Monte Carlo (MC) integration 

The basic idea that underlies Monte Carlo (MC) integration is that properties of random variables (such as the mean) can be studied by simulating many instances of a variable and analysing the results. Each replicate of the MC simulations is independent and the procedure is therefore equivalent to taking repeated samples from a Markov chain that is ‘stationary’ at points that are sufficiently separated so that they are not correlated. MC integration has been widely applied in statistical genetics. The MC simulation method has the advantage that the estimates obtained are unbiased and the standard error of the estimates can be accurately estimated because the simulated random variables are independent and identically distributed. A disadvantage is that with complex multidimensional variables that have a large state space (for example, a range of possible values), enormous numbers of replicate simulations are needed to obtain accurate parameter estimates. (Beaumont 2004)