from beta to stretched beta
Hello all,
I am preparing a single introductory lecture on Bayesian stats for my (medical) biology undergrads, and would like to give some insights in how and why prior parameter distributions are selected.
A beta distribution with domain (0, 1) is suitable when the parameter of interest is a probability, p (because 0 <= p <= 1), and the interpretation of beta's parameters a and b is easily explained.
A so-called stretched beta distribution (parameters a = b, if I am correct) is used for a prior distribution of correlation coefficients for which the domain (-1, 1) is appropriate.
I now just can't seem to find out how a beta distribution is calculated/transformed/stretched to go from domain (0, 1) to (-1, 1). I hope you can share your insights!
Regards,
Peter K.
Comments
A mathematician-colleague just provided me with an answer: a "four parameter" beta distribution includes besides alpha and beta two extra parameters a and c for the minimum and maximum values of the distribution's range, respectively. (https://en.wikipedia.org/wiki/Beta_distribution#Four_parameters)
The x-axis (with values of theta) is then transformed as:
x' = x(c - a) + a
With values a = -1 and c = 1, the transformation becomes x' = 2x - 1.
Sorted!
PK
Great!
Cheers,
E.J.
...the stretched beta distribution is also (and perhaps more conventionally) called the "scaled" beta distribution. I guess that when you are unaware of nomenclature it is a bit difficult to dig up information?
PK