The purpose of this document is to explain how Mantid deals with Error Propogation and how it is used in its algorithms.
In order to deal with error propagation, Mantid treats errors as guassian probabilities (also known as a bell curve or normal probabilities) and each observation as independent. Meaning that if X = 100 +- 1 then it is still possible for a value of 102 to occur, but less likely than 101 or 99, and a value of 105 is far less likely still than any of these values.
The plus algorithm adds a selection of datasets together, including their margin of errors. Mantid has to therefore adapt the margin of error so it continues to work with just one margin of error. The way it does this is by simply adding together the certain values. Consider the example where: X1 = 101 ± 2 and X2 = 99 ± 2. Then for the Plus algorithm
X = 200 = (101 + 99).
The propagated error is calculated by taking the root of the sum of the squares of the two error margins:
(√2:sup:2 + 22) = √8
Hence the result of the Plus algorithm can be summarised as:
X = 200 ± √8
Mantid deals with the Minus algorithm similarly.
The Multiply and Divide Algorithm work slightly different from the Plus and Minus Algorithms, in the sense that they have to be more complex, see also here.
To calculate error propagation, of say X1 and X2. X1 = 101 ± 2 and X2 = 99 ± 2 ,Mantid would undertake the following calculation for divide:
Q = X1/X:sub:2 = 101/99
Error Propogation = (√ ± 2/99 + ±2/101) All multiplied by Q = 0.22425
For the multiply algorithm, the only difference is in how Q is created, which in turn affects the Error Propogation,
Q = X1*X2 = 101*99
Error Propogation = (√ ± 2/99 + ±2/101) All multiplied by Q = 0.22425
Category: Concepts