== Choice of coefficients for a beta distribution (prior for binomial distribution) ==

The Beta distribution is the conjugate prior to the binomial test since the beta density function has a similar form to the binomial density. The Beta distribution, Be(a,b), has two parameters corresponding to shape (a) and scale (b).

These two values for the prior distribution, a and b, can be specified in JASP to specify the prior distribution. SPSS allows for separate values of a and b to be specified for the prior null and alternative distributions.

Jeffrey's prior of Be(0.5,0.5) is recommended as an uninformative prior for the binomial test.

__Choice of informative Beta priors__

The Beta expected value of a Be(a,b) distribution is a/(a+b). So that if we expect 9 tails in 10 coin tosses our expected value of the Beta distribution is 9/(9+1) = 0.9.  

The variance of the beta distribution is ab/[(a+b)^ 2^ (a+b+1)] so that higher values of a and b are more informative priors having smaller variances.[[https://stats.stackexchange.com/questions/64852/how-do-i-choose-parameters-for-my-beta-prior | See here.]]