  Several gamma-ray burst (GRB) luminosity indicators (LIs)have been proposed.
Unlike SNe Ia, calibration of GRB LIs using a low-redshift sample is difficult.
Based on the Bayesian theory, here we propose an approach to calibrate these
LIs without introducing a low-redshift GRB sample. The essential points of our
approach include, (1) calibrate the power-law indices in the LIs with a sample
of GRBs in a narrow redshift range (Delta z); and (2) marginalize the
coefficient of the LIs over a reasonable range of cosmological parameters. We
take our newly discovered multivariable GRB LIs as an example and test the
validity of our approach through simulations. We show that while the
coefficient strongly depends on the cosmological parameters, the power-law
indices do not as long as Delta z is small enough. The selection of Delta z for
a particular GRB sample could be judged according to the size and the
observational uncertainty of the sample. There is no preferable redshift to
perform the calibration of the indices, while a lower redshift is preferable
for the marginalization of the coefficient. The best strategy would be to
collect GRBs within a narrow redshift bin around a fiducial intermediate
redshift (e.g. z~1 or z~2), since the observed GRB redshift distribution is
found to peak around z=(1 - 2.5). Our simulation suggests that with the current
observational precision of measuring GRB isotropic energy, spectral break
energy, and the optical temporal break time, 25 GRBs within a redshift bin of
Delta z ~ 0.30 would give fine calibration to our luminosity
indicator(abridged).
