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.