We present a scheme for simulating conditioned semimartingales taking values in Riemannian manifolds. Extending the guided bridge proposal approach used for simulating Euclidean bridges, the scheme replaces the drift of the conditioned process with an approximation in terms of a scaled radial vector field. This handles the fact that transition densities are generally intractable on geometric spaces. We prove the validity of the scheme by a change of measure argument, and we show how the resulting guided processes can be used in importance sampling and for approximating the density of the unconditioned process. The bridge sampling is experimentally illustrated on two- and three-dimensional manifolds. Here, we compare density estimates using the sampling scheme to approximations using heat kernel expansions, and we use the scheme to estimate the diffusion mean of sampled data.

翻译：我们提出了一个模拟在里曼尼方块中测值的半成像半成像方案。 推广用于模拟欧几里得桥桥桥桥的引导桥建议方法, 以一个缩放的射线矢量场的近似值来取代测距过程的漂移。 这处理了在几何空间中过渡密度通常难以测到的事实。 我们通过改变测量参数来证明这个方案的有效性, 我们展示了由此产生的制导过程如何用于重要取样和接近无修整过程的密度。 桥桥取样是实验性地用二维和三维的方块来展示的。 在这里, 我们用取样方法比较密度估计密度估计使用热内核膨胀的近似值, 我们用这个方法来估计抽样数据的传播值。