s in the chain approaches the target
distribution and in that limit the expected value of the Monte Carlo
estimator of any integrable function converges to the true
expectation. There is nothing like warmup here, because in the limit,
the effects of initial state are completely washed out.</p>
</div>
<div id="multivariate-convergence-of-functions" class="section level4">
<h4 number="16.3.3.2"><span class="header-section-number">16.3.3.2</span> Multivariate convergence of functions</h4>
<p>The <span class="m