It is patently clear that research preprints should be posted immediately to ones personal website, but it probably also makes sense to post your work on one of the general purpose preprint servers.
For more mathematical preprints Math ArXiv seems to be the server of choice. One finds a considerable amount of probability and statistics here, but new machine learning work seems to go to other servers. As I scope these out, I will up-date this page.
[Much more to come on this snippet. The web puts all editorial gate keeping to the test, but mathematical writing seems particularly well adapted to internet publication. Why put something in a journal that sits on the paper for two years, has 400 library subscriptions, and no individual subscriptions. Is the paper imprint really that much more "immortal" than a mirrored electronic imprint. I don't think so....anyway, more later]