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    65 <h1><a class="anchor" id="user_guide2">BDM Use - Estimation and Bayes Rule </a></h1><p>Baysian theory is predominantly used in system identification, or estimation problems. This section is concerned with recursive estimation, as implemneted in prepared scenario <code>estimator</code>.</p> 
     65<h1><a class="anchor" id="userguide2">BDM Use - Estimation and Bayes Rule </a></h1><p>Baysian theory is predominantly used in system identification, or estimation problems. This section is concerned with recursive estimation, as implemneted in prepared scenario <code>estimator</code>.</p> 
    6666<p>The function of the <code>estimator</code> is graphically illustrated: </p> 
    6767<div align="center"> 
     
    7575<li>Result Logger is an object (class logger) dedicated to storing important data from the experiment.</li> 
    7676</ul> 
    77 <p>Since objects datasource and the logger has already been introduced in section <a class="el" href="user_guide.html">BDM Use - System, Data, Simulation</a>, it remains to introduce object <code>Bayesian</code> <code>Model</code> (<a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.">bdm::BM</a>).</p> 
     77<p>Since objects datasource and the logger has already been introduced in section <a class="el" href="userguide.html">BDM Use - System, Data, Simulation</a>, it remains to introduce object <code>Bayesian</code> <code>Model</code> (<a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.">bdm::BM</a>).</p> 
    7878<h2><a class="anchor" id="ug2_theory"> 
    7979Bayes rule and estimation</a></h2> 
     
    9595<h2><a class="anchor" id="ug2_arx_basic"> 
    9696Estimation of ARX models</a></h2> 
    97 <p>Autoregressive models has already been introduced in <a class="el" href="user_guide.html#ug_arx_sim">Simulating autoregressive model</a> where their simulator has been presented. We will use results of simulation of the ARX datasource defined there to provide data for estimation using MemDS.</p> 
     97<p>Autoregressive models has already been introduced in <a class="el" href="userguide.html#ug_arx_sim">Simulating autoregressive model</a> where their simulator has been presented. We will use results of simulation of the ARX datasource defined there to provide data for estimation using MemDS.</p> 
    9898<p>The following code is from bdmtoolbox/tutorial/userguide/arx_basic_example.m </p> 
    9999<div class="fragment"><pre class="fragment">A1.class = <span class="stringliteral">&apos;ARX&apos;</span>; 
     
    105105<ul> 
    106106<li>logbounds - store also lower and upper bounds on estimates (obtained by calling BM::posterior().qbounds()),</li> 
    107 <li>logll - store also loglikelihood of each step of the Bayes rule. These values are stored in given logger (ug_loggers). By default, only mean values of the estimate are stored.</li> 
     107<li>logll - store also loglikelihood of each step of the Bayes rule. These values are stored in given logger (<a class="el" href="userguide.html#ug_loggers">Loggers for flexible handling of results</a>). By default, only mean values of the estimate are stored.</li> 
    108108</ul> 
    109109<p>Storing of the log-likelihood is useful, e.g. in model selection task when two models are compared.</p> 
     
    193193 <p>Note: error bars in this case are not directly comparable with those of previous examples. The MPF class implements the qbounds function as minimum and maximum of bounds in the condidered set (even if its weight is extreemly small). Hence, the bounds of the MPF are probably larger than it should be. Nevertheless, they provide great help when designing and tuning algorithms. </p> 
    194194</div> 
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    197197<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.6.1 </small></address>