> They have different priors and according to CDC a prior exposure to Covid yields better protection than vaccine alone, and vaccine in addition to prior exposure does not yield statistical significant reduction in hazard ratio.

I wouldn't read too much into that:

https://apnews.com/article/coronavirus-pandemic-science-heal...

> The new study’s findings do make sense, said Christine Petersen, a University of Iowa epidemiologist. She said a vaccine developed against an earlier form of the coronavirus is likely to become less and less effective against newer, mutated versions....

> Another thing to consider: The “staunchly unvaccinated” aren’t likely to get tested and the study only included lab-confirmed cases, Wherry said....

> CDC officials noted other limitations. The study was done before the omicron variant took over and before many Americans received booster doses, which have been shown to dramatically amplify protection by raising levels of virus-fighting antibodies. The analysis also did not include information on the severity of past infections, or address the risk of severe illness or death from COVID-19.

> — 6-fold lower in California and 4.5-fold lower in New York in those who were vaccinated but not previously infected.

> — 29-fold lower in California and 15-fold lower in New York in those who had been infected but never vaccinated.

> — 32.5-fold lower in California and 20-fold lower in New York in those who had been infected and vaccinated.

So 29 fold lower rates in California for unvaccinated with prior infection, how much of that do you want to attribute to behavior vs actual immunity? Why is it so unbelievable that getting infected actually gives immunity?