an issue in small pilot regions Unlikely in large complex regions There is no unbiased estimator of the variance The usual variance estimators are conservative (overestimate the variance)

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Variance estimation in LUCAS Usual variance estimator for two-phase random sampling (incomplete stratification) The estimated variance of Y in stratum h can be written This estimator is strongly biased for systematic sampling The bias is reduced with a local estimator of the variance of Y:

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Example of sophisticated sampling scheme TREES-2: estimation of tropical deforestation Very efficient in terms of variance, but strongly attacked in the political forum

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Alternative by FAO for general land cover monitoring One tile of 10x10 or 20x20 km each lat-long degree Half-rate above 60º Problem of bias Less problematic in tropical countries

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Definitions Periodic Function: f(t +T) = f(t)t, (Period T)(1) Ex: f(t) = A sin(2Πωt + )(2) has period T = (1/ω) and ω is said to be the frequency (angular),

Definitions Periodic Function: f(t +T) = f(t)t, (Period T)(1) Ex: f(t) = A sin(2Πωt + )(2) has period T = (1/ω) and ω is said to be the frequency (angular),

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