Package dev.nm.stat.random.rng.multivariate.mcmc.hybrid

Class AbstractHybridMCMC

java.lang.Object

dev.nm.stat.random.rng.multivariate.mcmc.metropolis.AbstractMetropolis

dev.nm.stat.random.rng.multivariate.mcmc.hybrid.AbstractHybridMCMC

All Implemented Interfaces:

RandomVectorGenerator, Seedable

Direct Known Subclasses:

HybridMCMC, MultipointHybridMCMC

public abstract class AbstractHybridMCMC
extends AbstractMetropolis

Hybrid Monte Carlo, or Hamiltonian Monte Carlo, is a method that combines the traditional Metropolis algorithm, with molecular dynamics simulation. The idea is to make use of the equations from classical mechanics, to guide our choice of proposed state. At each step we generate a random momentum vector, where each component is drawn from a Gaussian distribution. Considering the target density as the potential energy field of the system and the current state as the initial position of the molecules, we perform a molecular dynamics simulation (using the LeapFrogging algorithm) for the given time period. The final position of the molecules is taken as the next proposed state. The acceptance-rejection decision is then done like as in the classical Metropolis algorithm.

Field Summary

Fields

Modifier and Type	Field	Description
protected double	dt

Constructor Summary

Constructors

Constructor	Description
AbstractHybridMCMC(Vector initialState, RandomNumberGenerator rng)	Constructs a new instance with the given parameters.

Method Summary

Modifier and Type	Method	Description
static RealVectorFunction	dUdx(RealVectorFunction dLogF)	Gets the derivative of the potential function, given the derivative of the log density.
static double	H(LeapFrogging.DynamicsState state, RealScalarFunction logF, Vector m)	Evaluates a system's total energy at a given state.
static double	k(Vector p, Vector m)	Evaluates the standard kinetic energy, k = p^2 / 2m.
final void	setDeltaT(double dt)	Sets the value of dt that will be used in the subsequent iterations.

Methods inherited from class dev.nm.stat.random.rng.multivariate.mcmc.metropolis.AbstractMetropolis

acceptanceRate, isProposalAccepted, nextProposedState, nextVector, seed

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

dt

protected double dt

Constructor Details

AbstractHybridMCMC

public AbstractHybridMCMC(Vector initialState,
 RandomNumberGenerator rng)

Constructs a new instance with the given parameters.

Parameters:

initialState - the initial state of the algorithm

rng - a random number generator

Method Details

setDeltaT

public final void setDeltaT(double dt)

Sets the value of dt that will be used in the subsequent iterations. This is useful for varying the time step size between iterations.

Parameters:

dt - the value of dt

dUdx

public static RealVectorFunction dUdx(RealVectorFunction dLogF)

Gets the derivative of the potential function, given the derivative of the log density.

Parameters:

dLogF - the derivative of the log density, density logF = -U(x)

Returns:

the derivative of the potential function

H

public static double H(LeapFrogging.DynamicsState state,
 RealScalarFunction logF,
 Vector m)

Evaluates a system's total energy at a given state.

Parameters:

state - the state of the system

logF - the log-density function, -U(x)

m - the mass of the components

Returns:

the total energy, H(x, p)

k

public static double k(Vector p,
 Vector m)

Evaluates the standard kinetic energy, k = p^2 / 2m.

Parameters:

p -

m -

Returns:

k