### REDCAT Documentation Table of Contents

# 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 ε*i* and -ε*i* 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 ErrorRDC*j*. Here, *j* is the current Monte Carlo sample being taken.

ErrorRDC*i j*= RDC*i* + ε ̂

An new tensor for the current Monte Carlo sample, referred to here as SampleTensor*j*, is then back-calculated from the loaded structure and ErrorRDC*j*. A the new list of RDCs, denoted here as SampleRDC*j*, is calculated from the loaded structure and SampleTensor*j*. For each equation, *i*; we observe the absolute value of the difference of SampleRDC*j i* and RDC*i*. 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 SampleTensor*j* 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 SampleTensor*j* is provided to the user.