One of the beautiful aspects of Bayesian methods is that they are subjective. Due to that I think you should really be asking "What sort of priors are reasonabl

One of the beautiful aspects of Bayesian methods is that they are subjective. Due to that I think you should really be asking "What sort of priors are reasonable here?" From that perspective the uniform prior I use is reasonable (though non-committal and fairly uninformative), a triangular distribution with its peak at 50% (http://en.wikipedia.org/wiki/Triangular_distribution http://en.wikipedia.org/wiki/Triangular_distribution), the prior I have after updating tails and then heads, a normal distribution, or using the beta distribution with an equal number of both parameters. Honestly you may decide there's a fair chance the coin is heads biased so you choose a prior that has most of the mass of the probability above 50%. As long as you have a reason, it's reasonable. You don't have to worry too much that you've chosen the optimal prior since more data makes equals of priors in the long run. The only terrible thing you can do, is pick a prior that absolutely excludes certain hypotheses with 0% likelihood. No amount of data can overcome that.