I need to implement an algorithm of Metropolis Independence Sampler, where the proposal distribution is a Multivariate Normal with 3 parameters.

Since my function $f$ is really difficult to analyize,I was thinking if is reasonable to choose as $mean$ of my normal the point that maximizes $f$ (this I can find!) and only adjust the covariance matrix as desired.

Thanks in advance :)


Yes, choosing the mean of your normal proposal distribution to be the point that maximizes $f$ is reasonable. A common justification for this is that the MLE/posterior distribution is approximately normally distributed in large samples. As you note, just make sure to adjust the covariance matrix accordingly to allow the sampler to fully explore the parameter space.

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