Restricting sampling of parameters about particles HOT 4 CLOSED

Hi,
The proposal distribution in mcmc.pmmh is a Gaussian random walk; i.e. the proposed parameter value is simulated from $\theta^p | \theta \sim N(\theta, \Sigma)$. The proposal covariance $\Sigma$ is either given by the user, or, if not, it is adapted (as in adaptive MCMC, i.e. it is estimated sequentially from past MCMC states).
First, can you ask you whether this point was clear to you? Otherwise, I think I should review the documentation. (This point is explained at least in the corresponding notebook tutorial, but maybe not in the docstrings.)

Anyway, I guess what happens here is that eventually the algorithm proposes a value of theta which gives you singular cov matrices (I'm talking about the cov matrix of the proposal of the states this time, inside each PF). Could you adapt the prior so that the prior probability of this happening is really zero?
In that case, pmmh will not even run the PF, and the problem should not arise.

from particles.

Thanks for your response.
It isn't clear to me how I could give the proposal covariance for the simulation of the new $\theta^p$. But unless this it is well explaind in the notebook tutorials.

My covariance matrix gets singular if it appears that $\gamma=0$ is chosen.
But since I gave as a prior a truncated normal distirbution which is truncated at $10^{-5}$ this should not be possible, because 0 is out of range.
But still it simulates $\gamma=0$ or at least so small that the values in the covariance matrix become numerically indistinguishable close I guess.

from particles.

First, to set the covariance matrix of the proposal, use argument rw_cov; see here:
https://particles-sequential-monte-carlo-in-python.readthedocs.io/en/latest/_autosummary/particles.mcmc.PMMH.html#particles.mcmc.PMMH

But now that you mention it, I can see that the docstring is not super-clear... I'll try to fix it shortly.

Second, yes, you're right, a value below $10^{-5}$ should not be proposed, since it's outside the prior range. I'll look into it, but, in the mean time, you could adapt your model to forbid values below $10^{-5}$ (e.g. by forcing $\gamma$ to be $=10^{-5}$ whenever the supplied value is smaller.

from particles.

More details are now given in the docstrings of PMMH and parent classes regarding parameter rw_cov, and more generally how to calibrate random walk proposals.

from particles.