I am sort of new to HMC and believe that I understand the fundamentals after reading “A Conceptual Introduction to Hamiltonian Monte Carlo”. But I am struggling with E-BFMI and how it used E, the energy level set, in its definition. I have searched around, but can not find a definition of E, but only that it is the energy level set.

Can anyone elaborate on this or point me the right direction?

Thanks in advance.

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Thank you, I did find that article too.
I keep wanting to find an expression like E(q,p)=?, but I guess it is in there just not in the format I understand.

Energy is the Hamiltonian.

E\left(q,p\right) = H\left(q,p\right) = \frac{1}{2}p^TM^{-1}p + V\left(q\right)

where M is the mass matrix and V\left(q\right) is the potential energy, i.e. negative log probability density at q. The Conceptual Introduction paper has more about energy level sets in section 4.


Thank you for clarifying!