com.numericalmethod.suanshu.stats.dlm
Class ObservationEquation

java.lang.Object
  com.numericalmethod.suanshu.stats.dlm.ObservationEquation

public class ObservationEquation
extends java.lang.Object

The observation equation in a controlled dynamic linear model.

y_t = F_t * x_t + v_t (Observation Equation),

Constructor Summary

ObservationEquation(Matrix F, Matrix V)
Construct a time-invariant an observation equation.

ObservationEquation(ObservationEquation that)
Copy constructor.

ObservationEquation(R1toMatrix F, R1toMatrix V)
Construct an observation equation.

Method Summary

int	dimension() Get the dimension of each observation y_t.
Matrix	F(int t) Get F(t), the coefficient matrix of x_t.
Matrix	V(int t) Get V(t), the covariance matrix of v_t.
Vector	yt_mean(int t, Vector xt) Predict for the next observation.
Matrix	yt_var(int t, Matrix var_t_tlag) Variance of the (a prior) prediction for the next observation.
Vector	yt(int t, Vector xt) Compute 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)

Construct an observation equation.

Parameters:

F - the coefficient matrix function of x_t

V - the covariance matrix function of {v_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 that)

Copy constructor.

Parameters:

that - another ObservationEquation

Method Detail

dimension

public int dimension()

Get the dimension of each observation y_t.

Returns:

the dimension of observations

F

public Matrix F(int t)

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

Parameters:

t - time

Returns:

F(t)

V

public Matrix V(int t)

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

Parameters:

t - time

Returns:

V(t)

yt_mean

public Vector yt_mean(int t,
                      Vector xt)

Predict for the next observation.

E(y_t) = F_t * x_t

Parameters:

t - time

xt - state x_t

Returns:

x_t

yt_var

public Matrix yt_var(int t,
                     Matrix var_t_tlag)

Variance of the (a prior) 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(x_{t | t - 1}), the variance of the a prior prediction

Returns:

Var(y_{t | t - 1})

yt

public Vector yt(int t,
                 Vector xt)

Compute the observation equation.

y_t = F_t * x_t + v_t

Parameters:

t - time

xt - state x_t

Returns:

x_t