The Error Budget

An error budget lists every source of uncertainty and how much each contributes to the final number, so no claim travels without its bar.

Where the uncertainty comes from

An error budget is a ledger. For any headline result, it enumerates the contributing uncertainties -- inputs, model form, discretization, correlations -- and shows how each propagates to the output. The point is to know not just how uncertain a number is, but why, and which term to attack to reduce it.

Combining terms honestly

Independent uncertainties combine in quadrature; correlated ones do not, and pretending they are independent understates the total. We track correlations where they matter and state when we have assumed independence. The dominant term usually decides where the next unit of effort should go.

No number without a budget

The standard is simple: a quantitative claim that cannot show its error budget is not ready to publish. When the budget is dominated by an unvalidated model form -- as it is for the burner plug regime -- the honest conclusion is that the central value is not yet meaningful, and we say that instead of quoting a tidy figure.

An error budget is also a to-do list. It tells us, before any hardware, which measurement at FOAK will most reduce what we do not know. Because it is a ledger rather than a single figure, the error budget can be checked line by line, argued with, and improved -- which is exactly the property a headline uncertainty should have if anyone is meant to rely on it. We build the budget before we quote the headline, not after, because a central value chosen first and justified later is how false precision enters a design and then proves nearly impossible to remove.