### treedepth

Quick definition The depth of tree used by NUTS.

#### More details

Configuring NUTS involves putting a cap on the depth of the trees that it evaluates during each iteration. This is controlled through a maximum depth parameter. `n_leapfrog` is then bounded by 2 to the power of the maximum depth minus 1.

Tree depth is an important diagnostic tool for NUTS. For example, a `treedepth = 0` occurs when the first leapfrog step is immediately rejected and the initial state returned, indicating extreme curvature and poorly-chosen `stepsize` (at least relative to the current position).

On the other hand, `treedepth = max_treedepth` equal to the maximum depth indicates that NUTS is taking many leapfrog steps and being terminated prematurely to avoid excessively long execution time.

Taking very many steps may be a sign of poor adaptation, may be due to targeting a very high acceptance rate, or may simply indicate a difficult posterior from which to sample. In the latter case, reparameterization may help with efficiency. But in the rare cases where the model is correctly specified and a large number of steps is necessary, the maximum depth should be increased to ensure that that the NUTS tree can grow as large as necessary.