ARX Class Reference

Linear Autoregressive model with Gaussian noise. More...

#include <arx.h>

Inheritance diagram for ARX:

Collaboration diagram for ARX:

List of all members.

Public Member Functions

ARX (RV &rv, mat &V0, double &nu0, double frg0=1.0)

Full constructor.

void set_parameters (mat &V0, double &nu0)

Set sufficient statistics.

void get_parameters (mat &V0, double &nu0)

Returns sufficient statistics.

void bayes (const vec &dt)

Here $dt = [y_t psi_t] $ .

epdf & _epdf ()

Returns a pointer to the epdf representing posterior density on parameters. Use with care!

ivec structure_est (egiw Eg0)

Brute force structure estimation.

double _tll ()

access function

void bayes (mat Dt)

Batch Bayes rule (columns of Dt are observations).

const RV & _rv () const

access function

double _ll () const

access function

Protected Attributes

egiw est

Posterior estimate of $\theta,r$ in the form of Normal-inverse Wishart density.

ldmat & V

cached value of est.V

double & nu

cached value of est.nu

double frg

forgetting factor

double last_lognc

cached value of lognc() in the previous step (used in evaluation of ll )

double tll

total likelihood

RV rv

Random variable of the posterior.

double ll

Logarithm of marginalized data likelihood.

bool evalll

If true, the filter will compute likelihood of the data record and store it in ll . Set to false if you want to save time.

Detailed Description

Linear Autoregressive model with Gaussian noise.

Regression of the following kind:

$y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t$

where unknown parameters rv are $[\theta r]$ , regression vector $\psi=\psi(y_{1:t},u_{1:t})$ is a known function of past outputs and exogeneous variables $u_t$ . Distrubances $e_t$ are supposed to be normally distributed:

$e_t \sim \mathcal{N}(0,1).$

Extension for time-variant parameters $\theta_t,r_t$ may be achived using exponential forgetting (Kulhavy and Zarrop, 1993). In such a case, the forgetting factor frg $\in <0,1>$ should be given in the constructor. Time-invariant parameters are estimated for frg = 1.

Member Function Documentation

ivec ARX::structure_est ( egiw Eg0 )

Brute force structure estimation.

Returns:: indeces of accepted regressors.

References RV::count(), est, egiw::lognc(), and BM::rv.

The documentation for this class was generated from the following files:

work/git/mixpp/bdm/estim/arx.h
work/git/mixpp/bdm/estim/arx.cpp


Public Member Functions
	ARX (RV &rv, mat &V0, double &nu0, double frg0=1.0)
	Full constructor.
void	set_parameters (mat &V0, double &nu0)
	Set sufficient statistics.
void	get_parameters (mat &V0, double &nu0)
	Returns sufficient statistics.
void	bayes (const vec &dt)
	Here .
epdf &	_epdf ()
	Returns a pointer to the epdf representing posterior density on parameters. Use with care!
ivec	structure_est (egiw Eg0)
	Brute force structure estimation.
double	_tll ()
	access function
void	bayes (mat Dt)
	Batch Bayes rule (columns of Dt are observations).
const RV &	_rv () const
	access function
double	_ll () const
	access function
Protected Attributes
egiw	est
	Posterior estimate of $\theta,r$ in the form of Normal-inverse Wishart density.
ldmat &	V
	cached value of est.V
double &	nu
	cached value of est.nu
double	frg
	forgetting factor
double	last_lognc
	cached value of lognc() in the previous step (used in evaluation of `ll` )
double	tll
	total likelihood
RV	rv
	Random variable of the posterior.
double	ll
	Logarithm of marginalized data likelihood.
bool	evalll
	If true, the filter will compute likelihood of the data record and store it in `ll` . Set to false if you want to save time.