The target probability distribution is even more complex, and indeed might be non-identifiable. Now, I add a survival submodel on top of the ODE mix-effects model. Yes, this model is ODE based it was not straightforward to have it run appropriately, and informative priors were needed. How is this deterministic trajectory achieved numerically ? It is based on gradient descent? This trajectories should be different for different chains, is it only based on the initial condition? Thank you.
I still have a question regarding " Hamiltonian Monte Carlo explores a given probability distribution with deterministic trajectories that are able to span large regions of your model configuration (i.e. Instead you’ll have to investigate your target distribution as discussed in that link to identify what the problem is and then react to that particular problem. There are an infinite number of ways that your target probability distribution could be complicated that could lead to this warning and so there’s no immediate fix. For some more discussion on these two terms and strategies for responding to maximum tree depth warnings see for example Identity Crisis. If you’re saturating that maximum trajectory size then your target probability distribution is probably highly degenerate, and may even be non-identifiable. The default is 10 which implies that Stan should build a maximum of 2^, which equals 1024 steps for the default max_treedepth = 10, for safety. The max_treedepth parameter tells Stan the max value, in exponents of 2, of what the binary tree size in the NUTS algorithm should have.
NUTS builds a binary tree by taking forward/backwards “directional” steps to explore the target posterior distribution guided towards the highest probability density regions by the gradient of the log-posterior distribution. Stan uses the No-U-Turn-Sampler (NUTS) described in The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.
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