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

Class MultipointHybridMCMC

java.lang.Object

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

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

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

All Implemented Interfaces:

RandomVectorGenerator, Seedable

public class MultipointHybridMCMC
extends AbstractHybridMCMC

A multi-point Hybrid Monte Carlo is an extension of HybridMCMC, where during the proposal generation instead of considering only the last configuration after the dynamics simulation, we pick a proposal from a window of the last M configurations. Consider using ErgodicHybridMCMC if you are experiencing components that deviate little at each step.

See Also:

• • "Jun S. Liu. "Chapter 9.5.2," Monte Carlo Strategies in Scientific Computing. 2002."
  • "Jun S. Liu. "Chapter 10.4," Monte Carlo Strategies in Scientific Computing. 2002."

Field Summary

Fields inherited from class dev.nm.stat.random.rng.multivariate.mcmc.hybrid.AbstractHybridMCMC

dt

Constructor Summary

Constructors

Constructor	Description
MultipointHybridMCMC(RealScalarFunction logF, RealVectorFunction dLogF, Vector m, double dt, int L, int M, Vector w, Vector initialState, RandomLongGenerator uniform)	Constructs a new instance with the given parameters.
MultipointHybridMCMC(RealScalarFunction logF, RealVectorFunction dLogF, Vector m, double dt, int L, int M, Vector initialState, RandomLongGenerator uniform)	Constructs a new instance with equal weights to the M configurations.

Method Summary

Modifier and Type	Method	Description
protected boolean	isProposalAccepted(Vector currentState, Vector proposedState)	Decides whether the given proposed state should be accepted, or whether the system should remain in it's current state.
protected Vector	nextProposedState(Vector currentState)	Proposes a next state for the system.

Methods inherited from class dev.nm.stat.random.rng.multivariate.mcmc.hybrid.AbstractHybridMCMC

dUdx, H, k, setDeltaT

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

acceptanceRate, nextVector, seed

Methods inherited from class java.lang.Object

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

Constructor Details

MultipointHybridMCMC

public MultipointHybridMCMC(RealScalarFunction logF,
 RealVectorFunction dLogF,
 Vector m,
 double dt,
 int L,
 int M,
 Vector w,
 Vector initialState,
 RandomLongGenerator uniform)

Constructs a new instance with the given parameters.

Parameters:

logF - the log of the unnormalized target density from which we wish to sample

dLogF - the derivative of the log target density for use by the LeapFrogging algorithm. You may choose a function that differs from the actual derivative of the log target density (i.e. that of a tempered version of the target density), in order to guide the leap-frogging algorithm

m - the mass of each component in the dynamics simulation. A lower mass for a given component will result in greater change over the simulated time

dt - the amount by which we advance time at each dynamics simulation step

L - the number of dynamics simulation steps

M - the number of configurations from which we select the candidate after the forward leap-frog iterations (M < L)

w - a vector of length M, which is used to emphasize certain steps along the leapfrog trajectory, where w(1) is the weight assigned to the to configuration at step L - M and w(M) corresponds to the configuration at step L.

initialState - the initial state of the algorithm

uniform - the random long generator to be used

MultipointHybridMCMC

public MultipointHybridMCMC(RealScalarFunction logF,
 RealVectorFunction dLogF,
 Vector m,
 double dt,
 int L,
 int M,
 Vector initialState,
 RandomLongGenerator uniform)

Constructs a new instance with equal weights to the M configurations.

Parameters:

logF - the log of the unnormalized target density from which we wish to sample

dLogF - the derivative of the log target density for use by the LeapFrogging algorithm. You may choose a function that differs from the actual derivative of the log target density (i.e. that of a tempered version of the target density), in order to guide the leap-frogging algorithm

m - the mass of each component in the dynamics simulation. A lower mass for a given component will result in greater change over the simulated time

dt - the difference in time for each simulation step. A smaller value, will make the simulation more accurate, but a larger value will give better performance by requiring less simulation steps

L - the number of forward leap-frog iterations at each step

M - the number of configurations from which we select the candidate after the forward leap-frog iterations (M < L)

initialState - the initial state of the algorithm

uniform - the random long generator to be used

Method Details

nextProposedState

protected Vector nextProposedState(Vector currentState)

Description copied from class: AbstractMetropolis

Proposes a next state for the system.

Specified by:

nextProposedState in class AbstractMetropolis

Parameters:

currentState - the current state of the system

Returns:

the proposed next state

isProposalAccepted

protected boolean isProposalAccepted(Vector currentState,
 Vector proposedState)

Description copied from class: AbstractMetropolis

Decides whether the given proposed state should be accepted, or whether the system should remain in it's current state.

Specified by:

isProposalAccepted in class AbstractMetropolis

Parameters:

currentState - the current state of the system

proposedState - the proposed next state of the system

Returns:

whether the system should accept the proposed next state