A priori weighting

It should be stressed that, in any experiment for which there is to be a least-squares refinement of parameters, intended to yield not only the best possible parameter values but also respectable estimates of their uncertainties and a test of the validity of the model, it is vital to take the trouble to analyze the methods and the circumstances of the experiment carefully in order to get the best possible values of the a priori weights. 

In this energy regime, the condition of the system is correctly represented not by any one state , M but rather by a quantum statistical ensemble in which all the accessible states appear with equal a priori weights and random a priori phases. The appropriate density operator is then... 

The Necessity of a priori Weighting Why is Character Quality the Same as Probability of Homology ... 

Waldhauser and Ellsworth [2000] use a two-step iterative solution procedure, where a priori weights describing data quality are first applied to the arrival times. Once a stable solution is obtained, the data are reweighted by multiplying the a priori quality weights with values that depend on the misfit of the data from the previous iteration and on the offset between events (to downweight event pairs with large inter-event differences). 

In summary, we have never found a case where PLSR has performed clearly worse than, say, SMLR or PCR, and we have found many cases where PLSR performs clearly better (in terms of understandable calibration models and low predictive errors). Thus we regard PLSR, with proper a priori weighting of the input variables, proper outlier detection, and conservative validation, to be a relatively safe and informative calibration method of general applicability. 

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