Bayesian Statistics

[John 6IX Breezy]

Unfortunately, the standard curriculum in psychology often doesn't include Bayesian approaches to statistics, only frequentist ones. So I've always struggled to understand it conceptually.

I think part of my struggle comes from the hype around it being overly ambitious and taking it's inferences out of context (I think). You'll hear people say it's a way to update your beliefs, but since regular statistics isn't about beliefs it already feels like a separate thing all together.

Point is I'm trying to understand Bayesian statistics. So I'm curious what everyone's experience with it has been. What textbooks or resources you recommend. And any theoretical issues or debates you guys have with it.

[HappySkeptic]

As you say, Bayesian statistics are about updating prior probabilities (beliefs). They can be used for decision making, but it takes a lot of data to update a bad prior probability (especially if close to 1.0 or 0.0).

If we start with a prior probability of 0.5 for the existence of a biblical God, I wonder how many pieces of evidence we could come up with to get it towards 0? I think it would be pretty easy.

[tackattack]

statistics on the level of evidence required for belief.... too math-y for me 

[John 6IX Breezy]

If we start with a prior probability of 0.5 for the existence of a biblical God...

How do you calculate that initial probability? Or does it not matter, such that it could be .5 for you but .75 for someone else?

I've heard there is a subjective element to Bayesian statistics but I'm not sure if this is where it comes in.

[HappySkeptic]

Whether the prior probability is a guess, or based on sound reasoning doesn't matter. Eventually, data will update the probability toward a better guess via inference.

However, a guess of 0 or 1 never updates.

Ideally, one would use the best available data (i.e. an initial distribution of data, or a result of previous Bayesian analysis). When applied to a scientific theory, the prior probability would be a guess of the certainty around the null hypothesis.

[Jehanne]

Bayesian Statistics is pretty standard and treatments of it can be found all throughout the undergraduate curriculum. Professor Sheldon M. Ross' undergraduate text "Introduction to Probability and Statistics for Engineers and Scientists" has a good introduction.

[John 6IX Breezy]

When applied to a scientific theory, the prior probability would be a guess of the certainty around the null hypothesis.

Hmm does the Bayesian approach still aim to reject the null hypothesis? Because the process of updating priors sounds like its doing something else, or doing it less directly.

[brewer]

Not familiar with 'Bayesian Statistics', but I agree with you (I think). Bayesian logic application to psychiatric/psychological conditions seems ilimited. Basically because each individual and their underlying condition is often unique. The logic might be able to set up broad diagnostic/treatment generalities, but individual conditions are, well, individual and require individualized treatment.

That's where the 'art' portion of medicine/treatment is applicable.

[John 6IX Breezy]

Bayesian logic application to psychiatric/psychological conditions seems ilimited. Basically because each individual and their underlying condition is often unique. The logic might be able to set up broad diagnostic/treatment generalities, but individual conditions are, well, individual and require individualized treatment.

That's where the 'art' portion of medicine/treatment is applicable.

Well, that's actually what I'm starting to find interesting. I think traditional "frequentist" statistics aligns better with scientific research in the way that it can falsify hypothesis and describe data. But the individual is typically lost within this data. Now, if I'm understanding Bayesian statistics correctly, it means that for clinical purposes I can start off knowing the prior population data for a treatment and then begin to update it so that it's starts to describe an individual more and more.

[brewer]

Bayesian logic application to psychiatric/psychological conditions seems ilimited. Basically because each individual and their underlying condition is often unique. The logic might be able to set up broad diagnostic/treatment generalities, but individual conditions are, well, individual and require individualized treatment.

That's where the 'art' portion of medicine/treatment is applicable.

Well, that's actually what I'm starting to find interesting. I think traditional "frequentist" statistics aligns better with scientific research in the way that it can falsify hypothesis and describe data. But the individual is typically lost within this data. Now, if I'm understanding Bayesian statistics correctly, it means that for clinical purposes I can start off knowing the prior population data for a treatment and then begin to update it so that it's starts to describe an individual more and more.

OK. You can start out with the stats and use it for a general starting diagnostic/treatment point but I think that as you get to know the individual and their condition the treatment may vary. Sometimes enough that you'll need to re-categorize the individuals condition/diagnosis/treatment.

When it comes to psych individuals are, well, lets say tricky. They can initially present as something that they are not.