By Kronig R.
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Extra info for A Theorem on Space Quantization
Thus, changes seen in a measurement series may not come from the process itself. 1 Measurement: The Illusion! Almost always, the methods will not measure the process itself but rather a surrogate strongly associated with it. The reasons for this vary. Sometimes direct measurement is just not possible. Doing so may be too expensive, dangerous, or socially unacceptable. Direct measurement, although more accurate may be too slow. Thus the surrogate may yield timely data at a lower cost but with a loss in quality.
For completeness we therefore describe developments from that perspective beginning with the taxonomy oﬀered in this section. Moreover, nothing more explicit needs to be said about measurement error within a Bayesian perspective. For continuous exposure variables, measurement error is generally characterized as either of classical or Berkson type, diﬀerential or nondiﬀerential, structural or functional. Errors can also be of mixed type. , studies of individuals; the exposure measurement W = X + U where X denotes the true exposure and U independent noise.
The inevitability of such error means it must be embraced in any statistical method used in any analysis of the resulting data. Instrument failures provide another source of error. For instance, volumetric air samplers can fail or malfunction for periods of time until they are detected. Moreover, early gauges for measuring the acidity of precipitation could be contaminated by bird droppings with a resulting measurement bias. 3 arising from analytical services are important. 4 Measurement Error 47 cannot eliminate this source of error so these too must be recognized and accommodated in the analysis.