Analytic Donut#

Overview#

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

Contour Samples

Authors#

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.