2.4  Adaptive and Stratified sampling

Another strategy to improve sampling in simulations is adaptive importance sampling (also called variance reduction technique), where McStas during the simulations will determine the most interesting directions and gradually change the focusing according to that. Implementation of this idea is found in the Source_adapt and Source_Optimizer components.

An other class of efficiency improvement technique is the so-called stratified sampling. It consists in partitioning the event distributions in representative sub-spaces, which are then all sampled individually. The advantage is that we are then sure that each sub-space is well represented in the final integrals. This means that instead of shooting \(N\) events, we define \(D\) partitions and shoot \(r=N/D\) events in each partition. In conjunction with adaptive sampling, we may define partitions so that they represent ’interesting’ distributions, e.g. from events scattered on a monochromator or a sample. The sum of partitions should equal the total space integrated by the Monte Carlo method, and each partition must be sampled randomly.

In the case of McStas, an ad-hoc implementation of adaptive stratified is used when repeating events, such as in the Virtual sources (Virtual_input, Vitess_input, Virtual_mcnp_input, Virtual_tripoli4_input) and when using the SPLIT keyword in the TRACE section on instrument descriptions. We emphasize here that the number of repetitions \(r\) should not exceed the dimensionality of the Monte Carlo integration space (which is \(d=10\) for neutron events) and the dimensionality of the partition spaces, i.e. the number of random generators following the stratified sampling location in the instrument.