Columbia University
IEOR4703 – Monte Carlo Simulation (Hirsa)
Assignment 6 – Due on Thursday April 20th, 2023 by midnight
Problem 1 (Conjugate Prior for Exponential Distribution): Assume the likelihood distribution is exp(λ) with λ unknown and
prior is Γ(α, β) find the posterior π(λ|y). Write a Python code for it. In your code posterior should get updated as data being processed.
Problem 2 (Conjugate Prior for Gamma Distribution): Assume the likelihood distribution is Γ(ν, θ) with θ unknown and prior
is Γ(α, β) find the posterior π(θ|y). Write a Python code for it. In your code posterior should get updated as data being processed.
Problem 3 (Conjugate Prior for Poisson Distribution): Assume the likelihood distribution is Poisson(θ) with θ unknown and
prior is Γ(α, β) find the posterior π(θ|y). Write a Python code for it. In your code posterior should get updated as data being processed.