A family of toroidal diffusions with exact likelihood inference
提出一类用于连续时间多元角数据的扩散过程，具有显式转移概率密度，支持精确似然推断，可应用于蚂蚁运动同质性检验和蛋白质骨架桥接模拟。
Abstract We provide a class of diffusion processes for continuous time-varying multivariate angular data with explicit transition probability densities, enabling exact likelihood inference. The presented diffusions are time reversible and can be constructed for any prespecified stationary distribution on the torus, including highly multimodal mixtures. We give results on asymptotic likelihood theory, allowing one-sample inference and tests of linear hypotheses for $ k $ groups of diffusions, including homogeneity. We show that exact and direct diffusion bridge simulation is possible too. A class of circular jump processes with similar properties is also proposed. Several numerical experiments illustrate the methodology for the circular and two-dimensional torus cases. The new family of diffusions is applied (i) to test several homogeneity hypotheses on the movement of ants and (ii) to simulate bridges between the three-dimensional backbones of two related proteins.