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Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithmthat avoids the random walk behavior and sensitivity to correlated parametersthat plague many MCMC methods by taking a series of steps informed byfirst-order gradient information. These features allow it to converge tohigh-dimensional target distributions much more quickly than simpler methodssuch as random walk Metropolis or Gibbs sampling. However, HMC's performance ishighly sensitive to two user-specified parameters: a step size {\epsilon} and adesired number of steps L. In particular, if L is too small then the algorithmexhibits undesirable random walk behavior, while if L is too large thealgorithm wastes computation. We introduce the No-U-Turn Sampler (NUTS), anextension to HMC that eliminates the need to set a number of steps L. NUTS usesa recursive algorithm to build a set of likely candidate points that spans awide swath of the target distribution, stopping automatically when it starts todouble back and retrace its steps. Empirically, NUTS perform at least asefficiently as and sometimes more efficiently than a well tuned standard HMCmethod, without requiring user intervention or costly tuning runs. We alsoderive a method for adapting the step size parameter {\epsilon} on the flybased on primal-dual averaging. NUTS can thus be used with no hand-tuning atall. NUTS is also suitable for applications such as BUGS-style automaticinference engines that require efficient "turnkey" sampling algorithms.

The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo