  Many of the current round of experiments searching for anisotropies in the
MBR are confronting the problem of how to disentangle the cosmic signal from
contamination due to galactic and intergalactic foreground sources. Here we
show how commonly used likelihood function techniques can be generalized to
account for foreground. Specifically we set some restrictions on the spectrum
of foreground contamination but allow the amplitude to vary arbitrarily. The
likelihood function thus generalized gives reasonable limits on the MBR
anisotropy which, in some cases, are not much less restrictive than what one
would get from more detailed modeling of the foreground. Furthermore, the
likelihood function is exactly the same as one would obtain by simply
projecting out foreground contamination and just looking at the reduced data
set. We apply this generalized analysis to the recent medium angle data sets of
ACME-HEMT and MAX. The resulting analysis constrains the one free parameter in
the standard cold dark matter theory to be Q=18_-5^+8 microK. This best fit
value, although in striking agreement with the normalization from COBE, is not
a very good fit, with an overall chi^2/ degree of freedom =208/168. We also
argue against three commonly used methods of dealing with foreground: (i)
ignoring it completely; (ii) subtracting off a best fit foreground and treating
the residuals as if uncontaminated; and (iii) culling data which appears to be
contaminated by foreground.
