Analytic Donut

Overview

This benchmark consists of an analytically defined PDF \(\pi : \mathbb{R}^2 \rightarrow \mathbb{R}\) resembling the shape of a donut.

Authors

• Linus Seelinger

Run

docker run -it -p 4243:4243 linusseelinger/benchmark-analytic-donut

Properties

Model	Description
posterior	Posterior density

posterior

Mapping	Dimensions	Description
input	[2]	2D coordinates \(x \in \mathbb{R}^2\)
output	[1]	Log PDF \(\pi\) evaluated at \(x\)

Feature	Supported
Evaluate	True
Gradient	True
ApplyJacobian	True
ApplyHessian	False

Config	Type	Default	Description
None

Mount directories

Mount directory	Purpose
None

Source code

Model sources here.

Description

The PDF \(\pi\) is defined as

\[ \pi(x) := - \frac{(\| x \| - r)^2}{\sigma^2}, \]

where \(r = 2.6\) and \(\sigma^2 = 0.033\).

The implementation then returns the log PDF \(\log(\pi(x))\).

This distribution is inspired by Chi Feng’s excellent online mcmc-demo.