### divergent

Quick definition The number of leapfrog transitions with diverging error. Because NUTS terminates at the first divergence this will be either 0 or 1 for each iteration. The average value of `divergent` over all iterations is therefore the proportion of iterations with diverging error.

#### More details

When numerical issues arise during the evaluation of the parameter Jacobians or the model log density, an exception is raised in the underlying code and the current expansion of the Hamiltonian forward and backward in time is halted. This is marked as a divergent transition.

The primary cause of divergent transitions in Euclidean HMC (other than bugs in the model code) is numerical instability in the leapfrog integrator used to simulate the Hamiltonian evaluation. The fundamental problem is that a fixed step size is being multiplied by the gradient at a particular point, to determine the next simulated point. If the stepsize is too large, this can overshoot into ill-defined portions of the posterior.

If there are (post-warmup) divergences then the results may be biased and should not be used.

In some cases, simply lowering the initial step size and increasing the target acceptance rate will keep the step size small enough that sampling can proceed.

The exact cause of each divergent transition is printed as a warning message in the output console. This can be useful in cases where managing the step size is insufficient. In such cases, a reparameterization is often required so that the posterior curvature is more manageable; see the section about Neal's Funnel in the Stan manual for an example.

For more details see Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo.