Quantifying Uncertainty in Ecosystem Studies

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3/23/2015 12:51 pm  #1


What to do when random sampling produces impossible values

When sampling from a normal distribution, we can get negative concentrations, negative masses for trees, and the like.  Do these come out in the wash?  Some people delete the negative values, which introduces bias.

 

3/23/2015 1:12 pm  #2


Re: What to do when random sampling produces impossible values

Can you give more context for the random sampling that you are implementing? Is it just for calculating a standard error? Is it for error propagation?

 

3/23/2015 1:16 pm  #3


Re: What to do when random sampling produces impossible values

For example, we want to know the uncertainty in stream export of solutes that have analytical uncertainty.  If that uncertainty is described with a standard deviation, then we get rare negative numbers.  The same thing happens with a log-log regression describing tree biomass as a function of diameter.  The uncertainty in the regression can give us trees with negative mass.

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3/23/2015 4:12 pm  #4


Re: What to do when random sampling produces impossible values

You could choose a different distribution for what you are sampling from. It's possible to sample from a lognormal distribution instead of a normal distribution. The lognormal has the structure of having a non-negative support. I think if you use a normal distribution it may simplify the derivations of certain expressions (like error propagation). There are resources out there for you to use that can explain how to do so and what CI's or standard errors look like for a lognormal distribution. A lot of these might be in the health field as the lognormal distribution is really popular in pharmaceutical/clinical trials research for some reason.

 

4/29/2015 12:21 pm  #5


Re: What to do when random sampling produces impossible values

No idealized distribution will be a perfect fit. So just because you get some negatives doesn't mean that it isn't a good fit (otherwise the normal distribution would never be useful). I think you should be safe including them as long as you aren't trying to calculate any statistics at the tail (ie. if 95th percentile confidence intervals fall below zero there might be a problem). If you truncate the distribution by dropping those values you risk biasing other statistics.

Last edited by TimIvancic (4/29/2015 12:24 pm)

 

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