Hierarchical and Bayesian methods for data analysis

During this seminar, I will introduce hierarchical and Bayesian statistical techniques for analyzing data.  These methods can be very effective for reducing noisy data, as well as fitting models to observations.  After introducing Bayesian statistics, I will compare and contrast the results of Bayesian fits to commonly employed frequentist methods.  I will also discuss how hierarchical statistical methods are very well suited for analyzing structured data common in astronomy, as well as estimating a large number of parameters occurring in complex models.  Such methods can reveal latent correlations between model parameters, while simultaneously treating any possible degeneracies.  I will also discuss how Monte Carlo methods can be used to estimate parameters in the Bayesian approach. I will conclude the seminar by describing the hierarchical Bayesian techniques I have employed for investigating the Kennicutt-Schmidt relationship and dust spectral energy distributions from infrared and sub-millimeter observations from Spitzer, Herschel, and ground-based telescopes such as CARMA.