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Topic	Politics Containment Topic 268: Hope & Change
LordoftheMorons 02/14/20 11:26:29 PM #339:	red sox 777 posted... The setup is that you don't know the actual probability distribution. You know the outcome of 100 trials and you know that someone had a model before this set of trials that predicted all of them correctly while telling you that they assigned a 51% probability to their being right in each trial. You are being asked to create your model of the situation in light of these facts. Since you have the 51% model you can use it to generate future predictions. The reasonable conclusion is that the coin has a much higher probability than 51% of turning out the way the 51% model says is 51% likely. Notice how the number 51% is not based in any actual data. It was pulled out of thin air. The person who created that model could have replaced it with 62% or 35% and it wouldn't change the analysis one jot. By the outcome of the 100 trials (you can make it 1 million if you think 100 isn't a big enough sample to you intuitively), you know that these coin flips can be predicted to a high degree of accuracy. Because the 51% model has already done it. Even if it doesn't claim that it should be able to. Ah okay yeah your setup is different than what I was thinking. Anyway, I'm not sure that your example is in the same category of question. When I specify a model, the outputs are not binary predictions but probability distributions, whereas you seem to be both. Here you're saying that your model gives both a probability and a binary outcome. Is there any relationship between the two (e.g. is the binary outcome determined by saying that the outcome above 50% is the one that it "called")? Another point (which you kind of brought up earlier) is that 538 is not making 50 independent predictions, though the way they display their data may lead one to believe that. The probability distribution is over sets of 50 outcomes of each state (and those results are correlated). This makes it much more likely that they'll call 49 or 50 states right than we'd naively expect viewing the races as independent. --- Congrats to Advokaiser for winning the CBX Guru Challenge! <cite>LordoftheMorons posted [p:934397303] in Politics C... [t:78403764]...</cite> <quote>red sox 777 posted... </cite> <quote>The setup is that you don't know the actual probability distribution. You know the outcome of 100 trials and you know that someone had a model before this set of trials that predicted all of them correctly while telling you that they assigned a 51% probability to their being right in each trial. You are being asked to create your model of the situation in light of these facts. Since you have the 51% model you can use it to generate future predictions. The reasonable conclusion is that the coin has a much higher probability than 51% of turning out the way the 51% model says is 51% likely. Notice how the number 51% is not based in any actual data. It was pulled out of thin air. The person who created that model could have replaced it with 62% or 35% and it wouldn't change the analysis one jot. By the outcome of the 100 trials (you can make it 1 million if you think 100 isn't a big enough sample to you intuitively), you know that these coin flips can be predicted to a high degree of accuracy. Because the 51% model has already done it. Even if it doesn't claim that it should be able to.</quote>Ah okay yeah your setup is different than what I was thinking. Anyway, I'm not sure that your example is in the same category of question. When I specify a model, the outputs are not binary predictions but probability distributions, whereas you seem to be both. Here you're saying that your model gives both a probability and a binary outcome. Is there any relationship between the two (e.g. is the binary outcome determined by saying that the outcome above 50% is the one that it "called")? Another point (which you kind of brought up earlier) is that 538 is not making 50 independent predictions, though the way they display their data may lead one to believe that. The probability distribution is over sets of 50 outcomes of each state (and those results are correlated). This makes it much more likely that they'll call 49 or 50 states right than we'd naively expect viewing the races as independent. --- Congrats to Advokaiser for winning the CBX Guru Challenge!</quote> ... Copied to Clipboard!
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