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SciML / DiffEqBayes.jl

Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning
https://docs.sciml.ai/DiffEqBayes/stable/
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Multiple shooting analogue for MCMC #265

Open ArnoStrouwen opened 1 year ago

ArnoStrouwen commented 1 year ago

Optimization based parameter estimation techniques such as MAP can use state discretization techniques such as multiple shooting to speed up the optimization. But for MCMC based parameter estimation techniques all examples I've seen use single shooting.

I wonder if using a technique like: https://arxiv.org/pdf/1702.08446.pdf#page=5 might also work for combined sampling in the state and parameter space, where the manifold is defined by the system dynamics.

mschauer commented 1 year ago

If you have SDEs (a noisy relaxation of your ODE), you can do multiple shooting in MCMC