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25  <div class="navpath"><b>bdm</b>::<a class="el" href="classbdm_1_1ARX.html">ARX</a>
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29<h1>bdm::ARX Class Reference</h1><!-- doxytag: class="bdm::ARX" --><!-- doxytag: inherits="bdm::BMEF" -->Linear Autoregressive model with Gaussian noise. 
30<a href="#_details">More...</a>
31<p>
32<code>#include &lt;<a class="el" href="arx_8h-source.html">arx.h</a>&gt;</code>
33<p>
34<div class="dynheader">
35Inheritance diagram for bdm::ARX:</div>
36<div class="dynsection">
37<p><center><img src="classbdm_1_1ARX__inherit__graph.png" border="0" usemap="#bdm_1_1ARX__inherit__map" alt="Inheritance graph"></center>
38<map name="bdm_1_1ARX__inherit__map">
39<area shape="rect" href="classbdm_1_1BMEF.html" title="Estimator for Exponential family." alt="" coords="5,84,99,111"><area shape="rect" href="classbdm_1_1BM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="13,7,91,33"></map>
40<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
41<div class="dynheader">
42Collaboration diagram for bdm::ARX:</div>
43<div class="dynsection">
44<p><center><img src="classbdm_1_1ARX__coll__graph.png" border="0" usemap="#bdm_1_1ARX__coll__map" alt="Collaboration graph"></center>
45<map name="bdm_1_1ARX__coll__map">
46<area shape="rect" href="classbdm_1_1BMEF.html" title="Estimator for Exponential family." alt="" coords="5,343,99,369"><area shape="rect" href="classbdm_1_1BM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="13,236,91,263"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="104,87,179,113"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="173,183,259,209"><area shape="rect" href="classbdm_1_1base.html" title="Root class of BDM objects." alt="" coords="145,7,233,33"><area shape="rect" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD)." alt="" coords="89,289,148,316"><area shape="rect" href="classbdm_1_1egiw.html" title="Gauss&#45;inverse&#45;Wishart density stored in LD form." alt="" coords="152,396,237,423"><area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="88,183,149,209"><area shape="rect" href="classbdm_1_1eEF.html" title="General conjugate exponential family posterior density." alt="" coords="173,289,253,316"></map>
47<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
48
49<p>
50<a href="classbdm_1_1ARX-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
51<tr><td></td></tr>
52<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
53<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="44914d0b259204b3446db82b989bd626"></a><!-- doxytag: member="bdm::ARX::ARX" ref="44914d0b259204b3446db82b989bd626" args="(const RV &amp;rv, const mat &amp;V0, const double &amp;nu0, const double frg0=1.0)" -->
54&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#44914d0b259204b3446db82b989bd626">ARX</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1BM.html#18d6db4af8ee42077741d9e3618153ca">rv</a>, const mat &amp;V0, const double &amp;nu0, const double frg0=1.0)</td></tr>
55
56<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Full constructor. <br></td></tr>
57<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="73a55a3d66bfbeeee4df6c2ae40920ed"></a><!-- doxytag: member="bdm::ARX::ARX" ref="73a55a3d66bfbeeee4df6c2ae40920ed" args="(const ARX &amp;A0)" -->
58&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#73a55a3d66bfbeeee4df6c2ae40920ed">ARX</a> (const <a class="el" href="classbdm_1_1ARX.html">ARX</a> &amp;A0)</td></tr>
59
60<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Copy constructor. <br></td></tr>
61<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="20ff2de8d862f28de7da83444d65bcdb"></a><!-- doxytag: member="bdm::ARX::_copy_" ref="20ff2de8d862f28de7da83444d65bcdb" args="(bool changerv=false)" -->
62<a class="el" href="classbdm_1_1ARX.html">ARX</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#20ff2de8d862f28de7da83444d65bcdb">_copy_</a> (bool changerv=false)</td></tr>
63
64<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Auxiliary function. <br></td></tr>
65<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cab0a1de5355b1027d24fd3d4862c9b0"></a><!-- doxytag: member="bdm::ARX::set_parameters" ref="cab0a1de5355b1027d24fd3d4862c9b0" args="(const ldmat &amp;V0, const double &amp;nu0)" -->
66void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#cab0a1de5355b1027d24fd3d4862c9b0">set_parameters</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;V0, const double &amp;nu0)</td></tr>
67
68<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set sufficient statistics. <br></td></tr>
69<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="539f9d0127423c94b912708d390e67b8"></a><!-- doxytag: member="bdm::ARX::set_statistics" ref="539f9d0127423c94b912708d390e67b8" args="(const BMEF *BM0)" -->
70void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#539f9d0127423c94b912708d390e67b8">set_statistics</a> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *BM0)</td></tr>
71
72<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get statistics from another model <br></td></tr>
73<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1974409e022ea1efb3404b5c2fde66ad"></a><!-- doxytag: member="bdm::ARX::get_parameters" ref="1974409e022ea1efb3404b5c2fde66ad" args="(mat &amp;V0, double &amp;nu0)" -->
74void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#1974409e022ea1efb3404b5c2fde66ad">get_parameters</a> (mat &amp;V0, double &amp;nu0)</td></tr>
75
76<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns sufficient statistics. <br></td></tr>
77<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="17e7fe14654ab3c449846c3f43e66169"></a><!-- doxytag: member="bdm::ARX::bayes" ref="17e7fe14654ab3c449846c3f43e66169" args="(const vec &amp;dt, const double w)" -->
78void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#17e7fe14654ab3c449846c3f43e66169">bayes</a> (const vec &amp;dt, const double w)</td></tr>
79
80<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>
81<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#8bdf2974052e8ce74eb0d4f3791c58a3">bayes</a> (const vec &amp;dt)</td></tr>
82
83<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Incremental Bayes rule.  <a href="#8bdf2974052e8ce74eb0d4f3791c58a3"></a><br></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="16797df43f85f1ddbe9d64fd6d82c25d"></a><!-- doxytag: member="bdm::ARX::_epdf" ref="16797df43f85f1ddbe9d64fd6d82c25d" args="() const " -->
85const <a class="el" href="classbdm_1_1epdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#16797df43f85f1ddbe9d64fd6d82c25d">_epdf</a> () const </td></tr>
86
87<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a reference to the <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> representing posterior density on parameters. <br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#080a7e531e3aa06694112863b15bc6a4">logpred</a> (const vec &amp;dt) const </td></tr>
89
90<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e86ab499b116b837d3163ec852961eca"></a><!-- doxytag: member="bdm::ARX::flatten" ref="e86ab499b116b837d3163ec852961eca" args="(const BMEF *B)" -->
91void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#e86ab499b116b837d3163ec852961eca">flatten</a> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *B)</td></tr>
92
93<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flatten the posterior according to the given <a class="el" href="classbdm_1_1BMEF.html" title="Estimator for Exponential family.">BMEF</a> (of the same type!). <br></td></tr>
94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7c8d1fe774fe1da50293d50ad8aef43d"></a><!-- doxytag: member="bdm::ARX::predictor" ref="7c8d1fe774fe1da50293d50ad8aef43d" args="(const RV &amp;rv0, const vec &amp;rgr) const " -->
95<a class="el" href="classbdm_1_1enorm.html">enorm</a>&lt; <a class="el" href="classldmat.html">ldmat</a> &gt; *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#7c8d1fe774fe1da50293d50ad8aef43d">predictor</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0, const vec &amp;rgr) const </td></tr>
96
97<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conditional version of the predictor. <br></td></tr>
98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5b73b70457f49ce4ad8660d729172dfd"></a><!-- doxytag: member="bdm::ARX::predictor" ref="5b73b70457f49ce4ad8660d729172dfd" args="(const RV &amp;rv0) const " -->
99<a class="el" href="classbdm_1_1enorm.html">enorm</a>&lt; <a class="el" href="classldmat.html">ldmat</a> &gt; *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#5b73b70457f49ce4ad8660d729172dfd">predictor</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0) const </td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs a predictive density (marginal density on data). <br></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="02d9e91f21a700947a7b7eec1beed956"></a><!-- doxytag: member="bdm::ARX::predictor" ref="02d9e91f21a700947a7b7eec1beed956" args="(const RV &amp;rv0, const RV &amp;rvc0) const " -->
103<a class="el" href="classbdm_1_1mlnorm.html">mlnorm</a>&lt; <a class="el" href="classldmat.html">ldmat</a> &gt; *&nbsp;</td><td class="memItemRight" valign="bottom"><b>predictor</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0, const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rvc0) const </td></tr>
104
105<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2ce8c6599497ffb94dfcb66d1fe7aca6"></a><!-- doxytag: member="bdm::ARX::predictor_student" ref="2ce8c6599497ffb94dfcb66d1fe7aca6" args="(const RV &amp;rv0, const RV &amp;rvc0) const " -->
106<a class="el" href="classbdm_1_1mlstudent.html">mlstudent</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><b>predictor_student</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0, const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rvc0) const </td></tr>
107
108<tr><td class="memItemLeft" nowrap align="right" valign="top">ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#16b02ae03316751664c22d59d90c1e34">structure_est</a> (<a class="el" href="classbdm_1_1egiw.html">egiw</a> Eg0)</td></tr>
109
110<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Brute force structure estimation.  <a href="#16b02ae03316751664c22d59d90c1e34"></a><br></td></tr>
111<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ab2c55205a324e9d698fbd8ac229ad4f"></a><!-- doxytag: member="bdm::ARX::_e" ref="ab2c55205a324e9d698fbd8ac229ad4f" args="() const " -->
112const <a class="el" href="classbdm_1_1egiw.html">egiw</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#ab2c55205a324e9d698fbd8ac229ad4f">_e</a> () const </td></tr>
113
114<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a pointer to the <a class="el" href="classbdm_1_1epdf.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>
115<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1dee3fddaf021e62d925289660a707dc"></a><!-- doxytag: member="bdm::ARX::bayesB" ref="1dee3fddaf021e62d925289660a707dc" args="(const mat &amp;Dt)" -->
116virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#1dee3fddaf021e62d925289660a707dc">bayesB</a> (const mat &amp;Dt)</td></tr>
117
118<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr>
119<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0e8ebe61fb14990abe1254bd3dda5fae"></a><!-- doxytag: member="bdm::ARX::logpred_m" ref="0e8ebe61fb14990abe1254bd3dda5fae" args="(const mat &amp;dt) const " -->
120vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#0e8ebe61fb14990abe1254bd3dda5fae">logpred_m</a> (const mat &amp;dt) const </td></tr>
121
122<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix version of logpred. <br></td></tr>
123<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="40a3c891996391e3135518053a917793"></a><!-- doxytag: member="bdm::ARX::_rv" ref="40a3c891996391e3135518053a917793" args="() const " -->
124const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#40a3c891996391e3135518053a917793">_rv</a> () const </td></tr>
125
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
127<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5be65d37dedfe33a3671e7065f523a70"></a><!-- doxytag: member="bdm::ARX::_ll" ref="5be65d37dedfe33a3671e7065f523a70" args="() const " -->
128double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#5be65d37dedfe33a3671e7065f523a70">_ll</a> () const </td></tr>
129
130<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
131<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="236b3abbcc93594fc97cd86d82c1a83f"></a><!-- doxytag: member="bdm::ARX::set_evalll" ref="236b3abbcc93594fc97cd86d82c1a83f" args="(bool evl0)" -->
132void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#236b3abbcc93594fc97cd86d82c1a83f">set_evalll</a> (bool evl0)</td></tr>
133
134<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
135<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
136<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="11474a627367f81b76830cb8477cf026"></a><!-- doxytag: member="bdm::ARX::est" ref="11474a627367f81b76830cb8477cf026" args="" -->
137<a class="el" href="classbdm_1_1egiw.html">egiw</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#11474a627367f81b76830cb8477cf026">est</a></td></tr>
138
139<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>
140<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="de5b7d83ff5d3f5af2f80068db0abdfd"></a><!-- doxytag: member="bdm::ARX::V" ref="de5b7d83ff5d3f5af2f80068db0abdfd" args="" -->
141<a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#de5b7d83ff5d3f5af2f80068db0abdfd">V</a></td></tr>
142
143<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.V <br></td></tr>
144<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="740b0582f180ba13cae91d66e9bdb67f"></a><!-- doxytag: member="bdm::ARX::nu" ref="740b0582f180ba13cae91d66e9bdb67f" args="" -->
145double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#740b0582f180ba13cae91d66e9bdb67f">nu</a></td></tr>
146
147<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.nu <br></td></tr>
148<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1331865e10fb1ccef65bb4c47fa3be64"></a><!-- doxytag: member="bdm::ARX::frg" ref="1331865e10fb1ccef65bb4c47fa3be64" args="" -->
149double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BMEF.html#1331865e10fb1ccef65bb4c47fa3be64">frg</a></td></tr>
150
151<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">forgetting factor <br></td></tr>
152<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="06e7b3ac03e10017d4288c76888e2865"></a><!-- doxytag: member="bdm::ARX::last_lognc" ref="06e7b3ac03e10017d4288c76888e2865" args="" -->
153double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BMEF.html#06e7b3ac03e10017d4288c76888e2865">last_lognc</a></td></tr>
154
155<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>
156<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18d6db4af8ee42077741d9e3618153ca"></a><!-- doxytag: member="bdm::ARX::rv" ref="18d6db4af8ee42077741d9e3618153ca" args="" -->
157<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#18d6db4af8ee42077741d9e3618153ca">rv</a></td></tr>
158
159<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Random variable of the posterior. <br></td></tr>
160<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4064b6559d962633e4372b12f4cd204a"></a><!-- doxytag: member="bdm::ARX::ll" ref="4064b6559d962633e4372b12f4cd204a" args="" -->
161double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#4064b6559d962633e4372b12f4cd204a">ll</a></td></tr>
162
163<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of marginalized data likelihood. <br></td></tr>
164<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="faff0ad12556fe7dc0e2807d4fd938ee"></a><!-- doxytag: member="bdm::ARX::evalll" ref="faff0ad12556fe7dc0e2807d4fd938ee" args="" -->
165bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#faff0ad12556fe7dc0e2807d4fd938ee">evalll</a></td></tr>
166
167<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 computational time. <br></td></tr>
168</table>
169<hr><a name="_details"></a><h2>Detailed Description</h2>
170Linear Autoregressive model with Gaussian noise.
171<p>
172Regression of the following kind: <p class="formulaDsp">
173<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">
174<p>
175 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">
176<img class="formulaDsp" alt="\[ e_t \sim \mathcal{N}(0,1). \]" src="form_62.png">
177<p>
178<p>
179Extension 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>
180<a class="anchor" name="8bdf2974052e8ce74eb0d4f3791c58a3"></a><!-- doxytag: member="bdm::ARX::bayes" ref="8bdf2974052e8ce74eb0d4f3791c58a3" args="(const vec &amp;dt)" -->
181<div class="memitem">
182<div class="memproto">
183      <table class="memname">
184        <tr>
185          <td class="memname">void bdm::ARX::bayes           </td>
186          <td>(</td>
187          <td class="paramtype">const vec &amp;&nbsp;</td>
188          <td class="paramname"> <em>dt</em>          </td>
189          <td>&nbsp;)&nbsp;</td>
190          <td><code> [inline, virtual]</code></td>
191        </tr>
192      </table>
193</div>
194<div class="memdoc">
195
196<p>
197Incremental Bayes rule.
198<p>
199<dl compact><dt><b>Parameters:</b></dt><dd>
200  <table border="0" cellspacing="2" cellpadding="0">
201    <tr><td valign="top"></td><td valign="top"><em>dt</em>&nbsp;</td><td>vector of input data </td></tr>
202  </table>
203</dl>
204
205<p>Reimplemented from <a class="el" href="classbdm_1_1BMEF.html#c287f4c0c1ea31b91572ec45351838f1">bdm::BMEF</a>.</p>
206
207<p>References <a class="el" href="bdm_2estim_2arx_8cpp-source.html#l00005">bayes()</a>.</p>
208
209</div>
210</div><p>
211<a class="anchor" name="080a7e531e3aa06694112863b15bc6a4"></a><!-- doxytag: member="bdm::ARX::logpred" ref="080a7e531e3aa06694112863b15bc6a4" args="(const vec &amp;dt) const " -->
212<div class="memitem">
213<div class="memproto">
214      <table class="memname">
215        <tr>
216          <td class="memname">double bdm::ARX::logpred           </td>
217          <td>(</td>
218          <td class="paramtype">const vec &amp;&nbsp;</td>
219          <td class="paramname"> <em>dt</em>          </td>
220          <td>&nbsp;)&nbsp;</td>
221          <td> const<code> [virtual]</code></td>
222        </tr>
223      </table>
224</div>
225<div class="memdoc">
226
227<p>
228Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.
229<p>Reimplemented from <a class="el" href="classbdm_1_1BM.html#50257e0c1e5b5c73153ea6e716ad8ae0">bdm::BM</a>.</p>
230
231<p>References <a class="el" href="libEF_8h-source.html#l00207">bdm::egiw::_nu()</a>, <a class="el" href="libEF_8h-source.html#l00203">bdm::egiw::_V()</a>, <a class="el" href="arx_8h-source.html#l00039">est</a>, <a class="el" href="libBM_8h-source.html#l00422">bdm::BM::evalll</a>, <a class="el" href="libEF_8h-source.html#l00078">bdm::BMEF::frg</a>, <a class="el" href="libEF_8h-source.html#l00080">bdm::BMEF::last_lognc</a>, <a class="el" href="libEF_8cpp-source.html#l00044">bdm::egiw::lognc()</a>, <a class="el" href="arx_8h-source.html#l00043">nu</a>, <a class="el" href="libDC_8cpp-source.html#l00058">ldmat::opupdt()</a>, <a class="el" href="libEF_8h-source.html#l00209">bdm::egiw::pow()</a>, and <a class="el" href="arx_8h-source.html#l00041">V</a>.</p>
232
233</div>
234</div><p>
235<a class="anchor" name="16b02ae03316751664c22d59d90c1e34"></a><!-- doxytag: member="bdm::ARX::structure_est" ref="16b02ae03316751664c22d59d90c1e34" args="(egiw Eg0)" -->
236<div class="memitem">
237<div class="memproto">
238      <table class="memname">
239        <tr>
240          <td class="memname">ivec bdm::ARX::structure_est           </td>
241          <td>(</td>
242          <td class="paramtype"><a class="el" href="classbdm_1_1egiw.html">egiw</a>&nbsp;</td>
243          <td class="paramname"> <em>Eg0</em>          </td>
244          <td>&nbsp;)&nbsp;</td>
245          <td></td>
246        </tr>
247      </table>
248</div>
249<div class="memdoc">
250
251<p>
252Brute force structure estimation.
253<p>
254<dl class="return" compact><dt><b>Returns:</b></dt><dd>indeces of accepted regressors. </dd></dl>
255
256<p>References <a class="el" href="arx_8h-source.html#l00039">est</a>, and <a class="el" href="libEF_8cpp-source.html#l00044">bdm::egiw::lognc()</a>.</p>
257
258</div>
259</div><p>
260<hr>The documentation for this class was generated from the following files:<ul>
261<li>work/git/mixpp/bdm/estim/<a class="el" href="arx_8h-source.html">arx.h</a><li>work/git/mixpp/bdm/estim/arx.cpp</ul>
262</div>
263<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jan 27 16:30:39 2009 for mixpp by&nbsp;
264<a href="http://www.doxygen.org/index.html">
265<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
266</body>
267</html>
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