  The gravitationally lensed quasar HE 1104-1805 has been observed at a variety
of wavelengths ranging from the mid-infrared to X-ray for nearly 20 years. We
combine flux ratios from the literature, including recent Chandra data, with
new observations from the SMARTS telescope and HST, and use them to investigate
the spatial structure of the central regions using a Bayesian Monte Carlo
analysis of the microlensing variability. The wide wavelength coverage allows
us to constrain not only the accretion disk half-light radius r_1/2, but the
power-law slope \xi\ of the size-wavelength relation r_1/2 ~ \lambda^\xi. With
a logarithmic prior on the source size, the (observed-frame) R-band half-light
radius log(r_1/2/cm) is 16.0+0.3-0.4, and the slope \xi\ is 1.0+0.30-0.56. We
put upper limits on the source size in soft (0.4-1.2 keV) and hard (1.2-8 keV)
X-ray bands, finding 95% upper limits on log (r_1/2/cm) of 15.33 in both bands.
A linear prior yields somewhat larger sizes, particularly in the X-ray bands.
For comparison, the gravitational radius, using a black hole mass estimated
using the H\beta\ line, is log(r_g/cm) = 13.94. We find that the accretion disk
is probably close to face-on, with cos i = 1.0 being four times more likely
than cos i = 0.5. We also find probability distributions for the mean mass of
the stars in the foreground lensing galaxy, the direction of the transverse
peculiar velocity of the lens, and the position angle of the projected
accretion disk's major axis (if not face-on).
