Sometimes when optimizing parameter values only an approximate idea of the size of the parameter is available and sometimes parameters operate on vastly different scales.
The cauchy distribution is often used, when little information is known about the true parameter value, due to its large tails. It is particularly frustrating to sample parameters close to zero, when values smaller than zero are not allowed.
A way out seems to be the positive constrained cauchy distribution, which has the remarkable property of being symmetric on the log scale. Loc defaults to zero and scale determines the center of the distribution which spans then a range of approximately 4 orders of magnitude in the 95 percentile of the distribution.
I realize while writing, this is acutally a half-cauchy distribution 😎