This dissertation examines the multiplicity properties of stars in the Milky Way and their relationship with metallicity. We present methods and techniques for data mining individual, raw, sub-exposure information from spectroscopic surveys as a statistical approach to performing scientific analyses in this era of Big Data. We also describe how Bayesian inference and Markov Chain Monte Carlo simulations work in conjunction with these sub-exposure spectroscopy techniques. Binary interactions play a key role in many astrophysical processes, from altering surfaces abundances, to producing supernova. In Chapter 1, we give a brief introduction to stellar multiplicity, beginning with a description of the star formation process and possible scenarios for binary star formation. We discuss how binary stars interact through Roche-lobe overflow, and how binary systems lead to various astrophysical phenomena. We conclude the chapter with a look at our current understanding of multiplicity properties of stars in the Milky Way as determined empirically from observations and surveys, and with a discussion for the future outlook of multiplicity studies. In Chapter 2 we describe a methodology for measuring radial velocity variations in stellar sources using sub-exposure spectra from multi-fiber spectroscopic surveys. In particular, we describe a cross-correlation technique used on spectra that were observed as part of the SDSS survey. In Chapter 3 we give a brief introduction to Bayesian inference and the use of the MCMC python package emcee. We describe the methods used for detecting binarity in stellar sources from sparsely sampled radial velocity curves. Chapter 4 contains the peer-reviewed article Hettinger et al. (2015) published in the Astrophysical Journal Letters. In this Letter, we employ the sub-exposure radial velocity measurement techniques and the MCMC methods outlined in this dissertation to examine a population of F-type dwarf stars in the Milky Way. The sample was divided into three groups by metallicity, with the goal of investigating the metallicity dependence on multiplicity properties. We find a higher fraction of short-period binaries for the metal-rich disk stars than the metal-poor halo stars. Finally, in Chapter 5, we extend the work of Hettinger et al. (2015) to investigate possible constraints on the separation distribution of binaries in the F-dwarf population.
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