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09/12/09 11:41:43 (15 years ago)
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  • library/doc/html/classbdm_1_1MixEF.html

    r591 r608  
    103103<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aedc50e9640f049b846084748b18469a2"></a><!-- doxytag: member="bdm::MixEF::epredictor" ref="aedc50e9640f049b846084748b18469a2" args="() const " --> 
    104104<a class="el" href="classbdm_1_1emix.html">emix</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#aedc50e9640f049b846084748b18469a2">epredictor</a> () const </td></tr> 
    105 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs a predictive density <img class="formulaInl" alt="$ f(d_{t+1} |d_{t}, \ldots d_{0}) $" src="form_14.png"/>. <br/></td></tr> 
     105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs a predictive density <img class="formulaInl" alt="$ f(d_{t+1} |d_{t}, \ldots d_{0}) $" src="form_20.png"/>. <br/></td></tr> 
    106106<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="af0dfb4375fef4e61c4cb062e5bac7c8c"></a><!-- doxytag: member="bdm::MixEF::flatten" ref="af0dfb4375fef4e61c4cb062e5bac7c8c" args="(const BMEF *M2)" --> 
    107107void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#af0dfb4375fef4e61c4cb062e5bac7c8c">flatten</a> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *M2)</td></tr> 
     
    146146<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a598b25e3f3d96a5bc00a5faeb5b3c912"></a><!-- doxytag: member="bdm::MixEF::predictor" ref="a598b25e3f3d96a5bc00a5faeb5b3c912" args="() const " --> 
    147147virtual <a class="el" href="classbdm_1_1mpdf.html">mpdf</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a598b25e3f3d96a5bc00a5faeb5b3c912">predictor</a> () const </td></tr> 
    148 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs conditional density of 1-step ahead predictor <img class="formulaInl" alt="$ f(d_{t+1} |d_{t+h-1}, \ldots d_{t}) $" src="form_131.png"/>. <br/></td></tr> 
     148<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs conditional density of 1-step ahead predictor <img class="formulaInl" alt="$ f(d_{t+1} |d_{t+h-1}, \ldots d_{t}) $" src="form_21.png"/>. <br/></td></tr> 
    149149<tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr> 
    150150<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpb6eb094f9e6af11f8a7d9efa9d8e3623"></a> </p> 
     
    170170<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a90c21ab5a2af56d4b49e2eaef6eccc08"></a><!-- doxytag: member="bdm::MixEF::Coms" ref="a90c21ab5a2af56d4b49e2eaef6eccc08" args="" --> 
    171171Array&lt; <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> * &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#a90c21ab5a2af56d4b49e2eaef6eccc08">Coms</a></td></tr> 
    172 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Models for Components of <img class="formulaInl" alt="$\theta_i$" src="form_35.png"/>. <br/></td></tr> 
     172<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Models for Components of <img class="formulaInl" alt="$\theta_i$" src="form_43.png"/>. <br/></td></tr> 
    173173<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae39faa70cebadc3296bd249040105e86"></a><!-- doxytag: member="bdm::MixEF::weights" ref="ae39faa70cebadc3296bd249040105e86" args="" --> 
    174174<a class="el" href="classbdm_1_1multiBM.html">multiBM</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1MixEF.html#ae39faa70cebadc3296bd249040105e86">weights</a></td></tr> 
     
    229229<p>An approximate estimation method for models with latent discrete variable, such as mixture models of the following kind: </p> 
    230230<p class="formulaDsp"> 
    231 <img class="formulaDsp" alt="\[ f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i) \]" src="form_32.png"/> 
     231<img class="formulaDsp" alt="\[ f(y_t|\psi_t, \Theta) = \sum_{i=1}^{n} w_i f(y_t|\psi_t, \theta_i) \]" src="form_40.png"/> 
    232232</p> 
    233 <p> where <img class="formulaInl" alt="$\psi$" src="form_33.png"/> is a known function of past outputs, <img class="formulaInl" alt="$w=[w_1,\ldots,w_n]$" src="form_34.png"/> are component weights, and component parameters <img class="formulaInl" alt="$\theta_i$" src="form_35.png"/> are assumed to be mutually independent. <img class="formulaInl" alt="$\Theta$" src="form_36.png"/> is an aggregation af all component parameters and weights, i.e. <img class="formulaInl" alt="$\Theta = [\theta_1,\ldots,\theta_n,w]$" src="form_37.png"/>.</p> 
     233<p> where <img class="formulaInl" alt="$\psi$" src="form_41.png"/> is a known function of past outputs, <img class="formulaInl" alt="$w=[w_1,\ldots,w_n]$" src="form_42.png"/> are component weights, and component parameters <img class="formulaInl" alt="$\theta_i$" src="form_43.png"/> are assumed to be mutually independent. <img class="formulaInl" alt="$\Theta$" src="form_44.png"/> is an aggregation af all component parameters and weights, i.e. <img class="formulaInl" alt="$\Theta = [\theta_1,\ldots,\theta_n,w]$" src="form_45.png"/>.</p> 
    234234<p>The characteristic feature of this model is that if the exact values of the latent variable were known, estimation of the parameters can be handled by a single model. For example, for the case of mixture models, posterior density for each component parameters would be a BayesianModel from Exponential Family.</p> 
    235235<p>This class uses EM-style type algorithms for estimation of its parameters. Under this simplification, the posterior density is a product of exponential family members, hence under EM-style approximate estimation this class itself belongs to the exponential family.</p> 
     
    339339</ul> 
    340340</div> 
    341 <hr size="1"/><address style="text-align: right;"><small>Generated on Sun Aug 30 22:10:50 2009 for mixpp by&nbsp; 
     341<hr size="1"/><address style="text-align: right;"><small>Generated on Tue Sep 8 22:11:33 2009 for mixpp by&nbsp; 
    342342<a href="http://www.doxygen.org/index.html"> 
    343343<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.6.1 </small></address>