title: Why does JAGS require at least two chains to calculate DIC?
body: <p>I'm trying to understand how JAGS calculates deviance and the <a href="http://en.wikipedia.org/wiki/Deviance_information_criterion" rel="nofollow">Deviance Information Criterion</a> (DIC). </p>
  
  <p>The <code>dic.samples</code> function in <code>rjags</code> in R throws an error if you have only one chain.</p>
  
  <pre><code>stop("2 or more parallel chains required")
  </code></pre>
  
  <p>The formula for calculating DIC involves calculating the expected deviance and the deviance at the expected values of the parameters in the model. I imagine such estimates could be obtained from a single chain (albeit there might sometimes be convergence issues that can only be identified with more than one chain).</p>
  
  <p>The manual states that:</p>
  
  <blockquote>
    <p>The pD monitor estimates the contribution to the effective number of
    parameters (pD) [3] from an observed stochastic node by comparing the
    deviance deviance across multiple chains [1]. It is created by using
    the option type(pD). If the model has only one chain then a pD monitor
    cannot be defined.</p>
  </blockquote>
  
  <p>So my question is:</p>
  
  <ul>
  <li>Why does JAGS require at least two chains to calculate DIC?</li>
  <li>Or more specifically, why does the pD monitor require two chains?</li>
  </ul>