Changeset 354 for doc/html/tut_arx.html

Timestamp:

06/02/09 10:24:26 (16 years ago)

Author:

smidl

Message:

doc - oprava

Files:

• doc/html/tut_arx.html (modified) (3 diffs)

doc/html/tut_arx.html

@@ -65 +65 @@
 <img class="formulaDsp" alt="\[ y_t = \theta' \psi_t + \rho e_t \]" src="form_107.png">
 <p>
- where <img class="formulaInl" alt="$y_t$" src="form_42.png"> is the system output, <img class="formulaInl" alt="$[\theta,\rho]$" src="form_108.png"> is vector of unknown parameters, <img class="formulaInl" alt="$\psi_t$" src="form_109.png"> is an vector of data-dependent regressors, and noise <img class="formulaInl" alt="$e_t$" src="form_6.png"> is assumed to be Normal distributed <img class="formulaInl" alt="$\mathcal{N}(0,1)$" src="form_110.png">.<p>
+ where <img class="formulaInl" alt="$y_t$" src="form_41.png"> is the system output, <img class="formulaInl" alt="$[\theta,\rho]$" src="form_108.png"> is vector of unknown parameters, <img class="formulaInl" alt="$\psi_t$" src="form_109.png"> is an vector of data-dependent regressors, and noise <img class="formulaInl" alt="$e_t$" src="form_4.png"> is assumed to be Normal distributed <img class="formulaInl" alt="$\mathcal{N}(0,1)$" src="form_110.png">.<p>
 Special cases include: <ul>
 <li>estimation of unknown mean and variance of a Gaussian density from independent samples.</li>
@@ -105 +105 @@
 Statistics <img class="formulaInl" alt="$ V_0 , \nu_0 $" src="form_120.png"> are called alternative statistics, their role is to stabilize estimation. It is easy to show that for zero data, the statistics <img class="formulaInl" alt="$ V_t , \nu_t $" src="form_121.png"> converge to the alternative statistics.<h2><a class="anchor" name="str">
 Structure estimation</a></h2>
-For this model, structure estimation is a form of model selection procedure. Specifically, we compare hypotheses that the data were generated by the full model with hypotheses that some regressors in vector <img class="formulaInl" alt="$\psi$" src="form_15.png"> are redundant. The number of possible hypotheses is then the number of all possible combinations of all regressors.<p>
+For this model, structure estimation is a form of model selection procedure. Specifically, we compare hypotheses that the data were generated by the full model with hypotheses that some regressors in vector <img class="formulaInl" alt="$\psi$" src="form_13.png"> are redundant. The number of possible hypotheses is then the number of all possible combinations of all regressors.<p>
 However, due to property known as nesting in exponential family, these hypotheses can be tested using only the posterior statistics. (This property does no hold for forgetting <img class="formulaInl" alt="$ \phi<1 $" src="form_122.png">). Hence, for low dimensional problems, this can be done by a tree search (method <a class="el" href="classbdm_1_1ARX.html#16b02ae03316751664c22d59d90c1e34" title="Brute force structure estimation.">bdm::ARX::structure_est()</a>). Or more sophisticated algorithm [ref Ludvik]<h2><a class="anchor" name="soft">
 Software Image</a></h2>
@@ -123 +123 @@
 </ul>
 </div>
-<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:14 2009 for mixpp by&nbsp;
+<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:11:00 2009 for mixpp by&nbsp;
 <a href="http://www.doxygen.org/index.html">
 <img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>