Despite the importance of single particle motion in biological systems, systematic inference approaches to analyze particle trajectories and evaluate competing motion models are lacking. An automated approach for robust evaluation of motion models that does not require manual intervention is highly desirable to enable analysis of datasets from high-throughput imaging technologies that contain hundreds or thousands of trajectories of biological particles, such as membrane receptors, vesicles, chromosomes or kinetochores, mRNA particles, or whole cells in developing embryos. Bayesian inference is a general theoretical framework for performing such model comparisons that has proven successful in handling noise and experimental limitations in other biological applications. The inherent Bayesian penalty on model complexity, which avoids overfitting, is particularly important for particle trajectory analysis given the highly stochastic nature of particle diffusion. This thesis presents two complementary approaches for analyzing particle motion using Bayesian inference. The first method, MSD-Bayes, discriminates a wide range of motion models— including diffusion, directed motion, anomalous and confined diffusion—based on meansquare displacement analysis of a set of particle trajectories, while the second method, HMM-Bayes, identifies dynamic switching between diffusive and directed motion along individual trajectories using hidden Markov models. These approaches are validated on biological particle trajectory datasets from a wide range of experimental systems, demonstrating their broad applicability to research in cell biology.