Continuous time markov chain models are getting more popular in ecology. Especially Markov modulate Poisson processes. See Rushing 2023 paper for basic introduction for ecologists.
https://besjournals.onlinelibrary.wiley.com/doi/10.1111/1365-2656.13902
These require matrix exponentiation that NIMBLE doesn't currently support. However, it is much faster to compute exp(A) %*% v which is easy to implement in NIMBLE (See https://groups.google.com/g/nimble-users/c/emKC1NdNozg). See also RTMB::expAv.
It would be cool to work out a more general distribution similar to dHMM that we could call dMMPP or something along those lines that passes states and continuous times to get the marginal density. Most of the tooling would match with dHMM except a few little tricks. I think these models are starting to get popular but are still a bit inaccessible. Sina Mews has a few papers that use HMM approximations effectively as an alternative, but I think this depends on the resolution of the data and how much things have to be discretized.
Continuous time markov chain models are getting more popular in ecology. Especially Markov modulate Poisson processes. See Rushing 2023 paper for basic introduction for ecologists.
https://besjournals.onlinelibrary.wiley.com/doi/10.1111/1365-2656.13902
These require matrix exponentiation that NIMBLE doesn't currently support. However, it is much faster to compute exp(A) %*% v which is easy to implement in NIMBLE (See https://groups.google.com/g/nimble-users/c/emKC1NdNozg). See also RTMB::expAv.
It would be cool to work out a more general distribution similar to dHMM that we could call dMMPP or something along those lines that passes states and continuous times to get the marginal density. Most of the tooling would match with dHMM except a few little tricks. I think these models are starting to get popular but are still a bit inaccessible. Sina Mews has a few papers that use HMM approximations effectively as an alternative, but I think this depends on the resolution of the data and how much things have to be discretized.