Statistics for Making Decisions by Longford Nicholas T.;

Author:Longford, Nicholas T.;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2020-12-30T00:00:00+00:00

as a function of and R. Now, and involve neither nor R, so we can regard them as constants. Further, the expected loss functions and are effectively identical for any constant ; certainly, while and R are held constant, they do not alter the value of T∗. A change of R to for a constant can be compensated by altering to

(7.2)

and altering Q to

The factor is a decreasing function of d, equal to unity when . Therefore, an increase of R is equivalent to a reduction of , leaving the optimal cutpoint T∗ unchanged. Conversely, an increase of R accompanied by an increase of compounds their ‘individual’ reductions of T∗. This confirms that the extreme plausible values of T∗ arise with plausible pairs in the south-west and north-east vertices of the plausible rectangle.

Uncertainty about the expectations and variances of Y can be addressed similarly. Each element of uncertainty inflates the plausible range of T∗, so we have to be sparing with these uncertainties. By this statement we mean that the assessment of uncertainties should be as rigorous as possible, to keep the uncertainty in T∗ in check. But the uncertainties about the parameters involved should be reduced as much as possible, by a combined effort of data collection and elicitation. Also, at the planning stage, an exploration of the extent to which the uncertainty about a parameter converts to wider plausible range of T∗ may help us to distribute the available (research) resources among the competing goals of reducing the uncertainties about R, , and , S = D and H, and, indeed, in establishing the nature and shape of the within-status distributions of Y.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.