# Introduction

DynamicHMC.jl implements a variant of the “No-U-Turn Sampler” of Hoffmann and Gelman (2014), as described in Betancourt (2017).[1] This package is mainly useful for Bayesian inference.

In order to use it, you should be familiar with the conceptual building blocks of Bayesian inference, most importantly, you should be able to code a (log) posterior as a function in Julia.[2] The package aims to “do one thing and do it well”: given a log density function

$$$\ell: \mathbb{R}^k \to \mathbb{R}$$$

for which you have values $\ell(x)$ and the gradient $\nabla \ell(x)$, it samples values from a density

$$$p(x) \propto \exp(\ell(x))$$$

using the algorithm above.

The interface of DynamicHMC.jl expects that you code $\ell(x), \nabla\ell(x)$ using the interface of the LogDensityProblems.jl package. The latter package also allows you to just code $\ell(x)$ and obtain $\nabla\ell(x)$ via automatic differentiation.

While the NUTS algorithm operates on an unrestricted domain $\mathbb{R}^k$, some parameters have natural restrictions: for example, standard deviations are positive, valid correlation matrices are a subset of all matrices, and structural econometric models can have parameter restrictions for stability. In order to sample for posteriors with parameters like these, domain transformations are required.[3] Also, it is advantageous to decompose a flat vector x to a collection of parameters in a disciplined manner.

I recommend that you use TransformVariables.jl in combination with LogdensityProblems.jl for this purpose: it has built-in transformations for common cases, and also allows decomposing vectors into tuples, named tuples, and arrays of parameters, combined with these transformations.

## Use cases

This package has the following intended use cases:

1. A robust and simple engine for MCMC. The intended audience is users who like to code their (log)posteriors directly, optimize and benchmark them as Julia code, and at the same time want to have access detailed diagnostic information from the NUTS sampler.

2. A backend for another interface that needs a NUTS implementation.

3. A research platform for advances in MCMC methods. The code of this package is extensively documented, and should allow extensions and experiments easily using multiple dispatch. Contributions are always welcome.

## Support

If you have questions, feature requests, or bug reports, please open an issue. I would like to emphasize that it is perfectly fine to open issues just to ask questions. You can also address questions to @Tamas_Papp on the Julia discourse forum.

## Versioning and interface changes

Package versioning follows Semantic Versioning 2.0. Only major version increments change the API in a breaking manner, but there is no deprecation cycle. You are strongly advised to add a compatibility section to your Project.toml, eg

[compat]
DynamicHMC = "^2.1"

Only symbols (functions and types) exported directly or indirectly from the DynamicHMC module are considered part of the interface. Importantly, the DynamicHMC.Diagnostics submodule is not considered part of the interface with respect to semantic versioning, and may be changed with just a minor version increment. The rationale for this is that a good generic diagnostics interface is much harder to get right, so some experimental improvements, occasionally reverted or redesigned, will be normal for this package in the medium run. If you depend on this explicitly in non-interactive code, use

[compat]
DynamicHMC = "~2.1"

There is an actively maintained CHANGELOG which is worth reading after every release, especially major ones.

• 1In order to make the best use of this package, you should read at least the latter paper thoroughly.
• 2For various techniques and a discussion of MCMC methods (eg domain transformations, or integrating out discrete parameters), you may find the Stan Modeling Language manual helpful. If you are unfamiliar with Bayesian methods, I would recommend Bayesian Data Analysis and Statistical Rethinking.
• 3For nonlinear transformations, correcting with the logarithm of the determinant of the Jacobian is required.