gaussian-example.rst

Simple Gaussian example

This page show a complete example of running nessai including setting up the logger, defining a model, configuring the sampler and finally running the sampler. The code for this example is included in example directory.

Code

../examples/2d_gaussian.py

Output

In this examples the sampler with save the outputs to outdir/2d_examples/. The following is a explanation of the files in that directory.

Posterior distribution

The posterior distribution is plotted in posterior_distribution.png, this includes the distributions for the parameters that were sampled and the distribution of the log-prior and log-likelihood.

Trace

The trace plot shows the nested samples for each parameter as a function of the log-prior volume.

State

The state plot shows all the statistics which are tracked during sampling as a function of iteration. From top to bottom these are

• The minimum and maximum log-likelihood of the current set of live points
• The cumulative number of likelihood evaluations
• The current log-evidence log Z and fraction change in evidence dZ
• The acceptance of the population and proposal stages alongside the radius use for each population stage.
• The p-value of the insertion indices every nlive live points

The iterations at which the normalising flow has been trained are indicated with vertical lines and total sampling-time is shown at the top of the plot.

Insertion indices

The distribution of the insertion indices for all of the nested samples is shown on the left along with the expect uniform distribution and the 1-sigma bounds determined by the total number of live points. The cumulative mass function is shown on the right where the uniform function is shown with a dashed line, the overall distribution shown in blue and the distribution every nlive live point shown in light grey.

This plot is useful when checking if the sampler is correctly converged, a non-uniform distribution indicates the sampler is either under or over-constrained.