How to pre-tune proposal function

[florianhartig]

Question from a user:

Wie kann ich eine multivariate "jump distribution" vorgeben, die für das Ziehen des "Proposals" eines i+1'ten Parametervektors angenommen wird ?

Man kann Rechenzeit während des burn-ins einsparen, in dem eine gut geschätzte multivariate Verteilung dafür schon zu Beginn gegeben wird. Ich habe ein Boden-Pflanzenmodel, welches ca 1 min (im günstigsten Fall, in ungünstigeren Fällen ~ 3min) Rechenzeit benötigt. Ich bin wirklich auf eine schnelles burn-in angewiesen.

[florianhartig]

How to pre-tune the proposal depends on the sampler

• For Metropolis samplers, the covariance of the proposal generator can be set
• For the DE / DREAM family, one can set the z-Matrix (the default is to generate it from the prior)

I would not recommend Metropolis sampling for slow models, so assuming that you use e.g. DEzs, which is a robust MCMC for complex slow models, what one would do is:

• Sample a z-Matrix from the (hypothesized) posterior distribution, or just play around with z Matrices that are more narrow than the prior
• Provide this z Matrix in the start-up of the algorithm (see help of DEzs)

[florianhartig]

Reply:

In the past I did global optimisation + FOSM calculation of the parameters variance-covariance matrix, followed by MCMC (DRAM) sampling of the posterior around the "best fit". The reason was, Differential Evolution is formidable for parallel computating, while for MCMC chains, this is less so. I then start n chains around the best fit.

You answered:==> For Metropolis samplers, the covariance of the proposal generator can be set

Where, for example in BayesianTools::DRAM(startValue = NULL, iterations = 10000, nBI = 0, parmin = NULL, parmax = NULL, FUN, f = 1, eps = 0), is this done?

Via argument FUN, or through a matrix of startValues?

[florianhartig]

First of all, I would still not recommend to use DRAM, DEzs will work better. The internal DEzs chains can be partly parallelized in BT, default is 3, but you can increase if you want to have have more cores available. But even without parallelization, DEzs is more efficient than DRAM in my experience.

That being said, if you insist on using DRAM, you can set the proposalGenerator in the setup via https://rdrr.io/cran/BayesianTools/man/createProposalGenerator.html