  Please note that this abstract has been shortened from that found in the
paper. A brief history is given of the development of the correction for
observation selection bias inherent in the calibration of absolute magnitudes
using trigonometric parallaxes. As a tutorial to gain an intuitive
understanding of several complicated trigonometric bias problems, we study a
toy bias model of a parallax catalog which incorporates assumed parallax
measuring errors of various severities. The two effects of bias errors on the
derived absolute magnitudes are (1) the Lutz-Kelker correction itself that
depends on the fractional parallax error and the spatial distribution, and (2)
a Malmquist-like `incompleteness' correction of opposite sign due to various
apparent magnitude cut-offs as they are progressively imposed on the catalog.
The simulations involve 3 million stars spread with varying density
distributions in a volume bounded by a radius of 50,000 pc. A fixed absolute
magnitude of M_V = +0.6 is used to imitate RR Lyrae variables in the mean. The
bias is demonstrated for various assumed spatial densities and parallax error
models, including one that is projected for the FAME satellite. The effects of
imposing magnit ude limits and limits on the `observer's' error are displayed.
We contrast the method of calculating mean absolute magnitude directly from the
parallaxes where bias corrections are mandatory, with an inverse method using
maximum likelihood which is free of the Lutz-Kelker bias, although a Malmquist
bias is present. We discuss the level of accuracy that can be expected in a
calibration of RR Lyrae absolute magnitudes from the FAME data over the
metallicity range of [Fe/H] from 0 to -2, given the known frequency of the
local RR Lyraes closer than 1.5 kpc.
