Usage

I recommend going straight to the Chain Consumer API and the Examples page for details on how to use ChainConsumer.

The Process

The process of using ChainConsumer should be straightforward:

  1. Create an instance of ChainConsumer.

  2. Add your chains to this instance.

  3. Run convergence diagnostics, if desired.

  4. Update the configurations if needed (make sure you do this after loading in the data).

  5. Plot.

The main page and the examples page has code demonstrating these, so I won’t repeat it here.

Statistics

An area of some difference in analyses is how to generate summary statistics from marginalised posterior distributions. ChainConsumer comes equipped with the several different methods that can be configured with the configure method. The three methods are:

Maximum Likelihood Statistics

The default statistic used by ChainConsumer, maximum likelihood statistics report asymmetric uncertainty, from the point of maximum likelihood to the iso-likelihood levels above and below the maximal point.

Cumulative Statistics

For cumulative statistics , the lower \(1\sigma\) confidence bound, mean value, and upper bound are respectively given by the value of the cumulative function at points \(C(x) = 0.15865\), \(0.5\), and \(0.84135\).

Mean Statistics

Mean statistics report the same upper and lower confidence bound as cumulative statistics, however report symmetric error bars by having the primary statistic reported as the mean of the lower and upper bound.

Max Symmetric

See Figure 6(1) of Andrae (2010). Maximum likelihood with error with symmetric errors to get the desired confidence interval.

Max Shortest

See Figure 6(2) of Andrae (2010). Maximum likelihood with uncertainty bounds that minimise the distance between bounds.

Max Central

See Figure 6(3) of Andrae (2010). Maximum likelihood with uncertainty bounds from the CDF (i.e. same as cumulative stats but the central point is the maximum likelihood point and not the \(x\) such that \(C(x)=0.5\).

All three methods are illustrated below.

_images/stats.png