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What has a 1 in a million chance? (2010)

stat.berkeley.edu

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Re: What has a 1 in a million chance? (2010)

#191

Post by Strilanc »

neilkk wrote: post #185
Strilanc wrote: post #179

Earlier quoted context omitted.

Search "decibels" in https://www.yudkowsky.net/rational/bayes for the explanation. I think you're just wrong about needing everything to be in the form X:1 or 1:X. When I compute the ratio of 1000000:1 divided by 1:20 it gives 1000000:(1/20) then scaling both sides by the same factor gives 20000000:1.

Your reference definitely doesn't show a calculation of the type you are trying to do. Likelihood ratios are not the same as odds ratios; they do not have the problem I described. I would be very surprised if you can find any reference at all to the number you describe as 'evidence bits', or anything equivalent, made by anyone who can show an understanding of basic probability, statistics, or information theory. I un…

When you apply a statistical test, the various outcomes cause Bayesian updates that correspond to adding or subtracting fixed bits of evidence. When you repeat the test (and the repetitions are independent), the amount of bits of evidence you add or subtract remain the same. In other words, focusing on bits of evidence shows Bayesian updates behave like a biased random walk under repetition of a test and allow you to compute the properties of that walk.

For example, suppose you are trying to estimate how much rounding errors in a pseudo random number generator betray that it is not a true exact representation of the random process. One way to quantify this is to compute the expected bits of evidence revealed per call to the RNG.

Re: What has a 1 in a million chance? (2010)

#192

Post by atq2119 »

column wrote: post #103
egeozcan wrote: post #83

Earlier quoted context omitted.

Of course it's a very small step to make babies amounting to 3 times the current population of Switzerland (so assuming roughly a 50/50 female/male divide, everyone needs to make 6 babies on average, in the same year so they will still all be babies when the last one is born? that's probably impossible for the females but we are already way into the science-fiction category) and put them all in a committee. The more…

What do you mean, "that's *probably* impossible" to make 6 babies from the same mother in a single year? Takes about 9 months to output a human, you know?

Twins and larger multiples are a thing...

Re: What has a 1 in a million chance? (2010)

#193

Post by sebastiennight »

DeathArrow wrote: post #3

Picking a random integer between 1 and 1 million.

This is the right answer. I estimate no more than 1 human in a million can choose such a number at random.

Therefore if a human picks a number between 1 and 1 million, there's only a 1 in a million chance that the number was picked randomly.

Re: What has a 1 in a million chance? (2010)

#194

Post by dTal »

inasio wrote: post #173
Scarblac wrote: post #19

> "Scientists have calculated that the chances of something so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten." -- Terry Pratchett Making fun of the fact that if someone says "it's a million-to-one chance, but it might just work!" in fiction, you know it's going to work. In _Guards! Guards!_ this is taken to the point that…

Million-to-one chances are a running theme in a few of his books, but aiming specifically for it as in Guards, Guards! is one of the better awesome things in the Discworld

It seems like a pretty direct homage to the Infinite Improbability Drive from Hitchhiker's Guide to the Galaxy, which is created from thin air by working out exactly how improbable such a device is and plugging this number into a finite improbability generator (such machines themselves "often used to break the ice at parties by making all the molecules in the hostess's undergarments leap simultaneously one foot to the left, in accordance with the theory of indeterminacy.").

Re: What has a 1 in a million chance? (2010)

#196

Post by yboris »

DeRock wrote: post #162
yboris wrote: post #158

My favorite mental visualization I came up with: imagine driving from New Jersey to Florida (substitute with a long drive you had). Mine was about 1,200 miles which at 60 miles per hour is 20 hours. That's 72,000 seconds of mind-numbing driving. Now if during the entire, exhausting, 20 hours of driving, you press a button, and it falls within the "danger zone" that lasts 15 seconds, you lose. The above example is bet…

15 seconds danger zone / 72,000 seconds of driving = 1 in 4,800 Any reason you chose those numbers? Trying to understand the significance of those odds.

So sorry -- I think I got distracted while writing (doing things around the house) and got the math wrong :'(

I wanted something around 1:1million odds

Re: What has a 1 in a million chance? (2010)

#197

Post by egeozcan »

column wrote: post #103
egeozcan wrote: post #83

Earlier quoted context omitted.

Of course it's a very small step to make babies amounting to 3 times the current population of Switzerland (so assuming roughly a 50/50 female/male divide, everyone needs to make 6 babies on average, in the same year so they will still all be babies when the last one is born? that's probably impossible for the females but we are already way into the science-fiction category) and put them all in a committee. The more…

What do you mean, "that's *probably* impossible" to make 6 babies from the same mother in a single year? Takes about 9 months to output a human, you know?

> Takes about 9 months to output a human

Takes about 9 months to output N humans where N approaches to 1 on large averages as even twin births are like 1.2 percent.

Also many females cannot be pregnant again for a while after giving birth, even if we had sped up the pregnancy.

To average 6 babies, we need something like giving birth to triplets every 5 months in average, which improbable even if we had the technology, will and the economics that could support this.

But you know, "improbable" is such a funny word, especially out of context :)

Re: What has a 1 in a million chance? (2010)

#198

Post by [deleted] »

EricMausler wrote: post #132
strken wrote: post #65

Earlier quoted context omitted.

This is part of a very important principle: if someone approaches you about something, you should be far more suspicious than if you had randomly picked someone off the street. The most well known application of this is teaching kids to ask a random shopkeeper for help if they get lost, but to not get in a stranger's car when offered a lift.

This also applies to self defense. If someone has targeted you, the odds of you beating them in a fight is different than the odds you can take on a random person, or a random thief even

[deleted]

Re: What has a 1 in a million chance? (2010)

#199

Post by throwaway29812 »

EricMausler wrote: post #132
strken wrote: post #65

Earlier quoted context omitted.

This is part of a very important principle: if someone approaches you about something, you should be far more suspicious than if you had randomly picked someone off the street. The most well known application of this is teaching kids to ask a random shopkeeper for help if they get lost, but to not get in a stranger's car when offered a lift.

This also applies to self defense. If someone has targeted you, the odds of you beating them in a fight is different than the odds you can take on a random person, or a random thief even

Better or worse odds for you?
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