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Lets say we have two things as input, $N$ scalars (measurements) that we know are erroneous to some degree (i.e. the correct values are somewhat similar).

In addition, we also have a roughly more reliable order $O$ among the measurements. Using the ordering:

$O = <u_1, u_2, u_3 ... u_n>$ we can deduct that with some known probability, $p > 0.5$ the ordering is correct, $[i \geq j \rightarrow u_i \geq u_j]$ is true. Now, how would you then adjust the scalar values accordingly?

Currently:

  1. Creating a new set of values, cloning the original scalars.
  2. Making the minimal needed changes in order to satisfy the order. i.e. slightly increasing or decreasing the original values until we get a corrctly ordered $\{v_1, v_2, v_3 ... v_n\}$ such that $\sum\limits_{i=1}^n (u_i - v_i)^2$ is minimal.
  3. Doing a weighted average between the newly generated values and the original ones, using $p$ as the weight for the new value.

While $p$ is unknown, we can guesstimate it from data that is manually inspected.

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  • $\begingroup$ I have a hard time understanding your question. Statements like "after than, modifying each value with a weighted average with the new value, using p as the weight for the new value" are just difficult to translate into a concrete formula or algorithm. Can you rewrite your question with more details? As a side question, do you know the probability $p$ for each pair $i,j$? $\endgroup$ – Wolfgang Bangerth Jul 2 '15 at 23:24
  • $\begingroup$ @WolfgangBangerth Thanks.. I will fix the broken English. $\endgroup$ – AturSams Jul 4 '15 at 13:19

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