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

[answerhappygod]

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