  Since the advent of the space-based photometric missions such as CoRoT and
NASA's Kepler, asteroseismology has acquired a central role in our
understanding about stellar physics. The Kepler spacecraft, especially, is
still releasing excellent photometric observations that contain a large amount
of information not yet investigated. For exploiting the full potential of these
data, sophisticated and robust analysis tools are now essential, so that
further constraining of stellar structure and evolutionary models can be
obtained. In addition, extracting detailed asteroseismic properties for many
stars can yield new insights on their correlations to fundamental stellar
properties and dynamics. After a brief introduction to the Bayesian notion of
probability, I describe the code DIAMONDS for Bayesian parameter estimation and
model comparison by means of the nested sampling Monte Carlo (NSMC) algorithm.
NSMC constitutes an efficient and powerful method, in replacement to standard
Markov chain Monte Carlo, very suitable for high-dimensional and multimodal
problems that are typical of detailed asteroseismic analyses, such as the
fitting and mode identification of individual oscillation modes in stars (known
as peak-bagging). DIAMONDS is able to provide robust results for statistical
inferences involving tens of individual oscillation modes, while at the same
time preserving a considerable computational efficiency for identifying the
solution. In the tutorial, I will present the fitting of the stellar background
signal and the peak-bagging analysis of the oscillation modes in a red-giant
star, providing an example to use Bayesian evidence for assessing the peak
significance of the fitted oscillation peaks.
