the random variable X ∼ N(μ,σ2) distribution. The observations of X, that is, x =(0.7669, 1.6709, 0.8944, 1.0321, 0.0793
Posted: Mon Nov 15, 2021 10:20 am
the random variable X ∼ N(μ,σ2) distribution. The
observations of X, that is,
x =(0.7669, 1.6709, 0.8944, 1.0321, 0.0793, 0.1033, 1.2709,
0.7798, 0.6483, 0.3256)
were generated using unknown parameter values
μ0 and σ0. Further- more, let μ ∼ N(0,
(100)2) and σ2 ∼ Inverse − Gamma(5/2, 10/2)
distributions. Device a suitable Markov chain Monte Carlo algorithm
to simulate from the resulting posterior of (μ, σ2)
given X = x. Draw the histogram of the posterior densities of μ and
σ. Estimate μ0 and σ0, by the posterior
mean of μ and σ respectively. How would you estimate the standard
error of your estimates?
( try several versions of the MCMC algorithms and Gibb’s sampler
to get the best result, submit a description of the best algorithm
with the resulting plots to show the convergence of the algorithm)
Any software will be fine, the description part is valued the
most
observations of X, that is,
x =(0.7669, 1.6709, 0.8944, 1.0321, 0.0793, 0.1033, 1.2709,
0.7798, 0.6483, 0.3256)
were generated using unknown parameter values
μ0 and σ0. Further- more, let μ ∼ N(0,
(100)2) and σ2 ∼ Inverse − Gamma(5/2, 10/2)
distributions. Device a suitable Markov chain Monte Carlo algorithm
to simulate from the resulting posterior of (μ, σ2)
given X = x. Draw the histogram of the posterior densities of μ and
σ. Estimate μ0 and σ0, by the posterior
mean of μ and σ respectively. How would you estimate the standard
error of your estimates?
( try several versions of the MCMC algorithms and Gibb’s sampler
to get the best result, submit a description of the best algorithm
with the resulting plots to show the convergence of the algorithm)
Any software will be fine, the description part is valued the
most