We describe a robust Bayesian statistical method for determining Lyman alpha forest cloud sizes in spherical and in thin disk geometries, using absorption in adjacent sightlines toward closely separated QSO pairs and groups, 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- size and unclustered clouds, the data from Q1343+2640A/B give a 99% confidence lower and upper bounds 61<R<533 kpc/h on the radius of spherical clouds at z about 1.8, with a median value of 149 kpc/h [$(Omega_0, Lambda_0) =(1,0)$]. The baryonic mass of such large clouds is comparable to that of dwarf irregular galaxies. Their cosmic overdensity is close to the turn-around density but generally below the virialization density, suggesting a population of gravi- tationally bound but unvirialized protogalactic objects at z about 2. Their comoving volume density is similar to that of the faint blue galaxies (FBGs) at the limiting magnitude B of 26-27. The dynamical collapsing timescale of over- densities like these clouds is also comparable with the cosmic time difference between z of 2 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 about 1. We also investigate the other QSO pairs: Q0307-1931/1932, Q0107-0232/0235, and the triplet of Q1623+268. Imposing an uniform W_0 > 0.4 A threshold on all linelists, 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 clouds does not accurately describe the Ly alpha cloud population.
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