Hi,

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.

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.

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Thank you for clarifying!