Closely separated QSO pairs and groups make it possible to probe the size, geometry, and spatial clustering of Ly alpha forest clouds. Recent spectroscopic observations of Q1343 + 2640A/B give evidence that the transverse sizes of Ly alpha clouds are very large at redshifts approximate to 2 (as reported by Bechtold et al. in 1994). In this paper, we describe a robust Bayesian statistical method for determining cloud sizes in spherical and in thin disk geometries, apply this method to the available data, and discuss implications of our results for models of Ly alpha clouds. Under the assumption of a population of uniform-sized and unclustered Ly alpha clouds, the data from Q1343 + 2640A/B give a 99% confidence lower and upper bounds 61 < R < 533 h(-1) kpc on the radius of spherical clouds at z approximate to 1.8, with a median value 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 baryonic mass of dwarf irregular galaxies. Their cosmic overdensity is close to the turnaround density but generally below the virialization density, which suggests a population of gravitationally bound but unvirialized protogalactic objects at z approximate to 2. The comoving volume density 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 clouds is also comparable to the cosmic time difference between z approximate to 2 and z approximate to 1. Both populations of objects show similar weak clustering in space. All this evidence suggests a possible identification of Ly alpha clouds as the collapsing progenitors of the FBGs at z similar to 1. We also investigate the other closely separated QSO pairs with published high-quality spectra: Q0307 - 1931/0307 - 1932, Q0107 - 0232/0107 - 0235, and the triplet of Q1623 + 268. Imposing a uniform W-0 greater than or equal to 0.4 Angstrom counting threshold on all the line lists, we find a trend of larger inferred cloud radius with larger proper separation of QSO pairs, significant at the 3.4 sigma level. This indicates that the idealization of unclustered, uniform-sized spherical clouds does not accurately describe the Ly alpha cloud population. Present data are insufficient to resolve with confidence whether this effect is due to clustering, filamentary shape, or nonuniform cloud size. There is a suggestion, however, that at low redshifts a residual population of larger clouds remains.
