  We develop methods to account for experimental and observational
uncertainties in likelihood analyses of data from cosmic microwave background
(CMB) anisotropy experiments and apply them to an analysis of the UCSB South
Pole 1994 (SP94) experiment. Observationally motivated open and spatially-flat
$\Lambda$, cold dark matter cosmogonies are considered. Among the models we
consider, the full SP94 data set is most consistent with $\Omega_0 \sim
0.1-0.2$ open models and less so with old $(t_0 \gap 15 - 16 Gyr)$, high baryon
density $(\Omega_B \gap 0.0175 h^{-2})$, low density ($\Omega_0 \sim 0.2 -
0.4), flat-$\Lambda$ models. The SP94 data do not rule out any of the models we
consider at the $2\sigma$ level. The SP94 experiment is most sensitive to
anisotropies on a somewhat larger, model-dependent, angular scale than the
scale at which the window function peaks. For establishing the significance of
a detection of CMB anisotropy we derive limits using the highest posterior
density (HPD) prescription, since it yields smaller lower limits. Since HPD
limits lead to tighter constraints on the CMB amplitude, they also provide for
greater discrimination between models. Model normalizations deduced from the
SP94 data subsets are mostly consistent with those deduced from the two-year
COBE-DMR data, although the Ka-band data prefer a normalization $\sim 1\sigma$
lower than do the Q-band data, the Q and Ka + Q data favour a slightly higher
normalization for the $\Omega_0 = 0.1$ open model than does the DMR, and the Ka
and Ka + Q data prefer a somewhat lower normalization for the older, higher
$\Omega_B$, low-density $\Lambda$ models than does the DMR.
