Todo: use optim Hessian for proposals (Question: Variance covariance matrix of proposal distribution)

[NeilDiamond]

Can anyone please explain this code in bvar giving the variance covariance matrix for the multivariate normal proposals? For the alpha parameter with bounds 1 to 3, for example, why should the J term be larger for values near 1 than for values near 3?

H <- diag(length(opt[["par"]])) * mh[["scale_hess"]]
J <- unlist(lapply(names(hyper), function(name) {
exp(opt[["par"]][[name]])/(1 + exp(opt[["par"]][[name]]))^2 *
(priors[[name]][["max"]] - priors[[name]][["min"]])
}))
...
if (hyper_n != 1) {
J <- diag(J)
}
HH <- J %% H %% t(J)

Many thanks
Neil

[nk027]

Hi Neil,
This is a heuristic that is only set at the start. There's two parts – the sigmoid-like part using the ML estimates, and a scalar that depends on the potential range of the parameter.
The goal of these is to start off with a scale that allows the sampler to efficiently explore the posterior, which can be proxied by the acceptance rate. (There are also adaptations to the scale during the burn-in phase.) To be honest, I don't recall the idea behind the first part that would lead to larger scale for smaller values. Looking at it now, I'd think that the ² should be on the sigmoid and not the denominator...
I'll look into this. (It might lead to better acceptance rates, but I assume that most parameters fall in a similar range, so the impact might be limited.)

[NeilDiamond]

Hi Nikolas, Many thanks for that. I thought I had understood that in terms of a transformation from the constrained space to an unconstrained space (see attached), but obviously I was wrong since the partial derivatives in my equation (1) are in terms of the unconstrained parameters, not the original parameters. As you say the scale will be adapted during the burn-in phase in any case. Again, thanks for a great package and your response to my questions. Cheers, Neil

…

On 2024-09-26 21:08, Nikolas Kuschnig wrote: Hi Neil, This is a heuristic that is only set at the start. There's two parts – the sigmoid-like part using the _ML estimates_, and a scalar that depends on the potential range of the parameter. The goal of these is to start off with a scale that allows the sampler to efficiently explore the posterior, which can be proxied by the acceptance rate. (There are also adaptations to the scale during the burn-in phase.) To be honest, I don't recall the idea behind the first part that would lead to larger scale for smaller values. Looking at it now, I'd think that the ² should be on the sigmoid and not the denominator... I'll look into this. (It might lead to better acceptance rates, but I assume that most parameters fall in a similar range, so the impact might be limited.) -- Reply to this email directly, view it on GitHub [1], or unsubscribe [2]. You are receiving this because you authored the thread.Message ID: ***@***.***> Links: ------ [1] #94 (comment) [2] https://github.com/notifications/unsubscribe-auth/ABEJDFX6JFJNWSJG5RDGWL3ZYPTLTAVCNFSM6AAAAABO4VWL3SVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDGNZWGY2DANJYGI

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