Inference | Hyperparameter Updating
The Bayesian networks that are used in BayesiaLab are basically non parametric models. The easiest way to design parametric models consists in using equations for describing the probability distributions of the nodes that are part of the system you are modeling, i.e. what is usually called the parameters, and represent the parameters that are used in the equations, i.e. the hyperparameters, with additional nodes in the network.With such parametric model, observing the parameter Blood Sample allows updating the distributions of the hyperparameters via probabilistic inference. However, the node Blood Sample can just be used for capturing one piece of evidence, i.e one sample of the distribution that is described by the model.
The traditional approach for what is usually called Bayesian Updating is to create a parameter node per observation, while hyperparameters are shared by all parameter nodes.
The need to unroll the network, i.e. create as many parameter nodes as observations, is obviously not convenient, and makes exact inference quickly intractable when the number of observations increases.
The BayesiaLab's Hyperparameter Updating is a compact version where there is no need to unroll the network. It just requires:
- The association of the hyperparameter nodes with the predefined class Hyperparameter for identifying what are the nodes to update, and
- The representation of the conditional dependencies between the hyperparameters by adding an arc between these nodes. Indeed, even though the hyperparameters can be independent without any observation on the parameter, they become dependent after the first observation.
The new conditional probability distribution does not represent any dependency, i.e. we just need to select all the cells of the table and click on Normalize.
Renamed Feature: Hyperparameter Updating
Prior to version 8.0, this feature was available under Interactive Updating. It has been renamed Hyperparameter Updating.
New Feature: Manual Evidence-Setting
As of version 8.0, evidence scenario and/or internal data are not mandatory for using this feature. It is now possible to manually set evidence for updating the hyperparameters.