  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.
