  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
($\mathrm{d}E/\mathrm{d}x$) 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 ${\rm K}^0_S \rightarrow \pi^-\pi^+$, $\phi \rightarrow {\rm K}^-{\rm
K}^+$, and $\Lambda \rightarrow {\rm p}\pi^-$ in p-Pb collisions at
$\sqrt{s_{\rm NN}}=5.02$ TeV. In order to thoroughly assess the validity of the
Bayesian approach, this methodology was used to obtain corrected $p_{\rm T}$
spectra of pions, kaons, protons, and D$^0$ mesons in pp collisions at
$\sqrt{s}=7$ TeV. In all cases, the results using Bayesian PID were found to be
consistent with previous measurements performed by ALICE using a standard PID
approach. For the measurement of D$^0 \rightarrow {\rm K}^-\pi^+$, it was found
that a Bayesian PID approach gave a higher signal-to-background ratio and a
similar or larger statistical significance when compared with standard PID
selections, despite a reduced identification efficiency. Finally, we present an
exploratory study of the measurement of $\Lambda_{\rm c}^{+}\rightarrow {\rm p}
{\rm K}^-\pi^+$ in pp collisions at $\sqrt{s}=7$ TeV, using the Bayesian
approach for the identification of its decay products.
