MMP.17:4.4 - Locate errors and losses that change the receiving use

Compare the replacement with the source in the quantities the receiver consumes. A deterministic bound, an empirical error on selected cases and a statistical interval support different conclusions.

When bounds are available in the same response metric, propagate them. For example, if interpolation of accurate case values differs from (r) by at most (e_{\mathrm{int}}), and each supplied case value has error at most (e_{\mathrm{case}}), convex linear interpolation has error at most (e_{\mathrm{int}}+e_{\mathrm{case}}). Other fitting rules need their own propagation: a poorly conditioned fit can amplify errors in its cases. CMP.8 supplies that numerical approximation and conditioning work.

For a scalar test (r(x)\leq b), a justified bound (e(x)) gives an immediate rule:

• if (\widehat r(x)+e(x)\leq b), the bound supports the test;
• if (\widehat r(x)-e(x)>b), the bound rules it out;
• otherwise the replacement leaves this test unresolved.

An observed maximum error at finitely many cases is not automatically a bound over (D). A statistical coverage result retains its sampling and calibration conditions and its pointwise, marginal or simultaneous meaning. A fitted uncertainty indicator can guide the next query without supplying such a result.

Test lost operations as well as values. On ([0,1]), (r(x)=x) and (\widehat r(x)=x+0.01\sin(1000x)) differ in value by at most (0.01). Yet (r’(x)=1), while (\widehat r’(\pi/1000)=-9). If a receiver follows the derivative, this substitution can reverse the proposed direction. Include derivative information or a justified monotone family when that operation matters, or keep the source calculation for it.

A discrepancy with the source calls for examination of case coverage, representation or fitting. A discrepancy with observations can instead require MMP.14 to revise the source or its observation model. Agreement with the source cannot close that second question.