# Non-Metropolis Samplers

These methods do not include a Metropolis-Hastings step, and, consequently, will sample from a distribution, $\mu_{\Delta t}(x)$, which is a biased approximation of $\mu(x) \propto e^{-\beta V(x)}$. This bias vanishes with Δt, and is often negligible in comparison to the statistical variance error.

## First Order Methods

These methods are in the spirit of first order in time discretizations.

BasicMD.EMMethod
EM(∇V!, β, Δt)

Set up the EM integrator for overdamped Langevin.

Fields

• ∇V! - In place gradient of the potential
• β - Inverse temperature
• Δt - Time step
BasicMD.LMMethod
LM(∇V!, β, Δt)

Set up the LM integrator for overdamped Langevin.

Fields

• ∇V! - In place gradient of the potential
• β - Inverse temperature
• Δt - Time step

## Second Order Methods

These methods are in the spirit of second order in time discretizations.

BasicMD.ABOBAMethod
ABOBA(∇V!, β, γ, M, Δt)

Set up the ABOBA integrator for inertial Langevin.

Fields

• ∇V! - In place gradient of the potential
• β - Inverse temperature
• γ - Damping Coefficient
• M - Mass (either scalar or vector)
• Δt - Time step
BasicMD.BAOABMethod
BAOAB(∇V!, β, γ, M, Δt)

Set up the BAOAB integrator for inertial Langevin.

Fields

• ∇V! - In place gradient of the potential
• β - Inverse temperature
• γ - Damping Coefficient
• M - Mass (either scalar or vector)
• Δt - Time step
BasicMD.BBKMethod
BBK(∇V!, β, γ, M, Δt)

Set up the BBK integrator for inertial Langevin.

Fields

• ∇V! - In place gradient of the potential
• β - Inverse temperature
• γ - Damping Coefficient
• M - Mass (either scalar or vector)
• Δt - Time step
BasicMD.GJFMethod
GJF(∇V!, β, γ, M, Δt)

Set up the G-JF integrator for inertial Langevin.

Fields

• ∇V! - In place gradient of the potential
• β - Inverse temperature
• γ - Damping Coefficient
• M - Mass (either scalar or vector)
• Δt - Time step