送交者: mangolasi 于 2006-1-28, 13:32:21:
That statement is very ambigous. I was simply pointing out that someone who can dash out so comfortably with the jargons "prior" and "posterior", should be able to answer that q in the perspective of a Bayesian within one line: the coin is baised. Not being able to do so and prescribing reading list and teasing a layman's ignorance instead, can not avoid giving an impression that he/she only knows "prior" and "possterior" as jargons, not concepts
但是，有问题在“抽象”之前：连续投７次与一次投七个同样的硬币能否等价？
如果认为是等价的，那么。。。。。then you are assuming the enviornment is neutral, and thinking in an i.i.d.(or memoryless) point of view: either you are take the unbiasness of the coin as a priori requirement, then the statement has nothing wrong. You decide the 50-50 probability a pirori, and the 7-heads is simply a rare event. In this case you can not make any prediction; Or you are taking a Bayesian point of view, which did not set the parameter (of the biasness) a priori. Rather, it thinks the parameter has some prob. distribution which will show up in the data. 7 heads up means the coin is indeed biased, hence not 50-50 for the prediction.
如果认为是不等价的，那么。。。。。unneutral environment problem (e.g. wind, gravity??? etc). So see it from the point of view of Time series. It's an AR process. For this case, it is not 50-50 either.
More comments on that article in general when I finish all those new year greeting emails (I hate friends every year this time).