I am trying to do Thompson sampling for continuous rewards. For simplicity reasons I am assuming that my rewards are coming from a Normal distribution (in my use-case the rewards are sampled from a right-skewed distribution with most of the values around 0). At first, I was struggling to find a proper prior, but after some research, I found out that Jeffreys Prior works in this type of scenarios Prior for continuous rewords. From this other post Jeffreys Prior for normal distribution with unknown mean and variance I understood how to compute the formula for the prior distribution, but now I am struggling to compute the parameters for the posterior distribution.
I tried computing the Posterior = Prior x Likelihood following the examples provided in Conjugate Bayesian analysis of the Gaussian distribution, but without any concrete results.
Any thoughts about how to can I find the type of the Posterior distribution and also its parameters? Thank you!
