Talk:Numeric error propagation: Difference between revisions

:Indeed it's a correlation issue again. Suppose <math>a = a_0 + \epsilon_a</math>, where <math>\epsilon_a</math> is a random variable with mean 0 and stddev <math>\sigma</math>; similiarly <math>b = a_0 + \epsilon_b</math>, then <math>a\times b = a_0^2 + (\epsilon_a + \epsilon_b) a_0 + O(\epsilon^2)</math>, whose standard deviation is the new error. If <math>\epsilon_a</math> and <math>\epsilon_b</math> are independent but with same stddev, then the <math>\epsilon</math>s are added by RMS and error is <math>\sqrt{2}a_0\sigma</math> (= 282); if they are the same variable (correlation = 1) such as in the case of <math>a^2</math>, <math>\epsilon</math>s are directly added and error is <math>2a_0\sigma</math> (400). As a side note, the <math>O(\epsilon^2)</math> will introduce a bias to the mean of the result, which is normally small and ignored.

:It's more work to keep track what's correlated with what, so for this task you can always assume the error terms are independent. If errors are small compared to mean, this is often acceptible. --[[User:Ledrug|Ledrug]] 00:11, 19 August 2011 (UTC)