optns 2.1.1

Optimized Nested Sampling: fast inference for non-linear additive models

Faster inference by parameter space reduction of linear parameters.

Context

For models that are composed of additive components:

y = A_1 * y_1(x|theta) + A_2 * y_2(x|theta) + ...

And data that are one of:

y_obs ~ Normal(y, sigma)
y_obs ~ Poisson(y)
y_obs ~ GP(y)

y may be one or multi-dimensional. sigma may be different for each y (heteroscadastic). GP may be a Gaussian process from celerite or george.

Here we see that each component y_i changes y linearly with its normalisation parameter A_i.

We therefore have two groups of parameters:

• linear parameters: A_i

• non-linear parameters: theta

We can define the predictive part of our model as:

y_1, y_2, ... = compute_components(x, theta)

What optns does

1. Profile likelihood inference with nested sampling. That means the normalisations are optimized away.

2. Post-processing: The full posterior (A_i and theta) is sampled by conditionally sampling A_i given theta.

Usage

See the demo scripts in the examples folder!