Automatic rhythm analysis is an important area of research in Music Information Retrieval (MIR) as it aims to develop algorithmic models to study the phenomenon of beat induction, an action intuitive and almost instinctual to human listeners. Automatic methods to detect rhythmic as well as musical attributes of a musical piece like tempo, beats, meter are studied widely in the literature. In this thesis, we explore time varying metrical structures in music from the perspective of meter inference and tracking. Time varying metrical structures are a part of various music cultures and genres like classical music, African music, progressive rock music etc. This thesis aims to infer and track the musical meter of such musical pieces by proposing extensions to a data driven Bayesian model which simultaneously infers the tempo, beats and downbeats of a musical piece. It is shown here that by adapting this method for time varying metrical structures, the model learns probabilistic relations for transitions between different rhythm patterns and hence, metrical changes can be detected within a musical piece. Audio files (containing percussion patterns) and their annotations (containing information about the metrical structure) are synthesized to validate the approach. Novel evaluation strategies are proposed for this case, as the present evaluation measures do not incorporate the metrical inference accuracy for musical pieces with changing metrical structures.