To work well, the Metropolis algorithm needs proposals that are accepted reasonably often. Here, I improve the model from the previous post by using draws from the posterior to iteratively improve proposals, resulting in more efficient sampling.
The Metropolis algorithm is a common MCMC method. Here, it is used for estimating a generalised logistic function to reconstruct a latitudinal climate gradient from a small sample of temperature values.
Assume we want to investigate the relationship between two variables, $x$ and $y$, that we have collected over a certain period of time. We have reason to believe that the relationship changed at some point, but we don't know when.