Linear Autoregressive model with Gaussian noise. More...
Linear Autoregressive model with Gaussian noise.
Regression of the following kind:
where unknown parameters rv are
, regression vector
is a known function of past outputs and exogeneous variables
. Distrubances
are supposed to be normally distributed:
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; }
#include <arx.h>
Public Member Functions | |
| void | set_statistics (const BMEF *BM0) |
| Set sufficient statistics. | |
| void | from_setting (const Setting &set) |
| void | validate () |
| This method TODO. | |
| virtual void | set_statistics (const BMEF *BM0) |
| get statistics from another model | |
| virtual void | flatten (const BMEF *B) |
| Flatten the posterior according to the given BMEF (of the same type!). | |
| 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. | |
Constructors | |
| ARX (const double frg0=1.0) | |
| ARX (const ARX &A0) | |
| ARX * | _copy_ () const |
| Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually! Prototype:. | |
| void | set_parameters (double frg0) |
| void | set_constant (bool const0) |
| 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) |
| 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. | |
| ivec | structure_est_LT (egiw Eg0) |
| Smarter structure estimation by Ludvik Tesar. | |
Access attributes | |
| const egiw & | posterior () const |
Connection | |
| void | set_rv (const RV &yrv0, const RV &rgrrv0) |
| 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_drv (const RV &rv) |
| 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 |
| RV | rgrrv |
| rv of regressor | |
| egiw | est |
Posterior estimate of in the form of Normal-inverse Wishart density. | |
| ldmat & | V |
| cached value of est.V | |
| double & | nu |
| cached value of est.nu | |
| bool | have_constant |
| switch if constant is modelled or not | |
| vec | _dt |
| cached value of data vector for have_constant =true | |
| egiw | alter_est |
| Alternative estimate of parameters, used in stabilized forgetting, see [Kulhavy]. | |
| 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) |
Save results to the given logger, details of what is stored is configured by LIDs and options. | |
| 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. | |
| ARX * bdm::ARX::_copy_ | ( | ) | const [virtual] |
Copy function required in vectors, Arrays of BM etc. Have to be DELETED manually! Prototype:.
BM* _copy_() const {return new BM(*this);}
Reimplemented from bdm::BMEF.
Reimplemented in bdm::ARXfrg.
| void bdm::ARX::bayes | ( | const vec & | dt | ) | [inline, virtual] |
| void bdm::ARX::from_setting | ( | const Setting & | set | ) | [virtual] |
class = 'ARX'; rv = RV({names_of_dt} ) // description of output variables rgr = RV({names_of_regressors}, [-1,-2]} // description of regressor variables constant = 1; // 0/1 switch if the constant term is modelled or not --- optional --- V0 = [1 0;0 1]; // Initial value of information matrix V --- OR --- dV0 = [1e-3, 1e-5, 1e-5, 1e-5]; // Initial value of diagonal of information matrix V // default: 1e-3 for rv, 1e-5 for rgr nu0 = 6; // initial value of nu, default: rgrlen + 2 frg = 1.0; // forgetting, default frg=1.0 rv_param = RV({names_of_parameters}} // description of parametetr names // default: ["theta_i" and "r_i"]
Reimplemented from bdm::BM.
References _dt, est, bdm::BMEF::frg, bdm::UI::get(), have_constant, bdm::BM::set_options(), bdm::epdf::set_rv(), and validate().
| 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 est, bdm::BM::evalll, bdm::BMEF::frg, bdm::BMEF::last_lognc, bdm::egiw::lognc(), nu, bdm::ldmat::opupdt(), bdm::egiw::pow(), and V.
| ivec bdm::ARX::structure_est | ( | egiw | Eg0 | ) |
Brute force structure estimation.
References bdm::epdf::dimension(), est, and bdm::egiw::lognc().
| ivec bdm::ARX::structure_est_LT | ( | egiw | Eg0 | ) |
Smarter structure estimation by Ludvik Tesar.
RV bdm::ARX::_yrv [protected] |
description of modelled data
in the likelihood function Do NOT access directly, only via get_yrv().
Referenced by validate().
1.6.1