Closely separated QSO pairs and groups make it possible to probe the s
ize, geometry, and spatial clustering of Ly alpha forest clouds. Recen
t spectroscopic observations of Q1343 + 2640A/B give evidence that the
transverse sizes of Ly alpha clouds are very large at redshifts appro
ximate to 2 (as reported by Bechtold et al. in 1994). In this paper, w
e describe a robust Bayesian statistical method for determining cloud
sizes in spherical and in thin disk geometries, apply this method to t
he available data, and discuss implications of our results for models
of Ly alpha clouds. Under the assumption of a population of uniform-si
zed and unclustered Ly alpha clouds, the data from Q1343 + 2640A/B giv
e a 99% confidence lower and upper bounds 61 < R < 533 h(-1) kpc on th
e radius of spherical clouds at z approximate to 1.8, with a median va
lue of 149 h(-1) kpc [(Omega(0), Lambda(0)) = (1, 0), and h = H-0/100
km s(-1) Mpc(-1)]. The baryonic mass of such large clouds, if they are
roughly homogeneous and quasi- spherical, is comparable to the baryon
ic mass of dwarf irregular galaxies. Their cosmic overdensity is close
to the turnaround density but generally below the virialization densi
ty, which suggests a population of gravitationally bound but unviriali
zed protogalactic objects at z approximate to 2. The comoving volume d
ensity of these clouds is similar to that of the faint blue galaxies (
FBGs) at the limiting magnitude B approximate to 26-27, if these FBGs
are distributed approximately over the range of redshift from 0.8 to 2
. The timescale for dynamical collapse of overdensities like these clo
uds is also comparable to the cosmic time difference between z approxi
mate to 2 and z approximate to 1. Both populations of objects show sim
ilar weak clustering in space. All this evidence suggests a possible i
dentification of Ly alpha clouds as the collapsing progenitors of the
FBGs at z similar to 1. We also investigate the other closely separate
d QSO pairs with published high-quality spectra: Q0307 - 1931/0307 - 1
932, Q0107 - 0232/0107 - 0235, and the triplet of Q1623 + 268. Imposin
g a uniform W-0 greater than or equal to 0.4 Angstrom counting thresho
ld on all the line lists, we find a trend of larger inferred cloud rad
ius with larger proper separation of QSO pairs, significant at the 3.4
sigma level. This indicates that the idealization of unclustered, uni
form-sized spherical clouds does not accurately describe the Ly alpha
cloud population. Present data are insufficient to resolve with confid
ence whether this effect is due to clustering, filamentary shape, or n
onuniform cloud size. There is a suggestion, however, that at low reds
hifts a residual population of larger clouds remains.