© 2016, CERN for the benefit of the ALICE Collaboration.We present a Bayesian approach to particle identification (PID) within the ALICE experiment. The aim is to more effectively combine the particle identification capabilities of its various detectors. After a brief explanation of the adopted methodology and formalism, the performance of the Bayesian PID approach for charged pions, kaons and protons in the central barrel of ALICE is studied. PID is performed via measurements of specific energy loss (dE/dx) and time of flight. PID efficiencies and misidentification probabilities are extracted and compared with Monte Carlo simulations using high-purity samples of identified particles in the decay channels K0S→ π-π+}, ɸ → K-K+, and Λ → p π- in p-Pb collisions at √sNN=5.02 TeV. In order to thoroughly assess the validity of the Bayesian approach, this methodology was used to obtain corrected pT spectra of pions, kaons, protons, and D0 mesons in pp collisions at √s=7 TeV. In all cases, the results using Bayesian