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lecture5and6 - Estimation of ensemble pdfs cdfs and moments...

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Estimation of ensemble pdfs, cdfs, and moments from limited sampling of random fields Stochastic Subsurface Hydrology CWR 6536
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Estimation of ensemble moments from field data Assume that random field is constructed of the following components: If only one replicate available, use visualization techniques to look for possible non-stationary behavior in space. If multiple replicates available (typically over time) can properly analyze for non-stationary moments
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Estimating a stationary mean Estimator of the mean: Estimate is itself a random variable because it depends on both the number of observations and the values of the observations
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Properties of Good Estimators Unbiased Consistent Efficient
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It can be shown that the sample mean calculated using standard estimator is unbiased for any sequence of independent identically distributed r.v.s with finite mean and variance It also can be shown that the standard estimator is consistent and the most efficient estimator of the population mean
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Analyzing data with an apparent mean trend Is there a physical reason for the trend? If so postulate a physical model for the mean trend Is there a change in geology or soil structure which might allow you to break the region up into stationary subregions?
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