com.numericalmethod.suanshu.stats.dlm.multivariate

Class ObservationEquation

java.lang.Object

com.numericalmethod.suanshu.stats.dlm.multivariate.ObservationEquation

All Implemented Interfaces:

java.io.Serializable

public class ObservationEquation
extends java.lang.Object
implements java.io.Serializable

This is the observation equation in a controlled dynamic linear model.

y_t = F_t * x_t + v_t

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ObservationEquation(Matrix F, Matrix V) Construct a time-invariant an observation equation.
ObservationEquation(Matrix F, Matrix V, NormalRvg rmvnorm) Construct a time-invariant an observation equation.
ObservationEquation(ObservationEquation obs) Construct a multivariate observation equation from a univariate observation equation.
ObservationEquation(ObservationEquation that) Copy constructor.
ObservationEquation(R1toMatrix F, R1toMatrix V) Construct an observation equation.
ObservationEquation(R1toMatrix F, R1toMatrix V, NormalRvg rmvnorm) Construct an observation equation.

Method Summary

Modifier and Type	Method and Description
int	dimension() Get the dimension of observation yt.
ImmutableMatrix	F(int t) Get F(t), the coefficient matrix of xt.
ImmutableMatrix	V(int t) Get V(t), the covariance matrix of vt.
ImmutableVector	yt_mean(int t, Vector xt) Predict the next observation.
ImmutableMatrix	yt_var(int t, Matrix var_t_tlag) Get the covariance of the apriori prediction for the next observation.
ImmutableVector	yt(int t, Vector xt) Evaluate the observation equation.

Methods inherited from class java.lang.Object

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

Constructor Detail

ObservationEquation

public ObservationEquation(R1toMatrix F,
                           R1toMatrix V,
                           NormalRvg rmvnorm)

Construct an observation equation.

Parameters:

F - the coefficient matrix function of x_t, a function of time

V - the covariance matrix function of v_t, a function of time

rmvnorm - a d-dimensional standard multivariate Gaussian random vector generator (for seeding); d = the dimension of V or y_t

ObservationEquation

public ObservationEquation(R1toMatrix F,
                           R1toMatrix V)

Construct an observation equation.

Parameters:

F - the coefficient matrix function of x_t, a function of time

V - the covariance matrix function of v_t, a function of time

ObservationEquation

public ObservationEquation(Matrix F,
                           Matrix V,
                           NormalRvg rmvnorm)

Construct a time-invariant an observation equation.

Parameters:

F - the coefficient matrix of x_t

V - the covariance matrix of v_t

rmvnorm - a d-dimensional standard multivariate Gaussian random vector generator (for seeding); d = the dimension of V or y_t

ObservationEquation

public ObservationEquation(Matrix F,
                           Matrix V)

Construct a time-invariant an observation equation.

Parameters:

F - the coefficient matrix of x_t

V - the covariance matrix of v_t

ObservationEquation

public ObservationEquation(ObservationEquation obs)

Construct a multivariate observation equation from a univariate observation equation.

Parameters:

obs - a univariate observation equation

ObservationEquation

public ObservationEquation(ObservationEquation that)

Copy constructor.

Parameters:

that - a ObservationEquation

Method Detail

dimension

public int dimension()

Get the dimension of observation y_t.

Returns:

the dimension of observations

F

public ImmutableMatrix F(int t)

Get F(t), the coefficient matrix of x_t.

Parameters:

t - time

Returns:

F(t)

V

public ImmutableMatrix V(int t)

Get V(t), the covariance matrix of v_t.

Parameters:

t - time

Returns:

V(t)

yt_mean

public ImmutableVector yt_mean(int t,
                               Vector xt)

Predict the next observation.

E(y_t) = F_t * x_t

Parameters:

t - time

xt - state x_t

Returns:

the mean observation

yt_var

public ImmutableMatrix yt_var(int t,
                              Matrix var_t_tlag)

Get the covariance of the apriori prediction for the next observation.

Var(y_{t | t - 1}) = F_t * Var(x_{t | t - 1}) * F_t' + V_t

Parameters:

t - time

var_t_tlag - Var(y_{t | t - 1}), the variance of the apriori prediction

Returns:

Var(y_{t | t - 1})

yt

public ImmutableVector yt(int t,
                          Vector xt)

Evaluate the observation equation.

y_t = F_t * x_t + v_t

Parameters:

t - time

xt - state x_t

Returns:

the mean observation