B. Extremes, Extrapolation, And Surprise

A.6. When and how do we address measurement error? Telescope analogy. Discerning uncertainty and measurement error from true variability in an observed distribution in which both are confounded together is just like deblurring an image from a telescope using optical measurements of the lens. The forward equations are image = signal + distortion observed distribution = variability + measurement error where + indicates convolution rather than simple addition. To solve these equations for (better) estiNeed for accuracy. Addressing measurement error is most important when you need to make accurate estimates of real variability in a population. For example, you might want to estimate the 99th or 99.9th percentile from a lognormal distribution of exposures or a pharmacokinetic parameter affecting disease susceptibility. mates of the signal or variability, we need to employ de-convolution. We need estimates of the distortion (which we can get by studying the lens) or an estimate of measurement error (which we can get by studying the measurement protocol that was employed). There may be some technical problems, but it is often worthwhile.