In both cases, these are tag remnants from an older system which was much more haphazardly put together. Sometimes it's easy to deal with. We can just delete and/or blacklist a tag. This can require an enormous amount of time. Currently there are over 2300 questions with only the analysis tag, and probably a few thousands more that would be in dire need of retagging if we remove that tag altogether.
Trying to manually go over these old tags while newbies keep pouring new questions into them is incredibly frustrating, and it truly feels like plugging a hole in a collapsing dam using your finger.
What do I suggest?
I suggest a "deprecated" flag for tags, which will disallow users to add this tag, with perhaps the exception of a rollback feature to ease rolling back defacement.
Of course, deprecation of a tag is a serious business, so it should be done by community managers, at the request of the moderators after a discussion on meta.
Now, I know what you're going to say. You're going to say that many newbies will complain that the system won't let them tag their question with this tag or another, and they get frustrated, and meta gets flooded with newbies etc.
So I suggest that with deprecation of a tag, there will also be a message with a short description of alternative tags and a link to the deprecation-related discussion (or some sort of localized FAQ) to meta to accommodate this confusion.
Let me also point out, this is not just about these two tags. I am sure that other sites on the network could find this feature useful, just like tag blacklisting is useful, even if you end up only blacklisting a handful of tags.