dev.nm.stat.dlm.multivariate

Class MultivariateObservationEquation

java.lang.Object

dev.nm.stat.dlm.multivariate.MultivariateObservationEquation

public class MultivariateObservationEquation
extends Object

This is the observation equation in a controlled dynamic linear model. \[ y_{t} = F_{t} \cdot x_{t} + v_{t} \]

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
int	dimension() Gets the dimension of observation \(y_{t}\).
ImmutableMatrix	F(int t) Gets F(t), the coefficient matrix of \(x_{t}\).
ImmutableMatrix	V(int t) Gets V(t), the covariance matrix of \(v_{t}\).
ImmutableVector	yt_mean(int t, Vector xt) Predicts the next observation. \[ E(y_t) = F_t \cdot x_t \]
ImmutableMatrix	yt_var(int t, Matrix var_t_tlag) Gets the covariance of the apriori prediction for the next observation. \[ \operatorname{Var}(y_\{t | t - 1\}) = F_t \cdot \operatorname{Var}(x_\{t | t - 1\}) \cdot F_t' + V_t \]
ImmutableVector	yt(int t, Vector xt) Evaluates the observation equation. \[ y_t = F_t \cdot x_t + v_t \]

Methods inherited from class java.lang.Object

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

Constructor Detail

MultivariateObservationEquation

public MultivariateObservationEquation(R1toMatrix F,
                                       R1toMatrix V,
                                       NormalRVG rmvnorm)

Constructs 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 \(y_{t}\)

MultivariateObservationEquation

public MultivariateObservationEquation(R1toMatrix F,
                                       R1toMatrix V)

Constructs 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

MultivariateObservationEquation

public MultivariateObservationEquation(Matrix F,
                                       Matrix V,
                                       NormalRVG rmvnorm)

Constructs 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 \(y_{t}\)

MultivariateObservationEquation

public MultivariateObservationEquation(Matrix F,
                                       Matrix V)

Constructs a time-invariant an observation equation.

Parameters:

F - the coefficient matrix of \(x_{t}\)

V - the covariance matrix of \(v_{t}\)

MultivariateObservationEquation

public MultivariateObservationEquation(ObservationEquation obs)

Constructs a multivariate observation equation from a univariate observation equation.

Parameters:

obs - a univariate observation equation

MultivariateObservationEquation

public MultivariateObservationEquation(MultivariateObservationEquation that)

Copy constructor.

Parameters:

that - a ObservationEquation

Method Detail

dimension

public int dimension()

Gets the dimension of observation \(y_{t}\).

Returns:

the dimension of observations

F

public ImmutableMatrix F(int t)

Gets F(t), the coefficient matrix of \(x_{t}\).

Parameters:

t - time

Returns:

F(t)

V

public ImmutableMatrix V(int t)

Gets V(t), the covariance matrix of \(v_{t}\).

Parameters:

t - time

Returns:

V(t)

yt_mean

public ImmutableVector yt_mean(int t,
                               Vector xt)

Predicts the next observation. \[ E(y_t) = F_t \cdot x_t \]

Parameters:

t - time

xt - state \(x_{t}\)

Returns:

the mean observation

yt_var

public ImmutableMatrix yt_var(int t,
                              Matrix var_t_tlag)

Gets the covariance of the apriori prediction for the next observation. \[ \operatorname{Var}(y_\{t | t - 1\}) = F_t \cdot \operatorname{Var}(x_\{t | t - 1\}) \cdot F_t' + V_t \]

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)

Evaluates the observation equation. \[ y_t = F_t \cdot x_t + v_t \]

Parameters:

t - time

xt - state \(x_{t}\)

Returns:

the mean observation