ManifoldMeasures

ManifoldMeasures extends Manifolds.jl to use MeasureTheory.jl to implement generic measures on manifolds as well as common specific measures, such as those that appear in directional statistics.

Goals

The implementations are designed with probabilistic programming in mind but are also generally useful. This includes the following goals:

• Constructors should be lightweight, so that arguments are not checked, and unnecessary normalization constants are not computed.
• Log-densities should be compatible with Julia's automatic differentiation (AD) frameworks. This implies avoiding problematic patterns like try..catch blocks or mutation. When necessary or significantly more efficient, we define custom ChainRules.jl-compatible AD rules.
• Log-densities and constructors should try to be friendly for symbolic computation, which implies wrapping any control flow in functions like ifelse that can be symbolically overloaded. Note that currently we don't do any symbolic overloading.
• Implement the most general forms of measures. For example, if a complex or quaternionic generalization of a measure are known or are straightforward, then the generalization is implemented.