This dissertation deals with the theory of the phonetic component of grammar in a formal probabilistic inference framework: (1) it has been recognized since the beginning of generative phonology that some language-specific phonetic implementation is actually context-dependent, and thus it can be said that there are gradient "phonetic processes" in grammar in addition to categorical "phonological processes." However, no explicit theory has been developed to characterize these processes. Meanwhile, (2) it is understood that language acquisition and perception are both really informed guesswork: the result of both types of inference can be reasonably thought to be a less-than-perfect commitment, with multiple candidate grammars or parses considered and each associated with some degree of credence. Previous research has used probability theory to formalize these inferences in implemented computational models, especially in phonetics and phonology. In this role, computational models serve to demonstrate the existence of working learning/perception/parsing systems assuming a faithful implementation of one particular theory of human language, and are not intended to adjudicate whether that theory is correct. The current dissertation (1) develops a theory of the phonetic component of grammar and how it relates to the greater phonological system and (2) uses a formal Bayesian treatment of learning to evaluate this theory of the phonological architecture and for making predictions about how the resulting grammars will be organized. The coarse description of the consequence for linguistic theory is that the processes we think of as "allophonic" are actually language-specific, gradient phonetic processes, assigned to the phonetic component of grammar; strict allophones have no representation in the output of the categorical phonological grammar. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]