com.numericalmethod.suanshu.stats.markovchain

Class SimpleMC

java.lang.Object

com.numericalmethod.suanshu.stats.markovchain.SimpleMC

All Implemented Interfaces:

RandomNumberGenerator, java.io.Serializable

Direct Known Subclasses:

HiddenMarkovModel

public class SimpleMC
extends java.lang.Object
implements RandomNumberGenerator

This is a time-homogeneous Markov chain with a finite state space. It is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property.

See Also:

Wikipedia: Markov chain, Serialized Form

Constructor Summary

Constructors

Constructor and Description
SimpleMC(Matrix A) Construct a time-homogeneous Markov chain with a finite state space using stationary state probabilities.
SimpleMC(Vector PI, Matrix A) Construct a time-homogeneous Markov chain with a finite state space.

Method Summary

Modifier and Type	Method and Description
ImmutableMatrix	A() Get the state transition probabilities.
static int	bin(MultinomialRvg rvg) Pick the first non-empty bin.
static Vector	getStationaryProbabilities(Matrix A) Get the stationary state probabilities of a Markov chain that is irreducible, aperiodic and strongly connected (positive recurrent).
double	nextDouble() Get the next simulated state.
int	nextState() Get the next simulated state.
int	nStates() Get the number of states.
ImmutableVector	PI() Get the initial state probabilities.
void	seed(long... seeds) Seed the random number generator to produce repeatable sequences.

Methods inherited from class java.lang.Object

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

Constructor Detail

SimpleMC

public SimpleMC(Vector PI,
                Matrix A)

Construct a time-homogeneous Markov chain with a finite state space.

Parameters:

PI - the initial state probabilities

A - the state transition probabilities

SimpleMC

public SimpleMC(Matrix A)

Construct a time-homogeneous Markov chain with a finite state space using stationary state probabilities.

Parameters:

A - the state transition probabilities

Method Detail

seed

public void seed(long... seeds)

Description copied from interface: RandomNumberGenerator

Seed the random number generator to produce repeatable sequences.

Specified by:

seed in interface RandomNumberGenerator

Parameters:

seeds - the seeds

nextDouble

public double nextDouble()

Get the next simulated state.

Specified by:

nextDouble in interface RandomNumberGenerator

Returns:

next state

nextState

public int nextState()

Get the next simulated state.

Returns:

next state

PI

public ImmutableVector PI()

Get the initial state probabilities.

Returns:

the initial state probabilities

A

public ImmutableMatrix A()

Get the state transition probabilities.

Returns:

the state transition probabilities

nStates

public int nStates()

Get the number of states.

Returns:

the number of states

getStationaryProbabilities

public static Vector getStationaryProbabilities(Matrix A)

Get the stationary state probabilities of a Markov chain that is irreducible, aperiodic and strongly connected (positive recurrent). A stationary distribution vector x (if exists) satisfies \[ x' \times A = x' \] where x' denotes the transpose of x, and the sum of all elements of x is 1.

Parameters:

A - the transition matrix

Returns:

the stationary state probabilities

bin

public static int bin(MultinomialRvg rvg)

Pick the first non-empty bin.

Parameters:

rvg - a MultinomialRvg

Returns:

the first non-empty bin