A study of Chinese blood donors 2 found that roughly 1 in 100,000 of them had HIV \(as determined by a very reliable gold\-standard test\)\. The non\-gold\-standard test used for initial screening had a sensitivity of 99\.7% and a specificity of 99\.8%, meaning respectively that $~$\\mathbb P({positive}\\mid {HIV}) \= .997$~$ and $~$\\mathbb P({negative}\\mid \\neg {HIV}) \= .998$~$, i\.e\., $~$\\mathbb P({positive} \\mid \\neg {HIV}) \= .002.$~$

It is really confusing to apply one of the initial steps of a study as evidence to a prior which is the **result** (last step) of the same study.