I will describe two projects in my astrophysics research where the application of improved statistical techniques leads to improved science. The first project concerns the total mass of the Milky Way Galaxy – a fundamental parameter for both theoretical predictions and observational studies. I will describe a hierarchical Bayesian method I developed to estimate not only the total mass but also the cumulative mass profile of the Milky Way. This approach is an improvement to traditional point mass estimates computed at particular distances from the Galactic centre. The second project concerns the study of astronomical objects (e.g. stars) whose brightness changes periodically. Astronomical time series data are often unevenly sampled in time, making the Lomb-Scargle periodogram (1976, 1982) a popular estimator of the power spectrum despite its poor statistical properties. I will outline an approximation to the Thomson (1982) multitaper estimator for unevenly sampled times (Springford, 2017). This method is being applied to astronomical time series data from past missions (e.g. Kepler) in anticipation of upcoming surveys such as the Large Synoptic Survey Telescope.