"It is a shame that Bayesian methods are not part of all introductory statistics classes." I don't know if they are now.
I'm a grad student/TA in the statistics department at Iowa State University. Bayes doesn't make it into any of our intro classes outside of maybe introducing Bayes' theorem... but I doubt it. It also doesn't make it into our stat classes for non-major grad students. Some non-stat major grad students take master's level stat courses instead. They introduce some Bayesian material depending on the prof, but not much. There is also a master's level course in Bayesian methods, and new PhD level Bayesian courses in both methods and theory.
Relevant info: our dept. is in the top 10 in the US and so relatively typical, but it is also known for being a bastion of frequentism. Bayesians are making inroads in the department though, but intro classes at Duke, for example, might be much more Bayesian.
In a recent article, John Ioannidis describes a very high proportion of medical research as wrong.
Part of the problem is that surprising results get more interest, and surprising results are more likely to be wrong. (I'm not dead certain of this-- if the baseline beliefs are highly likely to be wrong, surprising beliefs become somewhat less likely to be wrong.) Replication is boring. Failure to replicate a bright shiny surprising belief is boring. A tremendous amount isn't checked, and that's before you start considering that a lot of medical research is funded by companies that want to sell something.
Ioannidis' corollaries:
The culture at LW shows a lot of reliance on small inferential psychological studies-- for example that doing a good deed leads to worse behavior later. Please watch out for that.
A smidgen of good news: Failure to Replicate, a website about failures to replicate psychological findings. I think this could be very valuable, and if you agree, please boost the signal by posting it elsewhere.
From Failure to Replicate's author-- A problem with metastudies:
The people I've read who gave advice based on Ioannidis article strongly recommended eating paleo. I don't think this is awful advice in the sense that a number of people seem to actually feel better following it, and I haven't heard of disasters resulting from eating paleo. However, I don't know that it's a general solution to the problems of living with a medical system which does necessary work some of the time, but also is wildly inaccurate and sometimes destructive.
The following advice is has a pure base of anecdote, but at least I've heard a lot of them from people with ongoing medical problems. (Double meaning intended.)
Before you use prescription drugs and/or medical procedures, make sure there's something wrong with you. Keep an eye out for side effects and the results of combined medicines. Check for evidence that whatever you're thinking about doing actually helps. Be careful with statins-- they can cause reversible memory problems and permanent muscle weakness. Choose a doctor who listens to you.
Forum about self-experimentation-- note: even Seth Roberts is apt to oversell his results as applying to everyone.
Link about the failure to replicate site found here.