bdm::ARX Class Reference

#include <arx.h>

Inheritance diagram for bdm::ARX:

[legend]

List of all members.

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.

Public Member Functions

ARX (const double frg0=1.0)

Full constructor.

ARX (const ARX &A0)

Copy constructor.

ARX * _copy_ ()

Auxiliary function.

void set_parameters (const ldmat &V0, const double &nu0)

Set sufficient statistics.

void set_statistics (const BMEF *BM0)

get statistics from another model

void get_parameters (mat &V0, double &nu0)

Returns sufficient statistics.

void bayes (const vec &dt, const double w)

Here $dt = [y_t psi_t] $ .

void bayes (const vec &dt)

Incremental Bayes rule.

const epdf & _epdf () const

double logpred (const vec &dt) const

void flatten (const BMEF *B)

Flatten the posterior according to the given BMEF (of the same type!).

enorm< ldmat > * epredictor (const vec &rgr) const

Conditioned version of the predictor.

enorm< ldmat > * epredictor () const

Constructs a predictive density $f(d_{t+1} |d_{t}, \ldots d_{0})$ .

mlnorm< ldmat > * predictor () const

conditional version of the predictor

mlstudent * predictor_student () const

ivec structure_est (egiw Eg0)

Brute force structure estimation.

const egiw * _e () const

BMEF * _copy_ (bool changerv=false)

Flatten the posterior as if to keep nu0 data.

Mathematical operations

virtual void bayesB (const mat &Dt)

Batch Bayes rule (columns of Dt are observations).

vec logpred_m (const mat &dt) const

Matrix version of logpred.

Access to attributes

const RV & _drv () const

void set_drv (const RV &rv)

double _ll () const

void set_evalll (bool evl0)

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 )

RV drv

Random variable of the data (optional).

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 computational time.

Member Function Documentation

void bdm::ARX::bayes ( const vec & dt ) [inline, virtual]

Incremental Bayes rule.

Parameters:

dt

vector of input data

Reimplemented from bdm::BMEF.

References bayes().

double bdm::ARX::logpred ( const vec & dt ) const [virtual]

Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.

Reimplemented from bdm::BM.

References bdm::egiw::_nu(), bdm::egiw::_V(), est, bdm::BM::evalll, bdm::BMEF::frg, bdm::BMEF::last_lognc, bdm::egiw::lognc(), nu, ldmat::opupdt(), bdm::egiw::pow(), and V.

mlnorm< ldmat > * bdm::ARX::predictor ( ) const [virtual]

conditional version of the predictor

<----------- TODO

Reimplemented from bdm::BM.

References bdm::epdf::dimension(), est, bdm::egiw::mean_mat(), ldmat::rows(), bdm::mlnorm< sq_T >::set_parameters(), and V.

ivec bdm::ARX::structure_est ( egiw Eg0 )

Brute force structure estimation.

Returns:: indeces of accepted regressors.

References bdm::epdf::dimension(), bdm::egiw_bestbelow(), est, and bdm::egiw::lognc().

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

arx.h
bdm/estim/arx.cpp


Public Member Functions
	ARX (const double frg0=1.0)
	Full constructor.
	ARX (const ARX &A0)
	Copy constructor.
ARX *	_copy_ ()
	Auxiliary function.
void	set_parameters (const ldmat &V0, const double &nu0)
	Set sufficient statistics.
void	set_statistics (const BMEF *BM0)
	get statistics from another model
void	get_parameters (mat &V0, double &nu0)
	Returns sufficient statistics.
void	bayes (const vec &dt, const double w)
	Here .
void	bayes (const vec &dt)
	Incremental Bayes rule.
const epdf &	_epdf () const
double	logpred (const vec &dt) const
void	flatten (const BMEF *B)
	Flatten the posterior according to the given BMEF (of the same type!).
enorm< ldmat > *	epredictor (const vec &rgr) const
	Conditioned version of the predictor.
enorm< ldmat > *	epredictor () const
	Constructs a predictive density $f(d_{t+1} \|d_{t}, \ldots d_{0})$ .
mlnorm< ldmat > *	predictor () const
	conditional version of the predictor
mlstudent *	predictor_student () const
ivec	structure_est (egiw Eg0)
	Brute force structure estimation.
const egiw *	_e () const
BMEF *	_copy_ (bool changerv=false)
	Flatten the posterior as if to keep nu0 data.
Mathematical operations
virtual void	bayesB (const mat &Dt)
	Batch Bayes rule (columns of Dt are observations).
vec	logpred_m (const mat &dt) const
	Matrix version of logpred.
Access to attributes
const RV &	_drv () const
void	set_drv (const RV &rv)
double	_ll () const
void	set_evalll (bool evl0)
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` )
RV	drv
	Random variable of the data (optional).
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 computational time.