Brian Cole Jr Trial: Purchase data - Empirically equivalent theories and reasonable doubt.
Empirically equivalent theories: Separate, incompatible theories which make use of the exact same data.
In the case of Brian Cole Jr, the prosecution has a theory that this massive data set of purchases could only exist because Brian Cole built 2 devices on Jan 5th. They further claim that Cole never tested these devices or constructed them again, which means that only 2 pipe nipples and 4 end caps can be attributed to bomb construction. That data can only account for 1/3 of the ingredients of black powder, purchased 3 years before the crime, while necessary purchases only appear after Jan 5th.
The other theory is that these purchases can be attributed to DIY projects and OCD, which Cole was clinically diagnosed with. Cole coherently listed some of the DIY projects he attempted, and said that they were too hard causing him to give up. This fully explains why Cole would purchase 14 pipe nipples over 7 transactions, 33 end caps over 14 transactions, and 800 FEET of electrical wire over 10 transactions.
If we were to focus on JUST the items used on Jan 5th, that would be 13% of the data leaving 87% of the data unaccountable for by any theory of the prosecution since, again, no devices were tested or made afterward. To further complicate matters, these are HOME goods sold at HOME depot and already found in many households. As the image below shows, if you narrow the data to a cherry-picked selection, you can fully control how the data appears.
So how do you separate two empirically equivalent theories? - Explanatory scope. If your theory can only account for 13% of the data, and the other guy's theory accounts for 100% of the data, your theory is probably wrong and certainly incoherent. When it comes to the jury, they will have to rule on reasonable doubt, and 87% of the data left unaccounted for by any theory is a whole lot of reasonable doubt.
Now, you might say he had OCD, did DIY projects, and also built one set of devices. But to do that is to entail that OCD and DIY projects can already fully explain the data. If the data can be fully explained by OCD and DIY projects, then the data itself does not imply or suggest B-building.