The Interpretation and Estimation of Effective Sample Size

Statistical and dynamical relationships between observed values of a geophysical system or model effectively reduce the number of independent data. This reduction is expressible in terms of the covariance structure of the process and, in some instances, it is reasonable to devise a measure of the “effective sample size” in terms of sample statistics. Here we discuss the concept of “effective sample size,” and, having settled upon one of several possible definitions, examine various methods of estimating this quantity. It is found that “effective sample size” is quite difficult to estimate reliably. However, a procedure is described which we feel could be used successfully; it is noted that the concept could be extended to spatial arrays of data, in some circumstances.