I'm learning about Hamiltonian Monte Carlo and one of the stated benefits is that it can move around a parameter space more efficiently and that it can (from Bayesian Data Analysis, 3rd ed.)

turn corners in parameter space to preserve the total 'energy' of the trajectory.

What does BDA mean by a "corner" in the parameter space and why wouldn't a Gibbs or Metropolis-Hastings sampler be able to "turn the corner?"


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