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