I'm reading "Bernoulli's Fallacy" by Aubrey Clayton and finding it fascinating to understand better the "frequentist" vs. "inference" models for calculating probabilities. Though I'm only understanding about half of it, it seems to be quite controversial in some circles! 🙂
https://www.amazon.com/Bernoullis-Fallacy-Statistical-Illogic-Science/dp/0231199945
Since Bayesian probabilities include assumptions of prior conditions, e.g., the base rate of a disease in a population in conjunction with the accuracy of a test for that disease, I'm wondering how much of this applies to microanalysis. For example, apparently Bayesian models implicitly incorporate meta-analyses from previous studies...
So I asked Google: "are there applications of Bayesian probabilities to x-ray microanalysis?" and it responded: "As a result of the availability of modern software and hardware, Bayesian analysis is becoming more popular in neutron and X-ray reflectometry analysis." and I can actually find some references to using Bayesian probabilities in those fields.
But for microanalysis, I wonder if there are situations where including prior likelihoods could prove useful. For example, one of our colleagues suggested that a Bayesian approach might be useful when determining whether a specific trace element is possibly present or not (e.g., technetium in a natural sample). Since it is extremely unlikely that Tc is present in a geological material, one might want to require stronger evidence than one would typically utilize for trace element determinations.
Also discussed in Bernoulli's Fallacy: have you ever heard of Anscombe's quartet? I hadn't, but it demonstrates the importance of viewing your data graphically before interpreting the statistics. For example, take a look at the quartet data plotted up graphically:
(https://smf.probesoftware.com/gallery/395_22_12_24_2_04_33.png)
https://en.wikipedia.org/wiki/Anscombe%27s_quartet
Now note that the summary statistics are almost identical for all 4 datasets:
(https://smf.probesoftware.com/gallery/395_22_12_24_2_04_44.png)
Wiki sums it up as "The quartet is still often used to illustrate the importance of looking at a set of data graphically before starting to analyze according to a particular type of relationship, and the inadequacy of basic statistic properties for describing realistic datasets."
For fun also check out the Datasaurus:
https://en.wikipedia.org/wiki/Datasaurus_dozen