If X is an unbiased measurement of a true value , and U(X) is a nonlinear function of X, then in most cases U is a biased estimate of the true value . In most cases this bias is ignored. If it is important to reduce this bias, however, a bias-corrected estimate is . In general the bias-corrected estimate is not unbiased, but has a smaller bias than U(X). Assume that the radius of a circle is measured to be r=3.0 ± 0.1 cm.

Question

a. Estimate the area A, and find the uncertainty in the estimate, without bias correction.
b. Compute the bias-corrected estimate of A.
c. Compare the difference between the bias-corrected and non-bias-corrected estimates to the uncertainty in the non-bias-corrected estimate. Is bias correction important in this case? Explain.

Answer 1

(c) No. The difference between the two estimates is much less than the uncertainty.