Re: Coin flipping

daniel_nordlund_1982@xxxxxxxxxxx wrote:
Anon. skrev:
There are change-point models you could try, but you could probably get
a pretty good idea by using a GAM (generalised additive model) to smooth
the probability of a head (i.e. you plot H or T against the run number,
and smooth that). Depending on what you're doing, that might be enough.

Thanks! Looking into change-point models gave me some interesting
results. If I let heads=0 and tails=1, I can for example use a model
like

y(t) = 0.5 + 0.17*k(t) + e(t)

Where k(t) = 1 if t1<=t<=t2 (time is within the range [t1,t2] being
tested) and 0 otherwise. e(t) is the error term. I can then go through
all possible values of t1 and t2 and see for which values this model
gives the best fit (in a least square sense).

Or use maximum likelihood! If you're calculating this for all t1 and t2, then you could go to he extra effort of estimating the amount of bias (i.e. the 0.17). Actually, that's easy: the likelihood is beta distributed, and the point estimate is the proportion of tails (or the proportion of tails - 0.5, I suppose).

Now to my next question, when I have found likely values of t1 and t2
(the biased range), is it possible to calculate the probability of this
observation in fact being due to chance (with the unbiased coin)?

You can compare the likelihoods for the two cases. Oh, except that you're taking the maximum deviation, so I'm not sure what the null distribution looks like. Someone who knows more about classification problems might be able to help.

Bob

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