Graphical & Hierarchical Models

Graphical modeling allows us to compose a single model that is fitted to an entire dataset. This model includes a specific galaxy model for every individual galaxy in the sample, but also has shared parameters between these individual model components.

An example of such a model might have Cosmological parameters (e.g. the Hubble constant) as a global parameter which is fitted simultaneously to many galaxy datasets, each with their own unique light model.

An extension to a graphical model is a hierarchical model. Here, the shared parameter(s) of the model do not have exactly the same value in every dataset. Instead, the shared parameter(s) are drawn from a common parent distribution (e.g. a Gaussian). It is the parameters of this parent distribution that are shared across the dataset, and these are the parameters we ultimately wish to infer to understand the global behaviour of the model.

An example of such a model might be determining the parent distribution from which the Sersic index’s of galaxies are drawn.

A full description of graphical and hierarchical models can be found in the graphical package of the autogalaxy_workspace.