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kingaa / pomp

R package for statistical inference using partially observed Markov processes
https://kingaa.github.io/pomp
GNU General Public License v3.0
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more detail on delays in blowflies1 and blowflies2? #129

Closed slwu89 closed 3 years ago

slwu89 commented 3 years ago

I'm interested in implementing models with delays, as was shown in the blowflies example(s): https://github.com/kingaa/pomp/blob/aaaf7413c4362734d667a11220be1ceda91affd7/R/blowflies.R#L95

This method only works for discrete_time models? Is there any way to model delays for euler based process models? Is there an official method to incorporate delays?

kingaa commented 3 years ago

As the name implies, pomp assumes Markovian structure. In particular, the latent state process must be Markov. Of course, this is not necessarily incompatible with dependence on delayed variables. If one can use the usual tricks to enfold the delayed variables into the state, one can make a Markov process out of one that has delays. In the discrete-time case, this is particularly easy. It can also be accomplished in continuous time if the delayed variables enter via a Gamma-shaped kernel, i.e., using the linear chain trick. These two tricks can be used to make better or worse approximations to many systems with delays. Beyond this, pomp does not go.

slwu89 commented 3 years ago

Thanks for the explanation @kingaa, I also looked through the closed issues and saw someone asking about a lag-2 Markov chain. I think this is good to close!