Democrats are in denial. Their party is actually in deep trouble.

[The Minsky Moment]

It would be silly to revise a prior - even minimally based on a 6-4 split a 10 flips.  A 6-4 split is exactly the kind of result one would expect to see if a fair coin is flipped 10 times.

It's a very likely result for a fair coin.  But it's an even more likely result for a coin that is head-biased.  Of course your revision of a prior would be extremely minimal (and would depend on your initial judgmental confidence in the fairness of the coin), but the prior should still be revised.

But that's a very good example of how you can over-learn some things when getting to classical statistics stage.  A lot of people learn that a small sample size with not unusual outcomes doesn't tell you anything.  That's almost right.  It doesn't tell you a whole lot, but it tells you more than nothing.  Every single coin flip tells you something and should make you update your prior expectation.

I didn't say it tells you nothing.  I said it was silly to revise the prior on that basis.

[DGuller]

I didn't say it tells you nothing.  I said it was silly to revise the prior on that basis.

If it doesn't tell you nothing, then it's silly to NOT revise the prior.  That's precisely the point.  The concept of not changing your prior until some critical mass of contrary evidence accumulates is exactly the classical statistics viewpoint, which is reflected in level 3 thinking of my example.

[DGuller]

But that's a very good example of how you can over-learn some things when getting to classical statistics stage.  A lot of people learn that a small sample size with not unusual outcomes doesn't tell you anything.  That's almost right.  It doesn't tell you a whole lot, but it tells you more than nothing.  Every single coin flip tells you something and should make you update your prior expectation.

This type of micro adjustment is only meaningful if there will be no more trials available (meaning no further adjustment is possible) and there will be a really large number of outcomes that will have to be predicted.  Otherwise a later adjustment of the priors will be greatly more significant or the number of outcomes to be predicted will not meaningfully show the difference between the original prior and the changed one.

You make adjustments as the information comes in.  Yes, if you're making all the decisions only after observing all the 10 coin flips, and there will be no more coin flips after that, then there is no difference between doing 10 small updates or 1 bigger update.  But you're not worse off.

On the other hand, if you have to place your bets continuosly in between the coin flips, then you would've been better off updating your priors continuously.  Obviously all the differences are going to be on an atomic level, I made my example deliberately insignificant, but there is never a reason to act on less information rather than more, if you process it correctly.

[The Minsky Moment]

I didn't say it tells you nothing.  I said it was silly to revise the prior on that basis.

If it doesn't tell you nothing, then it's silly to NOT revise the prior.  That's precisely the point.  The concept of not changing your prior until some critical mass of contrary evidence accumulates is exactly the classical statistics viewpoint, which is reflected in level 3 thinking of my example.

You've completely lost sight of the purpose of statistical tools and reasoning in the first place.  It's not to make ridiculously precise calculations of probabilities based on little evidence.  It's an aid to practical reasoning.  In your example, the data provided is irrelevant on any practical consideration.  It would be foolish to spend even a second of time revising the prior.  It's like a truck at a weighing station in the fall - if a leaf falls on the truck, should you re-weigh?  Yes, there is new data, but so what?

[DGuller]

You've completely lost sight of the purpose of statistical tools and reasoning in the first place.  It's not to make ridiculously precise calculations of probabilities based on little evidence.  It's an aid to practical reasoning.  In your example, the data provided is irrelevant on any practical consideration.  It would be foolish to spend even a second of time revising the prior.  It's like a truck at a weighing station in the fall - if a leaf falls on the truck, should you re-weigh?  Yes, there is new data, but so what?

I didn't say anything about the practicality of it.  In my opinion, for most applications, Bayesian statistics is completely impractical, and classical statistics will serve you well enough.

But it was a thought experiment.  And if you can get your thinking right for the unintuitive and impractical thought experiments like this, it will help you get a grasp of things on a more practical scale as well.

[Razgovory]

DG, you really need to drop this "level" bullshit.

I think the point I'm trying to make it very real, even if I haven't developed it well in this case. 

We'd like to think that as we gain more thorough understanding, our conclusions would become more and more correct without reversals.  What you got right originally you'll still get right, but you'll also get right some of the things that you previously got wrong.  It unfortunately doesn't always work this way.  Sometimes you start off getting things right by dumb luck, then learn enough to be dangerous and thus get wrong some of the things you previous had right.

Even if you have a point, it's not going to work for you.  An argument isn't won by simply telling people that your thoughts are more important and relevant.  People who harp about their own intelligence are at best a bore and more likely a laughing stock.

[DGuller]

DG, you really need to drop this "level" bullshit.

I think the point I'm trying to make it very real, even if I haven't developed it well in this case. 

We'd like to think that as we gain more thorough understanding, our conclusions would become more and more correct without reversals.  What you got right originally you'll still get right, but you'll also get right some of the things that you previously got wrong.  It unfortunately doesn't always work this way.  Sometimes you start off getting things right by dumb luck, then learn enough to be dangerous and thus get wrong some of the things you previous had right.

Even if you have a point, it's not going to work for you.  An argument isn't won by simply telling people that your thoughts are more important and relevant.  People who harp about their own intelligence are at best a bore and more likely a laughing stock.

Of course.  There is a sometimes a difference between truthful statements and convincing arguments.  I wasn't trying to make a convincing argument.  For a large number of reasons, there will never be an argument that will convince Berkut that I understand how I reach my conclusions better than he understands how I reach my conclusions.

[alfred russel]

It's a very likely result for a fair coin.  But it's an even more likely result for a coin that is head-biased.  Of course your revision of a prior would be extremely minimal (and would depend on your initial judgmental confidence in the fairness of the coin), but the prior should still be revised.

You are missing necessary context.

Say I have 2 coins. I tell you one is fair and one is not. I flip one of the coins 10 times, and I get 6 heads. You must now answer whether it is the fair coin I flipped.

I don't know how you make such a prediction. If the non fair coin is weighted to give 60% heads, then the answer is obvious. If it is weighted to give 90% heads, it is also obvious. In the former case, I would agree with you that you are more likely to guess the flipped coin is not fair, but in the latter case the opposite conclusion is the correct one.

What we don't know is what the universe of unfair coins looks like.

[Eddie Teach]

I think his reasoning is that because 5 heads out of 10 is more common than (>6 || <4) heads out of 10, the result is ever-so-slightly more erratic than expected on a fair flip.

[DGuller]

You are missing necessary context.

Yes and no.  It's up to you to decide on how confident you are in the prior.  It can range from "I have absolutely no fucking idea, could be 0% head just as likely as 100% heads or anything in-between", to "Most coins are fair, it's probably fair", even to "Absolutely, positively, absolute zero chance this coin is unfair".  So, yes, there isn't enough information to say exactly whether the chance of heads is now 55%, 50.5%, 50.001%, or even 50%.  But unless you have a dead-certain prior, it's higher than it was before.

It may seem awfully imprecise to introduce judgment into such a mathematical calculation, but that's life.  You have to make a judgment somewhere anyway, so you're better off with a system that accounts for it explicitly.

[Razgovory]

Why are we talking about coin flips now?

[DGuller]

Why are we talking about coin flips now?

We're trying to pass time while waiting for Berkut.

[Eddie Teach]

Why are we talking about coin flips now?

We're trying to pass time while waiting for Berkut.

We could discuss TWD spoilers instead. Carol & Eugene- who saw that coming? 

[DGuller]

How can coin flipping be a boring subject? 

[The Minsky Moment]

I didn't say anything about the practicality of it. 

Right.
Silly.