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We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure. This result generalizes the Euclidean result of Delyon and Hu to Lie groups. We present numerical results of the guided process in the Lie group $SO(3)$. In particular, we apply importance sampling to estimate the metric on $SO(3)$ using an iterative maximum likelihood method.
We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Def
Data in non-Euclidean spaces are commonly encountered in many fields of Science and Engineering. For instance, in Robotics, attitude sensors capture orientation which is an element of a Lie group. In the recent past, several researchers have reported
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove the conve
Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which allows to g
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, infty)rightarrowmathtt{Aut}(G)$, $lambdamapstodelta_lambda$, so that $ d(delta_lambda x,del