Retrieve parameters of a Nonhomogeneous Poisson Process via MCMC

[Lucas Fernandes]

I have the occurrence time data for a non-homogeneous Poisson process, called a Weibull process, which has an intensity function 𝜆(t) = 𝜃αt^α-1, α, 𝜃 > 0. My goal is to recover the parameters α and 𝜃 that generated this process, using Monte Carlo simulations via Markov chains, and assess the convergence of the parameters. How can I do this in Stata?