Space missions like Kepler have revolutionized asteroseismology, the science that infers the stellar interiors by studying oscillation frequency spectra of pulsating stars.

Great advancements have been made in understanding solar-like oscillators. However, this is not the case for variable stars of intermediate masses, such asScutiand Doradus variables. By studying these stars in eclipsing binaries (EBs), model independent funda- mental parameters such as mass and radius can be inferred. On one hand, this synergy constrains the parameter space and facilitates the asteroseismic modeling, and this is shown for the Scuti type pulsating EB KIC 9851944. On the other hand, studies of binary stars must address the complexities such as mass transfer. KIC 8262223 is such an example, which

consists of a mass-gaining Scuti primary and a pre-He white dwarf secondary. Some of the eccentric binary systems, the ‘heartbeat’ stars, show tidally excited oscillations. After briefly reviewing the linear theory of tidally forced stellar oscillations, we study the tidal pulsating binary KIC 3230227 and demonstrate that both amplitude and phase can be used to identify the tidally excited pulsation modes. We also discuss the variability of a Slowly Pulsating B-star KOI-81 and a Cataclysmic variable KIC 9406652.

In the second part of this dissertation, we apply Bayesian statistics to some problems in binaries and asteroseismology with the help of packages BUGS and JAGS. Special attention is paid to the inverse problems (tomography) encountered in studying the double-line spectroscopic binaries.