MCMulti
Provides for the integration of a multidimensional function via Monte-Carlo sampling. The user is responsible for providing a function that when evaluated at the sample from the provided sampler will evaluate to the desired integral over the range of possible values of the sampler.
The sampler must have the same range as the desired integral and the function's domain (inputs) must be consistent with the range (output) of the sampler. There is no checking if the user does not supply appropriate functions or samplers.
As an example, suppose we want the evaluation of the integral of g(x) over the range from a to b. If the user selects the sampler as U(a,b) then the function to supply for the integration is NOT g(x). The function should be h(x) = (b-a)*g(x).
In general, if the sampler has pdf, w(x), over the range a to b. Then, the function to supply for integration is h(x) = g(x)/w(x). Again, the user is responsible for providing a sampler that provides values over the interval of integration. And, the user is responsible for providing the appropriate function, h(x), that will result in their desired integral. This flexibility allows the user to specify h(x) in a factorization that supports an importance sampling distribution as the sampler.
See the detailed discussion for the class MCExperiment.
Parameters
the representation of h(x), must not be null
the sampler over the interval, must not be null
true represents use of antithetic sampling
See also
The evaluation will automatically utilize antithetic sampling to reduce the variance of the estimates unless the user specifies not to do so. In the case of using antithetic sampling, the sample size refers to the number of independent antithetic pairs observed. Thus, this will require two function evaluations at each observation. The user can consider the implication of the cost of function evaluation versus the variance reduction obtained.