Another useful meta answer is stability: There are only a few distributions with the property that a linear combination of independent distributions is a distribution of the same type. This means they’re “attractors” for processes that can be described as consecutive sums of independent quantities and multiplications by nonrandom factors.
So if for structural reasons you know that what you’re looking at is the output of such a process, then you may want to use an alpha-stable distribution as prior. The value of alpha essentially controls how heavy the tails are. (And the normal distribution is a special case for alpha = 2.)
This is essentially a generalization of the central limit theorem to distributions with higher variance / heavier tails.
Another useful meta answer is stability: There are only a few distributions with the property that a linear combination of independent distributions is a distribution of the same type. This means they’re “attractors” for processes that can be described as consecutive sums of independent quantities and multiplications by nonrandom factors.
So if for structural reasons you know that what you’re looking at is the output of such a process, then you may want to use an alpha-stable distribution as prior. The value of alpha essentially controls how heavy the tails are. (And the normal distribution is a special case for alpha = 2.)
This is essentially a generalization of the central limit theorem to distributions with higher variance / heavier tails.