The Milky Way Galaxy serves as a vast laboratory for studying the dynamics and evolution of the dense interstellar medium and the processes of and surrounding massive star formation. From our vantage point within the Galactic plane, however, it has been extremely difficult to construct a coherent picture of Galactic structure; we cannot see the forest for the trees. The principal difficulties in studying the structure of the Galactic disk have been obscuration by the ubiquitous dust and molecular gas and confusion between objects along a line of sight. Recent technological advances have led to large-scale blind surveys of the Galactic plane at (sub-)millimeter wavelengths, where Galactic dust is generally optically thin, and have opened a new avenue for studying the forest.
The Bolocam Galactic Plane Survey (BGPS) observed over 190 deg2 of the Galactic plane in dust continuum emission near λ = 1.1 mm, producing a catalog of over 8,000 dense molecular cloud structures across a wide swath of the Galactic disk. Deriving the spatial distribution and physical properties of these objects requires knowledge of distance, a component lacking in the data themselves. This thesis presents a generalized Bayesian probabilistic distance estimation method for dense molecular cloud structures, and demonstrates it with the BGPS data set. Distance probability density functions (DPDFs) are computed from kinematic distance likelihoods (which may be double- peaked for objects in the inner Galaxy) and an expandable suite of prior information to produce a comprehensive tally of our knowledge (and ignorance) of the distances to dense molecular cloud structures. As part of the DPDF formalism, this thesis derives several prior DPDFs for resolving the kinematic distance ambiguity in the inner Galaxy.
From the collection of posterior DPDFs, a set of objects with well-constrained distance estimates is produced for deriving Galactic structure and the physical properties of dense molecular cloud structures. This distance catalog of 1,802 objects across the Galactic plane represents the first large-scale analysis of clump-scale objects in a variety of Galactic environments. The Galactocentric positions of these objects begin to trace out the spiral structure of the Milky Way, and suggest that dense molecular gas settles nearer the Galactic midplane than tracers of less-dense gas such as CO. Physical properties computed from the DPDFs reveal that BGPS objects trace a continuum of scales within giant molecular clouds, and extend the scaling relationships known as Larson\u27s Laws to lower-mass substructures. The results presented here represent the first step on the road to seeing the molecular content of the Milky Way as a forest rather than individual nearby trees
