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Has the latest update to IsotopeData caused a loss of precision?

Posted 1 month ago
POSTED BY: Otto Linsuain
2 Replies
Posted 1 month ago

Thanks a lot for your reply. This helps a lot. It seems to me that they have tried to incorporate the uncertainty range, which is a good thing, but one can have a poor implementation of a good idea, and it seems that is what has happened here.

The factor of 1.73 may be related to making the assumption of a uniform distribution, as explained here: https://www.itl.nist.gov/div898/handbook/mpc/section5/mpc541.htm

There are serious shortcomings in the implementation:

  1. The default output one gets does not reflect the mean or the range or the scatter of the distribution. One gets 0 and 1, which are very poor approximations.

  2. If one tries to get the best estimate value using, for example, the N function in your reply, one gets the mean of the minimum and the maximum (0.0485 for lithium-6). Normally, the value used for the best estimate for the abundance of lithium-6 is about 0.0759 (the value printed in previous versions), which probably means that the underlying distribution is not symmetric, but this seems to be ignored in the new implementation.

Anyway, thanks a lot again for your input. In a sense, you have put my suspicions on a firmer basis. I really feel I cannot use the new database for any serious calculations.

Best,

Otto LinsuaĆ­n

POSTED BY: Otto Linsuain
Posted 1 month ago

I don't understand how isotopes abundances are determined or how the uncertainties in the measures are modeled probabilistically, But the following comes very close to reproducing the intervals for the isotopes found at https://www.ciaaw.org/lithium.htm:

IsotopeData["Lithium6", "IsotopeAbundance"]/100 // QuantityMagnitude // 
 N@# + 10^-Accuracy[#] 1.73 {-1, 1} &
(*  {0.018917, 0.078083}  -- cf. [0.019, 0.078] (CIAAW) *)

IsotopeData["Lithium7", "IsotopeAbundance"]/100 // QuantityMagnitude // 
 N@# + 10^-Accuracy[#] 1.73 {-1, 1} &
(*  {0.921917, 0.981083}  -- cf. [0.922, 0.981] (CIAAW) *)

I cannot explain the 1.73 scaling factor. It is close, but not very close, to the $z$-score of 1.645, used in say, constructing a 95%-confidence interval. It's closer to $\sqrt{3}$, which means nothing to me.

My understanding extends no farther than the intervals are rather close to the CIAAW intervals, and that the precision in the arbitrary-precision quantities most likely encodes the uncertainty of the value in some form.

POSTED BY: Updating Name
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