ARX Class Reference

Linear Autoregressive model with Gaussian noise. More...

#include <arx.h>

Inheritance diagram for ARX:

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Collaboration diagram for ARX:

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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.
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 )
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:

Generated on Sat Aug 16 17:22:06 2008 for mixpp by  doxygen 1.5.6