There is a classic paper "Inference for a Bernoulli Process (A Bayesian View) by Dennis Lindley and L.D. Phillips in the American Statistician vol. 30 no. 3, 1976, pp. 112-119 which treats exactly the problem of determining if a coin is fair, and contrasts the Bayesian approach with frequentist approach. Victor PS. For those of you with access to jstor, it's on there. On Tue, Mar 8, 2016 at 12:10 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
If the coin has no internal state, then the sequence of tosses are necessarily i.i.d. random variables. Subject to the (true!) assumption of the tosses being i.i.d., the *only* information you discern from the sequence of outcomes is the multiset of outcomes -- or equivalently the number of heads and number of tails.
(Even for a biased coin, P(HT) = P(TH) = sqrt(P(TT) * P(HH)) and so on.)
Best wishes,
Adam P. Goucher
Sent: Sunday, March 06, 2016 at 7:42 AM From: "David Makin" <makinmagic@tiscali.co.uk> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] how to test whether a coin is fair
? even with no internal state change we know that say probabilities of 2 tosses giving hh, ht, th and tt *ought* to be equal in the long term.
On 5 Mar 2016, at 15:07, Adam P. Goucher wrote:
Because each time you toss a coin, its internal state changes?
Sent: Friday, March 04, 2016 at 11:06 PM From: "David Makin" <makinmagic@tiscali.co.uk> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] how to test whether a coin is fair
I'd guess that you'd actually have to check the evenness of all sample rates, not just a "1" and a "0" but also "00" vs. "01" vs. "10" vs. "11" and "000" vs."001" etc............... i.e, use the same check as for checking the randomness of a pseudo random generator.
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