## Why should I be a Bayesian?

Image credit: from a talk of Mike West

While I am thinking about Bayesian inference on hierarchical, multi-resolution data, I found an interesting stuff by googling.

*Bayesian is one who, vaguely expecting a horse, and catching a glimpse of a donkey, strongly believes he/she has seen a mule **— from Kevin Murphy’s slides*

That’s right. However if he/she had seen a donkey many, many, many times, he/she probably would become more confident about his/her conclusion which is a donkey not a mule.

Astronomy is a bit unique science comparing with other natural sciences (physics, chemistry, biology…) in a sense that we, astronomers, can not do experiments on our Universe. Astronomers observe events in the Universe like catching a glimpse of a donkey and can not control the Universe by experiments to confirm the existence of intrinsic/underlying process which make things we’re seeing now.

If we can generate data many times by experiment based on a hypothesis and understand what distribution data do have, we can set up our likelihood and try to find best theoretical model to produce observed data where likelihood has maximum for a given theory. But Bayesian thinks in different way. What we really should ask is, “what’s the degree of our belief of a theory for a given data?” not “what’s the probability of data for a given theory?”

Although Bayesian has to expect at least something in his/her mind a priori, this prior(eg. horse) becomes weak as Bayesian see many, many donkeys. However if chances of seeing donkeys are few, this prior starts to play important role for forming his/her conclusion about what he/she has seen. It’s fair statement.

As I study Astronomy more and more, I think that I should be a Bayesian rather than a frequentist.