  The antiparticle energy spectra of Galactic cosmic rays (CRs) have several
exciting features such as the unexpected positron excess at $E\sim$10-200\,GeV
and the remarkably hard antiproton flux at $E\sim$\,60--450\,GeV recently
measured by the \AMS{} experiment. In this paper, we report calculations of
antiparticle CR spectra arising from secondary production and their
corresponding uncertainties. Using the most recent data on CR protons, helium,
carbon, and nuclear ratios $^{10}$Be/$^{9}$Be and B/C, we have performed a
global Bayesian analysis, based on a Markov Chain Monte Carlo sampling
algorithm, under a scenario of spatial-dependent CR diffusion in the Galaxy
which reproduces well the observed spectral hardening in the CR hadron fluxes.
While the high-energy positron excess requires the contribution of additional
unknown sources, we found that the antiproton data are consistent within the
estimated uncertainties, with our predictions based on secondary production.
