we set our distribution to be f(x|u,p)=$\frac{1}{x}\sqrt{\frac{p}{2\pi}}exp[-\frac{p}{2\pi}(ln(x)-u)^2]$ with p>0,u=0 we consider n observations from $x_1...x_n$, p is unknown and we asssume a prior $Gamma(\frac{\alpha}{2},\frac{\beta}{2})$ on p
if we parametrize $\alpha=ab$ and $\beta=b$ a and b unknown, what is the posterior if we assume Gamma(1,2) hyperpriors for both parameters?
My strategy would be computing a $Gamma(\frac{ab}{2},\frac{b}{2})$ prior with the above likelihood and then multiplying it by both of the hyperpriors but my cancellation seems to be off im struggling to find the posterior distribution.