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Objective Bayesian Hypothesis Testing

objectivebayesian.com

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Re: Objective Bayesian Hypothesis Testing

#11

Post by LegionMammal978 »

shiandow wrote: post #10
Vecr wrote: post #9

Earlier quoted context omitted.

Why would you care about that though? Calculate the odds between your hypotheses, not the probability you'd ever see one.

The Bayesian stance is that you should not care. The frequentist stance is that a test that has a p-value of 1 is the worst possible. My stance is that you should know why to care about either. Oh and that the thing you're calculating an expected value off should somehow contribute linearly to your profits/costs, averages do strange things to nonlinear functions.

Eh, even an expected value that's linear with respect to profits can end up with strange results like the St. Petersburg paradox. In general, naively maximizing it breaks down at the point where you stop being insensitive to the possible risks.

Re: Objective Bayesian Hypothesis Testing

#14

Post by nalzok »

kqr wrote: post #8
vcdimension wrote: post #3

This article is very interesting and informative, however it's a bit ironic that an article about misinterpretations of the meaning of the p-value, misinterprets the misinterpretation; in the first blue box it's clear that Bernstein is interpreting the p-value as the probability of randomly rejecting the null (which is what you do when you get something statistically significant) yet in the text following that they s…

> correct interpretation; p-value = Prob(rejecting the null when the null is true) This is also not quite correct. The p-value is the probability of falsely rejecting the null due to sampling error . It is quiet on all other errors that are frequently committed. The real probability of falsely rejecting the null starts at 15 % thanks to mathematical slip-ups alone: https://two-wrongs.com/the-lying-p-value

> by kqr, published 2024-11-19

It's from the future! ;)

Re: Objective Bayesian Hypothesis Testing

#16

Post by shiandow »

LegionMammal978 wrote: post #11
shiandow wrote: post #10

Earlier quoted context omitted.

The Bayesian stance is that you should not care. The frequentist stance is that a test that has a p-value of 1 is the worst possible. My stance is that you should know why to care about either. Oh and that the thing you're calculating an expected value off should somehow contribute linearly to your profits/costs, averages do strange things to nonlinear functions.

Eh, even an expected value that's linear with respect to profits can end up with strange results like the St. Petersburg paradox. In general, naively maximizing it breaks down at the point where you stop being insensitive to the possible risks.

One possible resolution to that paradox is to recognise that money is not linearly proportional to 'value'.

Re: Objective Bayesian Hypothesis Testing

#17

Post by LegionMammal978 »

shiandow wrote: post #16
LegionMammal978 wrote: post #11

Earlier quoted context omitted.

Eh, even an expected value that's linear with respect to profits can end up with strange results like the St. Petersburg paradox. In general, naively maximizing it breaks down at the point where you stop being insensitive to the possible risks.

One possible resolution to that paradox is to recognise that money is not linearly proportional to 'value'.

If happiness is, e.g., log(money), then you can just adjust the game to have the payout be $2^2^n after the nth step. This cancels out the logarithm and recovers the paradox. The only way to get out of it with diminishing returns is to have happiness reach a finite asymptote.

Re: Objective Bayesian Hypothesis Testing

#18

Post by vcdimension »

clircle wrote: post #15
vcdimension wrote: post #13

Earlier quoted context omitted.

So I guess we'll never know the p-value of that event...

Since “that event” happened, its probability is 1.

but what if H0 = Hewlett Packard did not plan to eliminate Mike Lynch and Stephen Chamberlain...

Re: Objective Bayesian Hypothesis Testing

#19

Post by shiandow »

LegionMammal978 wrote: post #17
shiandow wrote: post #16

Earlier quoted context omitted.

One possible resolution to that paradox is to recognise that money is not linearly proportional to 'value'.

If happiness is, e.g., log(money), then you can just adjust the game to have the payout be $2^2^ n after the n th step. This cancels out the logarithm and recovers the paradox. The only way to get out of it with diminishing returns is to have happiness reach a finite asymptote.

When there is a decent probability that you may crash the financial system I'm nor even sure if a strictly monotonically increasing function is appropriate.
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