Return Bayesian confidence intervals for the mean, var, and std.
Assumes 1-d data all has same mean and variance and uses Jeffrey’s prior for variance and std.
alpha gives the probability that the returned confidence interval contains the true parameter.
Uses mean of conditional pdf as center estimate (but centers confidence interval on the median)
Returns (center, (a, b)) for each of mean, variance and standard deviation. Requires 2 or more data-points.