  Gamma Ray Burst (GRBs) are empirically classified as long-duration GRBs
(LGRBs, $>$ 2s) and short-duration GRBs (SGRBs, $<$ 2s). Physically they can be
grouped into two distinct progenitor categories: those originating from
collapse of massive stars (also known as Type II) and those related to mergers
of compact stars (also known as Type I). Even though most LGRBs are Type II and
most SGRBs are Type I, the duration criterion is not always reliable to
determine the physical category of a certain GRB. Based on our previous
comprehensive study of the multi-wavelength properties of long and short GRBs,
here we utilize the Naive Bayes method to physically classify GRBs as Type I
and Type II GRBs based on multi-wavelength criteria. It results in 0.5\%
training error rate and 1\% test error rate. Moreover, there is a gap [-1.2,
-0.16] in the distribution of the posterior Odds, $\log O({\rm II:I})$, the
Type II to Type I probability ratio. Therefore, we propose to use ${\cal O} =
\log O({\rm II:I})+0.7$ as the parameter to classify GRBs into Type I ($<0$) or
Type II ($>0$). The only confirmed Type I GRB, GRB 170817A, has log $O({\rm
II:I})=-10$. According to this criterion, the supernova-less long GRBs 060614
and 060505 belong to Type I, and two controversial short GRBs 090426 and 060121
belong to Type II.
