Asteroseismic Data Analysis with DIAMONDS.

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.