root/library/bdm/estim/arx.h @ 577

/*!
  \file
  \brief Bayesian Filtering for generalized autoregressive (ARX) model
  \author Vaclav Smidl.

  -----------------------------------
  BDM++ - C++ library for Bayesian Decision Making under Uncertainty

  Using IT++ for numerical operations
  -----------------------------------
*/

#ifndef AR_H
#define AR_H

#include "../math/functions.h"
#include "../stat/exp_family.h"
#include "../base/user_info.h"

namespace bdm {

/*!
* \brief Linear Autoregressive model with Gaussian noise

Regression of the following kind:
\f[
y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t
\f]
where unknown parameters \c rv are \f$[\theta r]\f$, regression vector \f$\psi=\psi(y_{1:t},u_{1:t})\f$ is a known function of past outputs and exogeneous variables \f$u_t\f$. Distrubances \f$e_t\f$ are supposed to be normally distributed:
\f[
e_t \sim \mathcal{N}(0,1).
\f]

See \ref tut_arx for mathematical treatment.

The easiest way how to use the class is:
\include arx_simple.cpp

        \todo sort out constant terms - bayes should accept vec without additional 1s
*/
class ARX: public BMEF {
protected:
        //!size of output variable (needed in regressors)
        int dimx;
        //!description of modelled data \f$ y_t \f$ in the likelihood function
        //! Do NOT access directly, only via \c get_yrv().
        RV _yrv;
        //! Posterior estimate of \f$\theta,r\f$ in the form of Normal-inverse Wishart density
        egiw est;
        //! cached value of est.V
        ldmat &V;
        //! cached value of est.nu
        double ν
public:
        //! \name Constructors
        //!@{
        ARX ( const double frg0 = 1.0 ) : BMEF ( frg0 ), est (), V ( est._V() ), nu ( est._nu() ) {};
        ARX ( const ARX &A0 ) : BMEF (), est (), V ( est._V() ), nu ( est._nu() ) {
                set_statistics ( A0.dimx, A0.V, A0.nu );
                set_parameters ( A0.frg );
        };
        ARX* _copy_() const;
        void set_parameters ( double frg0 ) {
                frg = frg0;
        }
        void set_statistics ( int dimx0, const ldmat V0, double nu0 = -1.0 ) {
                est.set_parameters ( dimx0, V0, nu0 );
                last_lognc = est.lognc();
                dimx = dimx0;
        }
        //!@}

//      //! Set parameters given by moments, \c mu (mean of theta), \c R (mean of R) and \c C (variance of theta)
//      void set_parameters ( const vec &mu, const mat &R, const mat &C, double dfm){};
        //! Set sufficient statistics
        void set_statistics ( const BMEF* BM0 );
//      //! Returns sufficient statistics
//      void get_parameters ( mat &V0, double &nu0 ) {V0=est._V().to_mat(); nu0=est._nu();}
        //!\name Mathematical operations
        //!@{

        //! Weighted Bayes \f$ dt = [y_t psi_t] \f$.
        void bayes ( const vec &dt, const double w );
        void bayes ( const vec &dt ) {
                bayes ( dt, 1.0 );
        };
        double logpred ( const vec &dt ) const;
        void flatten ( const BMEF* B ) {
                const ARX* A = dynamic_cast<const ARX*> ( B );
                // nu should be equal to B.nu
                est.pow ( A->nu / nu );
                if ( evalll ) {
                        last_lognc = est.lognc();
                }
        }
        //! Conditioned version of the predictor
        enorm<ldmat>* epredictor ( const vec &rgr ) const;
        //! Predictor for empty regressor
        enorm<ldmat>* epredictor() const {
                bdm_assert_debug ( dimx == V.rows() - 1, "Regressor is not only 1" );
                return epredictor ( vec_1 ( 1.0 ) );
        }
        //! conditional version of the predictor
        mlnorm<ldmat>* predictor() const;
        mlstudent* predictor_student() const;
        //! Brute force structure estimation.\return indeces of accepted regressors.
        ivec structure_est ( egiw Eg0 );
        //! Smarter structure estimation by Ludvik Tesar.\return indeces of accepted regressors.
        ivec structure_est_LT ( egiw Eg0 );
        //!@}

        //!\name Access attributes
        //!@{
        const egiw& posterior() const {
                return est;
        }
        //!@}

        //!\name Connection
        //!@{
        void set_drv ( const RV &drv0 ) {
                drv = drv0;
        }

        RV& get_yrv() {
                //if yrv is not ready create it
                if ( _yrv._dsize() != dimx ) {
                        int i = 0;
                        while ( _yrv._dsize() < dimx ) {
                                _yrv.add ( drv ( vec_1 ( i ) ) );
                                i++;
                        }
                }
                //yrv should be ready by now
                bdm_assert_debug ( _yrv._dsize() == dimx, "incompatible drv" );
                return _yrv;
        }
        //!@}

        // TODO dokumentace - aktualizovat
        /*! UI for ARX estimator

        The ARX is constructed from a structure with fields:
        \code
        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
        };
        \endcode

        The estimator will assign names of the posterior in the form ["theta_i" and "r_i"]
        */
        void from_setting ( const Setting &set );

};

UIREGISTER ( ARX );
SHAREDPTR ( ARX );

}

#endif // AR_H