Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bridge Simulation on Lie Groups and Homogeneous Spaces with Application
  to Parameter Estimation   We present three simulation schemes for simulating Brownian bridges on
complete and connected Lie groups and homogeneous spaces and use numerical
results of the guided processes in the Lie group $\SO(3)$ and on the
homogeneous spaces $\mathrm{SPD}(3) = \mathrm{GL}_+(3)/\mathrm{SO}(3)$ and
$\mathbb S^2 = \mathrm{SO}(3)/\mathrm{SO}(2)$ to evaluate our sampling scheme.
Brownian motions on Lie groups can be defined via the Laplace-Beltrami of a
left- (or right-)invariant Riemannian metric. Given i.i.d. Lie group-valued
samples on $\mathrm{SO}(3)$ drawn from a Brownian motion with unknown
Riemannian metric structure, the underlying Riemannian metric on
$\mathrm{SO}(3)$ is estimated using an iterative maximum likelihood (MLE)
method. Furthermore, the re-sampling technique is applied to yield estimates of
the heat kernel on the two-sphere considered as a homogeneous space. Comparing
this estimate to the truncated version of the closed-form expression for the
heat kernel on $\mathbb S^2$ serves as a proof of concept for the validity of
the sampling scheme on homogeneous spaces.

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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
1
The categories of this paper are: cs