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26<h1>ARX Class Reference</h1><!-- doxytag: class="ARX" --><!-- doxytag: inherits="BM" -->Linear Autoregressive model with Gaussian noise. 
27<a href="#_details">More...</a>
28<p>
29<code>#include &lt;<a class="el" href="arx_8h-source.html">arx.h</a>&gt;</code>
30<p>
31<div class="dynheader">
32Inheritance diagram for ARX:</div>
33<div class="dynsection">
34<p><center><img src="classARX__inherit__graph.png" border="0" usemap="#ARX__inherit__map" alt="Inheritance graph"></center>
35<map name="ARX__inherit__map">
36<area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="9,7,49,31"></map>
37<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
38<div class="dynheader">
39Collaboration diagram for ARX:</div>
40<div class="dynsection">
41<p><center><img src="classARX__coll__graph.png" border="0" usemap="#ARX__coll__map" alt="Collaboration graph"></center>
42<map name="ARX__coll__map">
43<area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="5,146,45,170"><area shape="rect" href="classRV.html" title="Class representing variables, most often random variables." alt="" coords="32,7,69,31"><area shape="rect" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="63,95,108,119"><area shape="rect" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD)." alt="" coords="132,196,185,220"><area shape="rect" href="classegiw.html" title="Gauss&#45;inverse&#45;Wishart density stored in LD form." alt="" coords="63,284,111,308"><area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="132,95,188,119"><area shape="rect" href="classeEF.html" title="General conjugate exponential family posterior density." alt="" coords="63,196,108,220"></map>
44<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
45
46<p>
47<a href="classARX-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
48<tr><td></td></tr>
49<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
50<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5fc6c18e73dcc0f1135eef33f42db8be"></a><!-- doxytag: member="ARX::ARX" ref="5fc6c18e73dcc0f1135eef33f42db8be" args="(RV &amp;rv, mat &amp;V0, double &amp;nu0, double frg0=1.0)" -->
51&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#5fc6c18e73dcc0f1135eef33f42db8be">ARX</a> (<a class="el" href="classRV.html">RV</a> &amp;<a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a>, mat &amp;V0, double &amp;nu0, double frg0=1.0)</td></tr>
52
53<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Full constructor. <br></td></tr>
54<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3ccef8dc9dbed00ec74dddc949845d39"></a><!-- doxytag: member="ARX::set_parameters" ref="3ccef8dc9dbed00ec74dddc949845d39" args="(mat &amp;V0, double &amp;nu0)" -->
55void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_parameters</b> (mat &amp;V0, double &amp;nu0)</td></tr>
56
57<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="29f55b43b8b6f5c4a55f6176aa85c494"></a><!-- doxytag: member="ARX::get_parameters" ref="29f55b43b8b6f5c4a55f6176aa85c494" args="(mat &amp;V0, double &amp;nu0)" -->
58void&nbsp;</td><td class="memItemRight" valign="bottom"><b>get_parameters</b> (mat &amp;V0, double &amp;nu0)</td></tr>
59
60<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ba82c956ca893826811aefe1e4af465d"></a><!-- doxytag: member="ARX::bayes" ref="ba82c956ca893826811aefe1e4af465d" args="(const vec &amp;dt)" -->
61void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#ba82c956ca893826811aefe1e4af465d">bayes</a> (const vec &amp;dt)</td></tr>
62
63<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Here <img class="formulaInl" alt="$dt = [y_t psi_t] $" src="form_58.png">. <br></td></tr>
64<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9d8eff7a9df81786191a4c55b27e5b8a"></a><!-- doxytag: member="ARX::_epdf" ref="9d8eff7a9df81786191a4c55b27e5b8a" args="()" -->
65<a class="el" href="classepdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#9d8eff7a9df81786191a4c55b27e5b8a">_epdf</a> ()</td></tr>
66
67<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a pointer to the <a class="el" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> representing posterior density on parameters. Use with care! <br></td></tr>
68<tr><td class="memItemLeft" nowrap align="right" valign="top">ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#130bb7336aac681ce14b027b8f1409fa">structure_est</a> (<a class="el" href="classegiw.html">egiw</a> Eg0)</td></tr>
69
70<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Brute force structure estimation.  <a href="#130bb7336aac681ce14b027b8f1409fa"></a><br></td></tr>
71<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b8827048ceec8999849e2ed15400cae7"></a><!-- doxytag: member="ARX::_tll" ref="b8827048ceec8999849e2ed15400cae7" args="()" -->
72double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#b8827048ceec8999849e2ed15400cae7">_tll</a> ()</td></tr>
73
74<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
75<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87b07867fd4c133aa89a18543f68d9f9"></a><!-- doxytag: member="ARX::bayes" ref="87b07867fd4c133aa89a18543f68d9f9" args="(mat Dt)" -->
76void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#87b07867fd4c133aa89a18543f68d9f9">bayes</a> (mat Dt)</td></tr>
77
78<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr>
79<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="126bd2595c48e311fc2a7ab72876092a"></a><!-- doxytag: member="ARX::_rv" ref="126bd2595c48e311fc2a7ab72876092a" args="() const " -->
80const <a class="el" href="classRV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#126bd2595c48e311fc2a7ab72876092a">_rv</a> () const </td></tr>
81
82<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
83<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87f4a547d2c29180be88175e5eab9c88"></a><!-- doxytag: member="ARX::_ll" ref="87f4a547d2c29180be88175e5eab9c88" args="() const " -->
84double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#87f4a547d2c29180be88175e5eab9c88">_ll</a> () const </td></tr>
85
86<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
87<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="691d023662beffa1dda611b416c0e27e"></a><!-- doxytag: member="ARX::est" ref="691d023662beffa1dda611b416c0e27e" args="" -->
89<a class="el" href="classegiw.html">egiw</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#691d023662beffa1dda611b416c0e27e">est</a></td></tr>
90
91<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Posterior estimate of <img class="formulaInl" alt="$\theta,r$" src="form_57.png"> in the form of Normal-inverse Wishart density. <br></td></tr>
92<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2291297861dd74ca0175a01f910a0ef7"></a><!-- doxytag: member="ARX::V" ref="2291297861dd74ca0175a01f910a0ef7" args="" -->
93<a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#2291297861dd74ca0175a01f910a0ef7">V</a></td></tr>
94
95<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.V <br></td></tr>
96<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a4182c281098b2d86b62518a7493d9be"></a><!-- doxytag: member="ARX::nu" ref="a4182c281098b2d86b62518a7493d9be" args="" -->
97double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#a4182c281098b2d86b62518a7493d9be">nu</a></td></tr>
98
99<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.nu <br></td></tr>
100<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e467144efb0a5acbc10dba4eff8638fe"></a><!-- doxytag: member="ARX::frg" ref="e467144efb0a5acbc10dba4eff8638fe" args="" -->
101double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#e467144efb0a5acbc10dba4eff8638fe">frg</a></td></tr>
102
103<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">forgetting factor <br></td></tr>
104<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6d0cd0f0734aa77cdc5e48f1cf6737ec"></a><!-- doxytag: member="ARX::last_lognc" ref="6d0cd0f0734aa77cdc5e48f1cf6737ec" args="" -->
105double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#6d0cd0f0734aa77cdc5e48f1cf6737ec">last_lognc</a></td></tr>
106
107<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of lognc() in the previous step (used in evaluation of <code>ll</code> ) <br></td></tr>
108<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="64ea7c8ff48bf2548bac3e985e24da19"></a><!-- doxytag: member="ARX::tll" ref="64ea7c8ff48bf2548bac3e985e24da19" args="" -->
109double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#64ea7c8ff48bf2548bac3e985e24da19">tll</a></td></tr>
110
111<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">total likelihood <br></td></tr>
112<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af00f0612fabe66241dd507188cdbf88"></a><!-- doxytag: member="ARX::rv" ref="af00f0612fabe66241dd507188cdbf88" args="" -->
113<a class="el" href="classRV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a></td></tr>
114
115<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Random variable of the posterior. <br></td></tr>
116<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5623fef6572a08c2b53b8c87b82dc979"></a><!-- doxytag: member="ARX::ll" ref="5623fef6572a08c2b53b8c87b82dc979" args="" -->
117double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#5623fef6572a08c2b53b8c87b82dc979">ll</a></td></tr>
118
119<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of marginalized data likelihood. <br></td></tr>
120<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bf6fb59b30141074f8ee1e2f43d03129"></a><!-- doxytag: member="ARX::evalll" ref="bf6fb59b30141074f8ee1e2f43d03129" args="" -->
121bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#bf6fb59b30141074f8ee1e2f43d03129">evalll</a></td></tr>
122
123<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">If true, the filter will compute likelihood of the data record and store it in <code>ll</code> . Set to false if you want to save time. <br></td></tr>
124</table>
125<hr><a name="_details"></a><h2>Detailed Description</h2>
126Linear Autoregressive model with Gaussian noise.
127<p>
128Regression of the following kind: <p class="formulaDsp">
129<img class="formulaDsp" alt="\[ y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t \]" src="form_61.png">
130<p>
131 where unknown parameters <code>rv</code> are <img class="formulaInl" alt="$[\theta r]$" src="form_51.png">, regression vector <img class="formulaInl" alt="$\psi=\psi(y_{1:t},u_{1:t})$" src="form_52.png"> is a known function of past outputs and exogeneous variables <img class="formulaInl" alt="$u_t$" src="form_53.png">. Distrubances <img class="formulaInl" alt="$e_t$" src="form_54.png"> are supposed to be normally distributed: <p class="formulaDsp">
132<img class="formulaDsp" alt="\[ e_t \sim \mathcal{N}(0,1). \]" src="form_62.png">
133<p>
134<p>
135Extension for time-variant parameters <img class="formulaInl" alt="$\theta_t,r_t$" src="form_55.png"> may be achived using exponential forgetting (Kulhavy and Zarrop, 1993). In such a case, the forgetting factor <code>frg</code> <img class="formulaInl" alt="$\in <0,1>$" src="form_56.png"> should be given in the constructor. Time-invariant parameters are estimated for <code>frg</code> = 1. <hr><h2>Member Function Documentation</h2>
136<a class="anchor" name="130bb7336aac681ce14b027b8f1409fa"></a><!-- doxytag: member="ARX::structure_est" ref="130bb7336aac681ce14b027b8f1409fa" args="(egiw Eg0)" -->
137<div class="memitem">
138<div class="memproto">
139      <table class="memname">
140        <tr>
141          <td class="memname">ivec ARX::structure_est           </td>
142          <td>(</td>
143          <td class="paramtype"><a class="el" href="classegiw.html">egiw</a>&nbsp;</td>
144          <td class="paramname"> <em>Eg0</em>          </td>
145          <td>&nbsp;)&nbsp;</td>
146          <td></td>
147        </tr>
148      </table>
149</div>
150<div class="memdoc">
151
152<p>
153Brute force structure estimation.
154<p>
155<dl class="return" compact><dt><b>Returns:</b></dt><dd>indeces of accepted regressors. </dd></dl>
156
157<p>References <a class="el" href="libBM_8h-source.html#l00057">RV::count()</a>, <a class="el" href="arx_8h-source.html#l00039">est</a>, <a class="el" href="libEF_8cpp-source.html#l00031">egiw::lognc()</a>, and <a class="el" href="libBM_8h-source.html#l00247">BM::rv</a>.</p>
158
159</div>
160</div><p>
161<hr>The documentation for this class was generated from the following files:<ul>
162<li>work/mixpp/bdm/estim/<a class="el" href="arx_8h-source.html">arx.h</a><li>work/mixpp/bdm/estim/arx.cpp</ul>
163</div>
164<hr size="1"><address style="text-align: right;"><small>Generated on Sat Aug 16 11:58:47 2008 for mixpp by&nbsp;
165<a href="http://www.doxygen.org/index.html">
166<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
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