Period-Luminosity Relations of Cepheid and Mira Variables and Their Application to the Extragalactic Distance Scale

In this dissertation, I present work towards accurate and precise distance determinations using both Cepheids and Miras. The work includes a Cepheid search in the galaxy M101, a study of near-infrared light curves and phase corrections for Galactic Cepheids, a Mira search in the galaxy M33, a study of near-infrared properties of Miras in the Large Magellanic Cloud, and an investigation into the suitability of the Large Synoptic Survey Telescope for detecting extragalactic Miras. Using time-series observations of two fields in M101, we identified hundreds of Cepheids and derived their mean magnitudes. We obtained optical Cepheid Period-Luminosity Relations and a reddening-corrected distance to this galaxy. Combining the ground-based time-series observations for 34 Galactic Cepheids with literature data, we determined the contemporary phases of a sample of Galactic Cepheids. We used the phases and light curves to correct the single-epoch space-based observations to their mean values. Collaborating with statisticians, we carried out a Mira search in the Local Group galaxy M33 by coupling a novel semi-parametric Gaussian process model and machine learning techniques. We discovered 1847 Mira candidates using I-band measurements and obtained preliminary Period-Luminosity Relations at multiple wavelengths. We studied the near-infrared properties of Large Magellanic Cloud Mira candidates using multi-epoch JHKs observations. We found that the color excesses of Oxygen- and Carbon-rich Miras are different and compared them with the interstellar extinction law. We obtained the near-infrared Mira Period-Luminosity Relations for the Oxygen-rich subtype. We investigated the feasibility of discovering Miras with the Large Synoptic Survey Telescope. We found that our method will discover a considerable number of Oxygen-rich Miras in dozens of systems within 15 Mpc