The No-U-Turn Sampler (NUTS) is an extension of Hamiltonian Monte Carlo (HMC) that eliminates the need to manually set the number of steps L. NUTS uses a recursive algorithm to build a set of likely candidate points that span a wide range of the target distribution, stopping automatically when it starts to double back. Empirically, NUTS performs at least as efficiently as and sometimes more efficiently than a well-tuned standard HMC method, without requiring user intervention or costly tuning runs. NUTS also includes a method for adapting the step size parameter ε on the fly based on primal-dual averaging, making it possible to run NUTS with no hand-tuning at all. NUTS is suitable for applications such as BUGS-style automatic inference engines that require efficient “turnkey” sampling algorithms. The main contribution of this paper is the No-U-Turn Sampler (NUTS), an MCMC algorithm that closely resembles HMC but eliminates the need to choose the problematic number-of-steps parameter L. We also provide a new dual averaging scheme for automatically tuning the step size parameter ε in both HMC and NUTS, making it possible to run NUTS with no hand-tuning at all. We will show that the tuning-free version of NUTS samples as efficiently as (and sometimes more efficiently than) HMC, even ignoring the cost of finding optimal tuning parameters for HMC. Thus, NUTS brings the efficiency of HMC to users (and generic inference systems) that are unable or disinclined to spend time tweaking an MCMC algorithm.The No-U-Turn Sampler (NUTS) is an extension of Hamiltonian Monte Carlo (HMC) that eliminates the need to manually set the number of steps L. NUTS uses a recursive algorithm to build a set of likely candidate points that span a wide range of the target distribution, stopping automatically when it starts to double back. Empirically, NUTS performs at least as efficiently as and sometimes more efficiently than a well-tuned standard HMC method, without requiring user intervention or costly tuning runs. NUTS also includes a method for adapting the step size parameter ε on the fly based on primal-dual averaging, making it possible to run NUTS with no hand-tuning at all. NUTS is suitable for applications such as BUGS-style automatic inference engines that require efficient “turnkey” sampling algorithms. The main contribution of this paper is the No-U-Turn Sampler (NUTS), an MCMC algorithm that closely resembles HMC but eliminates the need to choose the problematic number-of-steps parameter L. We also provide a new dual averaging scheme for automatically tuning the step size parameter ε in both HMC and NUTS, making it possible to run NUTS with no hand-tuning at all. We will show that the tuning-free version of NUTS samples as efficiently as (and sometimes more efficiently than) HMC, even ignoring the cost of finding optimal tuning parameters for HMC. Thus, NUTS brings the efficiency of HMC to users (and generic inference systems) that are unable or disinclined to spend time tweaking an MCMC algorithm.