# What does "fidelity" mean?

In particular I am interested in whether it is more closely related to "precision" or "accuracy". So a somewhat mathematical description might be appropriate.

For example the word "fidelity" occurs at 23:54 in the BICEP2 press release video, where it is emphasised as being different to sensitivity.

• From context, it appears fidelity is to sensitivity as accuracy is to precision. Fidelity is also a term in quantum mechanics though I doubt it's relevant. Commented Jan 6, 2016 at 22:53
• @knzhou Do you think that fidelity has a strict and agreed upon definition, or it was just the word that happened to be chosen at the spur of the moment? Commented Jan 6, 2016 at 23:33
• I think the latter. I'm no experimentalist though. Commented Jan 6, 2016 at 23:33
• FWIW, a "Hi-Fi" (high fidelity sound system) reproduced recorded music with high accuracy, i.e., without adding significant noise and (linear and non-linear) distortion. Commented Jan 7, 2016 at 1:17

Warning - a certain amount of personal interpretation here.

I would say that it has to first be accuracy and next precision. Here is my reasoning:

You can have a very precise measurement (when you repeat it 100 times, you get the same answer within 0.1%) that has a large systematic error (bias) - for example, measuring a length with a ruler that has a worn end. Such a measurement is not faithful to the thing being measured - it's "low fidelity".

If you have a measurement that is accurate but has low precision, you can repeat it 100 times and you will slowly converge on the correct answer (since accuracy implies low bias).

This makes accuracy more important - and means that "fidelity" in a measurement, while really requiring a fair amount of both, should primarily be equated with accuracy.

• Incidentally, "Hi-Fi" used to be the common word for a quality sound system - abbreviation of "high fidelity"... Commented Jan 8, 2016 at 2:24

I've used the term most often to describe the quality of a mathematical model relative to how well it can predict a real physical process. One speaks of a high fidelity model as one that can faithfully predict outcomes from measurements.

It would be in reference to precision. This may sound pendantic, but every measurement in science has some degree of error no matter how small. These small errors are important, because if they repeat in subsequent experiments, then a pattern is realized. The reproducability of errors that make patterns reveal degrees of precision, (among other things). This is a critical distinction from the notion of accuracy, which assumes a thing is perfectly known. I would expect the use of the term 'fidelity' is in reference to precision, as accuracy is a unicorn in science.