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

Full constructor.

ARX (const ARX &A0)

Copy constructor.

ARX * _copy_ (bool changerv=false)

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

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

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 > * predictor (const RV &rv)

Constructs a predictive density (marginal density on data).

ivec structure_est (egiw Eg0)

Brute force structure estimation.

virtual void flatten (double nu0)

Flatten the posterior as if to keep nu0 data.

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.

const RV & _rv () const

access function

double _ll () const

access function

void set_evalll (bool evl0)

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 )

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 computational 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

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

Incremental Bayes rule.

Parameters:

dt

vector of input data

Reimplemented from BMEF.

References bayes().

double 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 BM.

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

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 (const RV &rv, const mat &V0, const double &nu0, const double frg0=1.0)
	Full constructor.
	ARX (const ARX &A0)
	Copy constructor.
ARX *	_copy_ (bool changerv=false)
	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
	Returns a pointer to the epdf representing posterior density on parameters. Use with care!
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 > *	predictor (const RV &rv)
	Constructs a predictive density (marginal density on data).
ivec	structure_est (egiw Eg0)
	Brute force structure estimation.
virtual void	flatten (double nu0)
	Flatten the posterior as if to keep nu0 data.
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.
const RV &	_rv () const
	access function
double	_ll () const
	access function
void	set_evalll (bool evl0)
	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` )
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 computational time.