Analytic Funnel

Overview

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

Authors

• Linus Seelinger

Run

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

Properties

Model	Description
posterior	Posterior density

posterior

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

First, define a helper function

\[ f(x,m,s) := - \frac12 \log(2 \pi) - \log(s) - \frac12 ((x-m)/s)^2. \]

Now, the output log PDF is defined as

\[ \log(\tau(x)) := f(x_1, 0, 3) + f(x_2, 0, \exp(\frac12 x_1)). \]

This distribution is from Neal, Radford M. 2003, “Slice Sampling.” Annals of Statistics 31 (3): 705–67.