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Figure 1
(a) Illustration of the evolution of Hamiltonian dynamics to move an object from [{\bf{x}}_{k}] to [{\bf{x}}_{k+1}] in the parameter space. Flipping the direction of the momentum [{\bf{p}}_{k+1}] at [{\bf{x}}_{k+1}] reverses the energy and brings the object back to [{\bf{x}}_{k}]. (b) An HMCMC drawing sequence. Contour lines are the joint probability distribution [P({\bf{x}},{\bf{p}})]. The topmost and leftmost curves represent the marginal distributions of the parameter and the momentum, respectively. With an initial parameter [{\bf{x}}_{1}], a random momentum is generated to create a state [({\bf{x}}_{1},{\bf{p}}_{1})] of Hamiltonian [H({\bf{x}}_{1},{\bf{p}}_{1})] (blue arrow). Parameter [{\bf{x}}_{2}] is generated as the result of the evolution from state [({\bf{x}}_{1},{\bf{p}}_{1})] to state [({\bf{x}}_{2},{\bf{p}}_{2})] through the trajectory 1 → 1′ (red arrow). This process repeats to generate a sequence of parameters.

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Volume 29| Part 3| May 2022| Pages 721-731
https://doi.org/10.1107/S1600577522003034
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