Monte Carlo Sampling

An important feature of REDCAT's analysis is its use of Monte Carlo sampling of the solution space. This is done by taking the loaded RDCs and adding to each a random number between εi and -εi where i is the equation number, and ε is the error specified in the Main window for that equation. We will call this random number ε ̂, and we will refer to the new list of RDC data, as ErrorRDCj. Here, j is the current Monte Carlo sample being taken.

ErrorRDCi j= RDCi + ε ̂

An new tensor for the current Monte Carlo sample, referred to here as SampleTensorj, is then back-calculated from the loaded structure and ErrorRDCj. A the new list of RDCs, denoted here as SampleRDCj, is calculated from the loaded structure and SampleTensorj. For each equation, i; we observe the absolute value of the difference of SampleRDCj i and RDCi. If the absolute difference is larger than ε, then equation i contributes to the rejection of the Monte Carlo sample. In this case, we say Monte Carlo sample j fails and will not present SampleTensorj to the user. The number of failures that a single equation contributes to is accumulated and provided to the user for analysis purposes. If none of the equations are beyond error, then the Monte Carlo sample passes and SampleTensorj is provided to the user.