bdm::ARX Class Reference

#include <arx.h>

Inheritance diagram for bdm::ARX:

Inheritance graph
[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
mlstudentpredictor_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.
ldmatV
 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:

Generated on Wed Feb 11 23:34:01 2009 for mixpp by  doxygen 1.5.6