Bayesian statistics

So there is some, I think like Avi Feller and some other people have done some Bayesian principles graphification models in Stan.

And the idea is that you would characterize people that there's a latent variable.

Well, it's observed for the people who got the mailer and not observed for the others.

But basically you have to model the whole process.

I haven't done this myself, but I know people have done it.

It seems like a very natural Bayesian problem.

And I think that standard solutions such as instrumental variables would correspond to special cases of this model, assuming various things are zero or with flat priors and various...

Usually standard procedures usually correspond to some mix of some flat priors and some parameters and priors with spikes at zero on others.

And

speaking of stats, in this study, instead of doing exactly what you just laid out, they used a Bayesian multi-level meta-regression and simultaneously tested linear and non-linear models controlling for volume, intervention duration, training status, etc.

And, drumroll, For hypertrophy, they found that there was a negligible independent effect of frequency on muscle growth and essentially confirmed that with parallel analysis where they did contrast-based two-stage meta-regression using only direct frequency comparison, and they couldn't find an independent effect of frequency on hypertrophy.

For strength, things were a bit different.

Yeah, so let me just try and find the 95% highest density interval.

So I'll just kind of describe what that actually is for a listener as I try and look for it.

One of the strengths of Bayesian statistics is that it allows you to more directly estimate the range within which the true effect of, for example, higher frequencies false so you can say with a 95 percent credibility interval for example that there truly is a 95% chance that the true effect of higher versus lower frequencies on hypertrophy falls within a certain range.

For example, let's say it causes from, as an example, from 5% more relative growth to 45% more relative growth, with the midpoint being around 22.5 or whatever it is.

In two thousand eleven, three physicists named Mihran Vardanyan, Roberto Trotta, and Joseph Silk published a paper that put a specific number on this.

Using a statistical technique called Bayesian model averaging, a way of combining the predictions of multiple cosmological models weighted by how well each fits the data, they calculated a conservative lower bound on the size of the universe.

The Bayesian approach is worth a moment of explanation.

Most statistical methods ask, given my model, how well does it fit the data? Bayesian model averaging asks something different.

Given my data, which of my possible models is most likely to be correct? It is a form of statistical reasoning that combines evidence across multiple hypotheses rather than committing to a single one.

For the size of the universe, this approach combines estimates from different cosmological assumptions, closed universe, flat universe, open universe, weighted by how well each model fits the observed data.

The light from the most distant of them had been traveling for nearly the entire age of the universe.

But there was still no clear understanding of how large the universe actually was beyond what we could observe.