Show HN: An Uncertainty Calculator

Show HN: An Uncertainty Calculator(ollyfg.github.io)

13 points by ollyfg 11 years ago | 11 comments

ollyfg 11 years ago |

Hi, author here, I just want to say that if you happen to know more correct uncertainty propagation for scientific functions, please submit a pull request.

Also, this is aimed at undergraduates, so it ignores covariance.

spacehome 11 years ago | |

What you're really trying to do is interval arithmetic, and it's not calculating it correctly.

For instance: In (a+-b) * (c+-d), you're multiplying the intervals (a-b,a+b) and (c-d,c+d). If all those endpoints are positive, then you get the interval ((a-b) * (c-d),(a+b) * (c+d)).

The answer is then: ((a-b) * (c-d)+(a+b) * (c+d))/2 +- ((a+b) * (c+d) - (a-b) * (c-d))/2

If some of those endpoints have different signs, then you need to break it down into cases.

ollyfg 11 years ago | | |

Wow, this makes a lot of sense. In what ways is this different to the way I was taught through school and university (that for a+-b * c+-d, the answer was (ab)+-sqrt( (b/a)^2) + (d/c)^2 )?

I can see that ((a-b) (c-d)+(a+b) * (c+d))/2 is different to a*b, and that makes sense when you think about it, but the second part is confusing me a bit.

Also, I'm a bit confused by your suggestion to break it down into cases, do you mean if an uncertainty is negative? Because at the moment I'm making all uncertainties positive, but if there are cases where negative ones are correct, I need to fix that up.

TTPrograms 11 years ago | | |

Is uncertainty calculation modeled after a finitely supported variable like this, or is it tracking the variance of operations on gaussians?

bshimmin 11 years ago |

I was sort of hoping it might sometimes result in an answer of "a suffusion of yellow".

spacehome 11 years ago |

I think it doesn't work. It claims:

(1+-2) / (1+-2) = 1+-2.8

When, of course, the result could be any real number.

ollyfg 11 years ago | |

I'm not entirely sure I understand what you're saying here, but I think the difference you're noticing is due to co-variance, and the fact that this calculator doesn't take it into account (or just assumes that it's 0).

For example, when you use covariance properly you could say: x=2+/-2 x-x=0

since covariance = 1

But this calculator assumes that covariance is zero, so it does the calculation (2+/-2) - (2+/-2) = 0+/-sqrt(2^2 + 2^2) = 0+/-2.8

If I'm misunderstanding and this is another problem, please help me, I'm not all that good with uncertainties, but am trying to learn more in this area as it's very useful.

spacehome 11 years ago | | |

The issue is not covariance. And, if you were trying to use my example, you got the numbers and the operation wrong.

There's lots ways to measure uncertainty, but based on this quote "What this means is that the actual length of the pencil could be anywhere between 15.1+0.05cm (15.15cm) and 15.1-0.05cm (15.05cm)." from your page, I infer you're doing interval arithmetic. However, the calculator isn't calculating any measurement of uncertainty correctly. (The mathematics behind multiplying and dividing normally-distributed variables is nuanced and not close to as easy as the addition and subtraction cases.)

I recommend at least reading the Wikipedia article on interval arithmetic: http://en.wikipedia.org/wiki/Interval_arithmetic

alexbecker 11 years ago |

1/(1+-1) = 1+-1

Great idea, but as other comments have noted, completely wrong.