blackjax.mcmc.integrators#
Symplectic, time-reversible, integrators for Hamiltonian trajectories.
Module Contents#
Functions#
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The velocity Verlet (or Verlet-Störmer) integrator. |
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Two-stage palindromic symplectic integrator derived in [BCSS14]. |
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Three stages palindromic symplectic integrator derived in [McL95] |
- velocity_verlet(logdensity_fn: Callable, kinetic_energy_fn: blackjax.mcmc.metrics.EuclideanKineticEnergy) EuclideanIntegrator[source]#
The velocity Verlet (or Verlet-Störmer) integrator.
The velocity Verlet is a two-stage palindromic integrator [BRSS18] of the form (a1, b1, a2, b1, a1) with a1 = 0. It is numerically stable for values of the step size that range between 0 and 2 (when the mass matrix is the identity).
While the position (a1 = 0.5) and velocity Verlet are the most commonly used in samplers, it is known in the numerical computation literature that the value \(a1 pprox 0.1932\) leads to a lower integration error [McL95, Sch10]. The authors of [BRSS18] show that the value \(a1 pprox 0.21132\) leads to an even higher step acceptance rate, up to 3 times higher than with the standard position verlet (p.22, Fig.4).
By choosing the velocity verlet we avoid two computations of the gradient of the kinetic energy. We are trading accuracy in exchange, and it is not clear whether this is the right tradeoff.
- mclachlan(logdensity_fn: Callable, kinetic_energy_fn: Callable) EuclideanIntegrator[source]#
Two-stage palindromic symplectic integrator derived in [BCSS14].
The integrator is of the form (b1, a1, b2, a1, b1). The choice of the parameters determine both the bound on the integration error and the stability of the method with respect to the value of step_size. The values used here are the ones derived in [McL95]; note that [BCSS14] is more focused on stability and derives different values.
- yoshida(logdensity_fn: Callable, kinetic_energy_fn: Callable) EuclideanIntegrator[source]#
Three stages palindromic symplectic integrator derived in [McL95]
The integrator is of the form (b1, a1, b2, a2, b2, a1, b1). The choice of the parameters determine both the bound on the integration error and the stability of the method with respect to the value of step_size. The values used here are the ones derived in [McL95] which guarantees a stability interval length approximately equal to 4.67.