bdm::ARX Class Reference

Linear Autoregressive model with Gaussian noise. More...

#include <arx.h>

List of all members.

Public Member Functions

void set_statistics (const BMEF *BM0)

Set sufficient statistics.

void from_setting (const Setting &set)

virtual string to_string ()

This method returns a basic info about the current instance.

virtual void to_setting (Setting &set) const

This method save all the instance properties into the Setting structure.

virtual void validate ()

This method TODO.

Constructors

ARX (const double frg0=1.0)

ARX (const ARX &A0)

ARX * _copy_ () const

Flatten the posterior as if to keep nu0 data.

void set_parameters (double frg0)

void set_statistics (int dimx0, const ldmat V0, double nu0=-1.0)

Mathematical operations

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

Weighted Bayes $ dt = [y_t psi_t] $ .

void bayes (const vec &dt)

Incremental Bayes rule.

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

Predictor for empty regressor.

mlnorm< ldmat > * predictor () const

conditional version of the predictor

mlstudent * predictor_student () const

ivec structure_est (egiw Eg0)

Brute force structure estimation.

Access attributes

const egiw * _e () const

const egiw & posterior () const

Connection

void set_drv (const RV &drv0)

RV & get_yrv ()

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_rv (const RV &rv)

double _ll () const

void set_evalll (bool evl0)

Protected Attributes

int dimx

size of output variable (needed in regressors)

RV _yrv

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.

Extension to conditional BM

This extension is useful e.g. in Marginalized Particle Filter (bdm::MPF). Alternatively, it can be used for automated connection to DS when the condition is observed

const RV & _rvc () const

access function

virtual void condition (const vec &val)

Substitute val for rvc.

RV rvc

Name of extension variable.

Logging of results

virtual void set_options (const string &opt)

Set boolean options from a string recognized are: "logbounds,logll".

virtual void log_add (logger &L, const string &name="")

Add all logged variables to a logger.

virtual void logit (logger &L)

ivec LIDs

IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll].

ivec LFlags

Flags for logging - same size as LIDs, each entry correspond to the same in LIDs.

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:

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

See Theory of ARX model estimation for mathematical treatment.

The easiest way how to use the class is:

#include "estim/arx.h"
using namespace bdm;
        
// estimation of AR(0) model
int main() {
        //prior 
        mat V0 = 0.00001*eye(2); V0(0,0)= 0.1; //
        ARX Ar; 
        Ar.set_statistics(1, V0); //nu is default (set to have finite moments)
                                                          // forgetting is default: 1.0
        mat Data = concat_vertical( randn(1,100), ones(1,100) );
        Ar.bayesB( Data); 
                        
        cout << "Expected value of Theta is: " << Ar.posterior().mean() <<endl;
}

Todo:: sort out constant terms - bayes should accept vec without additional 1s

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().

Referenced by bayes().

void bdm::ARX::from_setting ( const Setting & set ) [virtual]

UI for ARX estimator

The ARX is constructed from a structure with fields:

        estimator = {
                type = "ARX";
                y = {type="rv", ...}   // description of output variables
                rgr = {type="rv", ...} // description of regressor variables
                constant = true;       // boolean switch if the constant term is modelled or not

                //optional fields
                dV0 = [1e-3, 1e-5, 1e-5, 1e-5]; 
                                                           // default: 1e-3 for y, 1e-5 for rgr
                nu0 = 6;               // default: rgrlen + 2
                frg = 1.0;             // forgetting, default frg=1.0
        };

The estimator will assign names of the posterior in the form ["theta_i" and "r_i"]

Reimplemented from bdm::root.

References bdm::RV::_dsize(), bdm::BMEF::frg, and bdm::UI::get().

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(), est, and bdm::egiw::lognc().

Member Data Documentation

RV bdm::ARX::_yrv [protected]

description of modelled data $ y_t $ in the likelihood function Do NOT access directly, only via get_yrv().

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

arx.h
bdm/estim/arx.cpp


Public Member Functions
void	set_statistics (const BMEF *BM0)
	Set sufficient statistics.
void	from_setting (const Setting &set)
virtual string	to_string ()
	This method returns a basic info about the current instance.
virtual void	to_setting (Setting &set) const
	This method save all the instance properties into the Setting structure.
virtual void	validate ()
	This method TODO.
Constructors
	ARX (const double frg0=1.0)
	ARX (const ARX &A0)
ARX *	_copy_ () const
	Flatten the posterior as if to keep nu0 data.
void	set_parameters (double frg0)
void	set_statistics (int dimx0, const ldmat V0, double nu0=-1.0)
Mathematical operations
void	bayes (const vec &dt, const double w)
	Weighted Bayes .
void	bayes (const vec &dt)
	Incremental Bayes rule.
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
	Predictor for empty regressor.
mlnorm< ldmat > *	predictor () const
	conditional version of the predictor
mlstudent *	predictor_student () const
ivec	structure_est (egiw Eg0)
	Brute force structure estimation.
Access attributes
const egiw *	_e () const
const egiw &	posterior () const
Connection
void	set_drv (const RV &drv0)
RV &	get_yrv ()
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_rv (const RV &rv)
double	_ll () const
void	set_evalll (bool evl0)
Protected Attributes
int	dimx
	size of output variable (needed in regressors)
RV	_yrv
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.
Extension to conditional BM
This extension is useful e.g. in Marginalized Particle Filter (bdm::MPF). Alternatively, it can be used for automated connection to DS when the condition is observed
const RV &	_rvc () const
	access function
virtual void	condition (const vec &val)
	Substitute `val` for `rvc`.
RV	rvc
	Name of extension variable.
Logging of results
virtual void	set_options (const string &opt)
	Set boolean options from a string recognized are: "logbounds,logll".
virtual void	log_add (logger &L, const string &name="")
	Add all logged variables to a logger.
virtual void	logit (logger &L)
ivec	LIDs
	IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll].
ivec	LFlags
	Flags for logging - same size as LIDs, each entry correspond to the same in LIDs.