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# 23. Monte Carlo Integration

This chapter describes routines for multidimensional Monte Carlo
integration. These include the traditional Monte Carlo method and
adaptive algorithms such as VEGAS and MISER which use
importance sampling and stratified sampling techniques. Each algorithm
computes an estimate of a multidimensional definite integral of the
form,
over a hypercubic region *((x_l,x_u)*, *(y_l,y_u), ...)* 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—random
sampling of the region may not uncover all the important features
of the function, resulting in an underestimate of the error.

The functions are defined in separate header files for each routine,
`gsl_monte_plain.h`

, ‘`gsl_monte_miser.h`’ and
‘`gsl_monte_vegas.h`’.

23.1 Interface | ||

23.2 PLAIN Monte Carlo | ||

23.3 MISER | ||

23.4 VEGAS | ||

23.5 Examples | ||

23.6 References and Further Reading |