  We present a catalog of the probabilistic redshift estimates and for 1366
individual Long-duration Gamma-Ray Bursts (LGRBs) detected by the Burst And
Transient Source Experiment (BATSE). This result is based on a careful
selection and modeling of the population distribution of 1366 BATSE LGRBs in
the 5-dimensional space of redshift and the four intrinsic prompt gamma-ray
emission properties: the isotropic 1024ms peak luminosity, the total isotropic
emission, the spectral peak energy, as well as the intrinsic duration, while
carefully taking into account the effects of sample incompleteness and the
LGRB-detection mechanism of BATSE. Two fundamental plausible assumptions
underlie our purely-probabilistic approach: 1. LGRBs trace, either exactly or
closely, the Cosmic Star Formation Rate and 2. the joint 4-dimensional
distribution of the aforementioned prompt gamma-ray emission properties is
well-described by a multivariate log-normal distribution.
  Our modeling approach enables us to constrain the redshifts of individual
BATSE LGRBs to within $0.36$ and $0.96$ average uncertainty ranges at $50\%$
and $90\%$ confidence levels, respectively. Our redshift predictions are
completely at odds with the previous redshift estimates of BATSE LGRBs that
were computed via the proposed phenomenological high-energy relations,
specifically, the apparently-strong correlation of LGRBs' peak luminosity with
the spectral peak energy, lightcurve variability, and the spectral lag. The
observed discrepancies between our predictions and the previous works can be
explained by the strong influence of detector threshold and
sample-incompleteness in shaping these phenomenologically-proposed high-energy
correlations in the literature.
