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The primary advantage of the alternate least squares approach is that it gives more weight to realizations that are better fits to the calibration data. This approach (1) allows explicit weighting of different calibration data, (2) produces no sharp divide between accepted and rejected values, and (3) weights realizations that are better fits to the calibration data more than those that are not. The primary disadvantages of this approach are that (1) it is difficult to build a rigorous objective function (a measure of the fit of the model results to the calibration data) and (2) realizations that are clearly inconsistent with the calibration data will be accepted. The sum of the squares of the residuals (or whatever difference measurement is used) may not be a good measure of the probability that a given model output matches a calibration point because some uncertainty ranges may not be symmetric and, because all realizations are accepted, many unlikely realizations may be accepted. In the additional temperature point example, this alternative approach provides results, but the modeler might not ever recognize that none of the realizations are consistent with both data points. If the same weights were used for each temperature, a most likely result would probably split the difference and not match either point. If the modeler did recognize the issue, it could be addressed by giving the points appropriate weights and/or reevaluating the quality of the calibration data.

The primary advantage of the alternate least squares approach is that it gives more weight to realizations that are better fits to the calibration data. This approach (1) allows explicit weighting of different calibration data, (2) produces no sharp divide between accepted and rejected values, and (3) weights realizations that are better fits to the calibration data more than those that are not. The primary disadvantages of this approach are that (1) it is difficult to build a rigorous objective function (a measure of the fit of the model results to the calibration data) and (2) realizations that are clearly inconsistent with the calibration data will be accepted. The sum of the squares of the residuals (or whatever difference measurement is used) may not be a good measure of the probability that a given model output matches a calibration point because some uncertainty ranges may not be symmetric and, because all realizations are accepted, many unlikely realizations may be accepted. In the additional temperature point example, this alternative approach provides results, but the modeler might not ever recognize that none of the realizations are consistent with both data points. If the same weights were used for each temperature, a most likely result would probably split the difference and not match either point. If the modeler did recognize the issue, it could be addressed by giving the points appropriate weights and/or reevaluating the quality of the calibration data.

The purpose of this article is not to recommend one of these approaches over the other, but to remind the modeler to think about the quality of the calibration data and to understand that multiple approaches are present to incorporate the data. The best option will commonly be problem dependent. For example, a least squares–type approach might be better for weighting a vitrinite reflectance data point from a cuttings sample, where uncertainty exists regarding the measurement, the sample depth, or whether the sample contains reworked material. A reject-accept approach might be better for considering known hydrocarbon accumulations. A spectrum of intermediate cases exists so a hybrid method might prove to be better in some cases than either of the above approaches. For example, there could be some range around each data point that is considered an exact match, a range around that to which some weighting function is applied and then an outer range that is not acceptable.

The purpose of this article is not to recommend one of these approaches over the other, but to remind the modeler to think about the quality of the calibration data and to understand that multiple approaches are present to incorporate the data. The best option will commonly be problem dependent. For example, a least squares–type approach might be better for weighting a [[vitrinite]] reflectance data point from a cuttings sample, where uncertainty exists regarding the measurement, the sample depth, or whether the sample contains reworked material. A reject-accept approach might be better for considering known hydrocarbon accumulations. A spectrum of intermediate cases exists so a hybrid method might prove to be better in some cases than either of the above approaches. For example, there could be some range around each data point that is considered an exact match, a range around that to which some weighting function is applied and then an outer range that is not acceptable.

[[:file:H4CH12FG11.JPG|Figure 11]] shows the resulting thermal profiles for 100 realizations of the hypothetical model described. In panel A of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations are accepted. In panel B of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations within the temperature error bars are accepted. In this filtered case example, it is assumed that a reasonable estimate of the accuracy of the single temperature point exists. Given that assumption, realizations outside the error bars are rejected and those inside the error bars are accepted. If the estimate of the accuracy of the temperature data was less precise, the least squares approach might be a good, or even a better, approach. In either case, if the calibration data are to be given any weight, taking all the realizations and weighting them equally would be a poor choice.

[[:file:H4CH12FG11.JPG|Figure 11]] shows the resulting thermal profiles for 100 realizations of the hypothetical model described. In panel A of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations are accepted. In panel B of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations within the temperature error bars are accepted. In this filtered case example, it is assumed that a reasonable estimate of the accuracy of the single temperature point exists. Given that assumption, realizations outside the error bars are rejected and those inside the error bars are accepted. If the estimate of the accuracy of the temperature data was less precise, the least squares approach might be a good, or even a better, approach. In either case, if the calibration data are to be given any weight, taking all the realizations and weighting them equally would be a poor choice.