Using a Gibbs sampler, draw $k=1000$ samples from the posterior distribution by repeatedly

sequentially sampling from the conditional posteriors $|Y,x$ and $x|Y,.$

For this numerical experiment, use the $3232$ phantom image with the CT imaging matrix $R$

created using the same MATLAB code from Lecture using angles $=0$:$10$:$180($or rewrite

in Python $-$ if this causes trouble, I can also provide the matrix in a $.$mat file$).R$ should be a

$9311024$ matrix.

For the other parameters, use ${}_{\text{t}\text{r}\text{u}\text{e}}={10}^4($i$.$e$.{}_{\text{t}\text{r}\text{u}\text{e}}={10}^{-2},$ only used to generate the data $Y),$

${}_{\text{p}\text{r}\text{i}\text{o}\text{r}}={10}^{-2},{}_{\text{p}\text{r}\text{i}\text{o}\text{r}}={10}^{-4},{}_{\text{p}\text{r}\text{i}\text{o}\text{r}}={10}^{-4},$ and an initial guess for $x$ equal to the least squares

solution $($compute via $R$ "backslash" $Y$ in MATLAB$).$ To draw samples from a multivariate

normal, use MATLAB's mvnrnd command, supplying the mean vector and covariance matrix.

Note: This may take a few minutes to run, depending on how powerful your machine is$.$

Please provide me the solution in Python.