Bayesian inference

Those who reacted with indignation or confusion that one would call it worse.

Isaac King challenges that no, you would have interpreted any number as worse, you're supposed to be Bayesians.

To which I reply that this is not the case.

I would prefer to see less attempts than soul in a way that lines up with other observations in the model card.

So we'll call this the truncated window hypothesis.

So in my new paper I throw the awesome power of Bayesian statistics at these two puzzles to figure out which explanation, if any, works.

The two puzzles represent our data, or here our observations, features that require explanation by our model.

And here our model actually encompasses all three hypotheses.

Let's use the symbol TWin.

Subtly, the look hypothesis is implicitly built into this because we can always evaluate this model at the extreme ends where both effects are negated.

So, in Bayesian parlance, our task is to figure out or infer this probability distribution.

The probability of getting various values of mcrit and twin given the data in hand, which here is our two puzzles.

And this is the percentage of participants with treatment-related adverse events or serious adverse events, again, within 30 days after surgery.

We used a pre-specified Bayesian analysis method, which combines prior evidence with current trial data, as is the appropriate framework within Bayesian analysis.

Bayesian analysis provides a posterior probability, i.e. looking back at the study as to whether a real treatment benefit exists.

You can compare this to a frequentist analysis, which is a more complex statistical question of whether the treatment could have produced an outcome that it did, should the hypothesis have been it didn't, which is a rather complex statistical question.

This question, whether or not a likelihood is a real treatment benefit exists, is an appropriate one for a study like ours.

There are hospitals with fewer beds in one surgical category than another.

There are hospitals that take patients from certain populations within the community and not others.

not a homogeneous income population and sparse outcomes ideal for Bayesian analysis.

Sure, sure.

So I do something where I've found, you know, it's a Bayesian model where it uses what they call the normal, normal distribution.

So it assumes, which is roughly correct, that there is a normal distribution of performance when we look at a quarterback level for their efficiency.

So I'm looking at that.

I think really after a full season, you don't care about draft position that much, but especially after two years in the NFL.

Yeah.

So let me ask you, thanks to Cade for putting your Bayesian quarterback rankings into the rundown.

I'm surprised.

Those who reacted with indignation or confusion that one would call it worse.

Isaac King challenges that no, you would have interpreted any number as worse, you are supposed to be Bayesians.

To which I reply that this is not the case.

I would prefer to see less attempts than Sol in a way that lines up with other observations in the model card.

Isaac King challenges that, "No, you would have interpreted any number as worse.

You're supposed to be Bayesians." To which I reply that this is not the case.

I would prefer to see less attempts than Sol in a way that lines up with other observations in the model card.

I would see this as good news on the margin up until a roughly fifty percent to seventy-five percent reduction in attempts.