  Context: Asteroseismology has entered a new era with the advent of the NASA
Kepler mission. Long and continuous photometric observations of unprecedented
quality are now available which have stimulated the development of a number of
suites of innovative analysis tools.
  Aims: The power spectra of solar-like oscillations are an inexhaustible
source of information on stellar structure and evolution. Robust methods are
hence needed in order to infer both individual oscillation mode parameters and
parameters describing non-resonant features, thus making a seismic
interpretation possible.
  Methods: We present a comprehensive guide to the implementation of a Bayesian
peak-bagging tool that employs a Markov chain Monte Carlo (MCMC). Besides
making it possible to incorporate relevant prior information through Bayes'
theorem, this tool also allows one to obtain the marginal probability density
function for each of the fitted parameters. We apply this tool to a couple of
recent asteroseismic data sets, namely, to CoRoT observations of HD 49933 and
to ground-based observations made during a campaign devoted to Procyon.
  Results: The developed method performs remarkably well at constraining not
only in the traditional case of extracting oscillation frequencies, but also
when pushing the limit where traditional methods have difficulties. Moreover it
provides an rigorous way of comparing competing models, such as the ridge
identifications, against the asteroseismic data.
