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

Class AbstractMetropolis

java.lang.Object

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

All Implemented Interfaces:

RandomVectorGenerator, Seedable

Direct Known Subclasses:

AbstractHybridMCMC, Metropolis, MetropolisHastings, RobustAdaptiveMetropolis

public abstract class AbstractMetropolis
extends Object
implements RandomVectorGenerator

The Metropolis algorithm is a Markov Chain Monte Carlo algorithm, which requires only a function f proportional to the PDF from which we wish to sample. As such it is useful for situations where normalizing the PDF is difficult. At each step, a proposed state is drawn as a perturbation from the current step, from a proposal distribution. The probability of the proposed state x* being accepted is then given by \(min\{1, f(x^*)/f(x_t-1)\}\). To obtain good results, the proposal function should be such that the acceptance rate is around 50% for one-dimensional and 23% for n-dimensional cases. To use a symmetric proposal function, consider using Metropolis. For cases where it may be difficult to choose an appropriate proposal distribution, consider using RobustAdaptiveMetropolis. To use an asymmetric proposal distribution, consider using MetropolisHastings.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double	acceptanceRate() Gets the acceptance rate, i.e. the proportion of proposed states that have been accepted by iterators returned by this instance.
protected abstract 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 abstract Vector	nextProposedState(Vector currentState) Proposes a next state for the system.
double[]	nextVector() Gets the next random vector.
void	seed(long... seeds) Seed the random number/vector/scenario generator to produce repeatable experiments.

Methods inherited from class java.lang.Object

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

Constructor Detail

AbstractMetropolis

public AbstractMetropolis(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 Detail

seed

public void seed(long... seeds)

Description copied from interface: Seedable

Seed the random number/vector/scenario generator to produce repeatable experiments.

Specified by:

seed in interface Seedable

Parameters:

seeds - the seeds

nextVector

public double[] nextVector()

Description copied from interface: RandomVectorGenerator

Gets the next random vector.

Specified by:

nextVector in interface RandomVectorGenerator

Returns:

the next random vector

nextProposedState

protected abstract Vector nextProposedState(Vector currentState)

Proposes a next state for the system.

Parameters:

currentState - the current state of the system

Returns:

the proposed next state

isProposalAccepted

protected abstract 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.

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

acceptanceRate

public final double acceptanceRate()

Gets the acceptance rate, i.e. the proportion of proposed states that have been accepted by iterators returned by this instance. This is useful for choosing an appropriate standard deviation of the proposal function. It has been shown theoretically that the ideal acceptance rate for a one dimensional Gaussian distribution is approximately 50%, decreasing to approximately 23% for an N-dimensional Gaussian target distribution.

Returns:

the acceptance rate