I have the following mode

$y_k \sim \mathcal{N}( a_0+a_1 x_k+a_2 x_k^2 , \sigma^2 ) $

I have a dataset $\mathcal{D} = \{y_k , x_k\}_1^N$. I am using Metropolis-hasting MCMC to estimate the model parameters $a_0, a_1, a_2$ and $\sigma^2$. I am getting a good estimation for $a_0, a_1, a_2$ but not equally good for the variance. The proposal distribution for $a$'s is multivariate Gaussian

$ a^{(k+1)} = a^{(k)} + \sigma_a \mathcal{N}(0,I) $

and for $1/\sigma^2$ is Gamma distribution. I can have better estimation of the variance using the WLS estimator! How can I use the results of the WLS to improve the MCMC estimation?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.