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<a name="Monte-Carlo-Integration"></a>
<div class="header">
<p>
Next: <a href="Simulated-Annealing.html#Simulated-Annealing" accesskey="n" rel="next">Simulated Annealing</a>, Previous: <a href="N_002dtuples.html#N_002dtuples" accesskey="p" rel="previous">N-tuples</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Monte-Carlo-Integration-1"></a>
<h2 class="chapter">25 Monte Carlo Integration</h2>
<a name="index-Monte-Carlo-integration"></a>
<a name="index-stratified-sampling-in-Monte-Carlo-integration"></a>
<a name="index-multidimensional-integration"></a>
<p>This chapter describes routines for multidimensional Monte Carlo
integration.  These include the traditional Monte Carlo method and
adaptive algorithms such as <small>VEGAS</small> and <small>MISER</small> which use
importance sampling and stratified sampling techniques. Each algorithm
computes an estimate of a multidimensional definite integral of the
form,
</p>
<div class="example">
<pre class="example">I = \int_xl^xu dx \int_yl^yu  dy ...  f(x, y, ...)
</pre></div>

<p>over a hypercubic region <em>((x_l,x_u)</em>, <em>(y_l,y_u), ...)</em> using
a fixed number of function calls.  The routines also provide a
statistical estimate of the error on the result.  This error estimate
should be taken as a guide rather than as a strict error bound&mdash;random 
sampling of the region may not uncover all the important features
of the function, resulting in an underestimate of the error.
</p>
<p>The functions are defined in separate header files for each routine,
<samp>gsl_monte_plain.h</samp>, <samp>gsl_monte_miser.h</samp> and
<samp>gsl_monte_vegas.h</samp>.
</p>
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<tr><td align="left" valign="top">&bull; <a href="Monte-Carlo-Interface.html#Monte-Carlo-Interface" accesskey="1">Monte Carlo Interface</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="PLAIN-Monte-Carlo.html#PLAIN-Monte-Carlo" accesskey="2">PLAIN Monte Carlo</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="MISER.html#MISER" accesskey="3">MISER</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="VEGAS.html#VEGAS" accesskey="4">VEGAS</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Monte-Carlo-Examples.html#Monte-Carlo-Examples" accesskey="5">Monte Carlo Examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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<tr><td align="left" valign="top">&bull; <a href="Monte-Carlo-Integration-References-and-Further-Reading.html#Monte-Carlo-Integration-References-and-Further-Reading" accesskey="6">Monte Carlo Integration References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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