<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
    <meta content="text/html; charset=ISO-8859-1"
          http-equiv="content-type">
    <title>PM</title>
</head>
<body vlink="#551a8b" alink="#ee0000" link="#0000ee"
      style="color: rgb(0, 0, 0);">
<table width="95%" border="1" bgcolor="maroon">
    <tr>
        <td><h2><font color="#FFFFFF">Bayes Parametric Model </font></h2></td>
    </tr>
</table>
<h3><br>
    Description of Model <span
            style="font-family: mon;">    </span></h3>
<p>Bayes Parametric Model (Bayes PM) takes a DAG and adds to it two bits of information:</p>
<ol>
    <li>For each named node in the graph, the <em>number of categories</em> for the variable by that name.</li>
    <li>For each variable, with a given number of categories, the <em>list of category names</em> for that variable.
    </li>
</ol>
<p>Given the graph and the additional information in (1) and (2), a Bayes net can be formally specified; it is
    determined what all the parameters of the Bayes net are, although no values for parameters are yet known. To specify
    a Bayes net up to parameter values, a Bayes Instantiated Model must be constructed, based on a Bayes PM. For details
    on the parameters of a Bayes IM, see <a href="../im/bayes_im.html">Bayes Instantiated Model</a>.</p>
<p>It is assumed in the current version of Tetrad that all discrete variables are nominal--that is, that the order of
    their categories is not important. See <a href="../../common_tasks/defining_discrete_variables.html">Defining
        Discrete Variables</a> for more details. </p>
<h3><br>
    How to Construct a Bayes PM</h3>
<p>For example, say you put the following boxes on the session, connected as follows:</p>
<p><img src="../../images/bayespm1.gif" width="188" height="65"></p>
<p>For example, say you start with this DAG. (It need not be, specifically, in a Directed Acyclic Graph box; all that
    matters is that it contain only directed edges with no cycles.)</p>
<p><img src="../../images/bayespm2.gif" width="587" height="577"></p>
<p>If you click &quot;Save&quot; and double click the PM1 box, you are given a choice of which model type you would like
    to construct. Choose &quot;Bayes Parametric Model.&quot;</p>
<p><img src="../../images/bayespm3.gif" width="300" height="138"></p>
<p>Once you click OK, the following dialog appears:</p>
<p><img src="../../images/bayespm4.gif" width="921" height="561"></p>
<p>In this dialog, you can click on a variable and edit its number of nodes and category names. For instance, we can
    change the number of categories for X1 to 3 and set its categories to &lt;Low, Medium, High&gt;.</p>
<p><img src="../../images/bayespm5.gif" width="920" height="560"></p>
<p>When you're finished editing categories for variables, click &quot;Save.&quot; <br>
</p>
<h3>Potential Parents for Bayes Parametric Model </h3>
<p>The Bayes PM can take any graph as parent that contains a DAG--that is, a graph that contains only directed edges (--&gt;)
    with no cycles (i.e. there is no X such that X--&gt;...--&gt;X in the graph). The simplest option is to construct
    Directed Acyclic Graph in the Graph box. (See <a href="../graph/dag.html">Directed Acyclic Graph</a> for more
    details.) If the parent is not a DAG, an error message will be displayed when the Bayes PM is constructed.</p>
</body>
</html>
