The MLE solution has no prior, and the ensemble based examples have priors centered around zero, making them fit less to the data than the MLE. It would be interesting to see the effect of an informative prior, e.g. with mean $\mu=\lambda *g(x) $ for $\lambda\in(0,1)$ as we should be able to converge by controlling $\lambda$ and $\sigma_x$ prior standard deviation.
The MLE solution has no prior, and the ensemble based examples have priors centered around zero, making them fit less to the data than the MLE. It would be interesting to see the effect of an informative prior, e.g. with mean $\mu=\lambda *g(x) $ for$\lambda\in(0,1)$ as we should be able to converge by controlling $\lambda$ and $\sigma_x$ prior standard deviation.