DAGs (Directed Acyclic Graphs)

1. Description

DAG (Directed Acyclic Graph) is a graphical structure where nodes are connected through directed edges. It relies on conditional independences which allow decomposition of information on strength of associations in BR models into distinct probability distributions.[1][2][3][4]

2. Evaluation

2.1 Principle
  • The principles of DAGs are mathematically exhaustive and require technical knowledge of probability theory.
  • Whenever a DAG is consistent with the conditional independences among variables, the joint probability distribution can be computed as the product of Conditional Probabilities Tables (CPTs).
  • The joint probability distribution can address the uncertainty of any subset of variables in the model, and conditionally on an observed subset of other variables (belief updating).

2.2 Features
  • The graphical structure of Bayesian Networks (BNs) may provide large domains with a compact probabilistic representation.
  • The CPTs are often difficult to elicit from the parameters reported in the literature or from the knowledge of experts.
  • The DAG structure can be exploited to facilitate the estimate of the quantitative BN component from data.
  • There are a few extensions to allow continuous random variables to be treated without discretisation and the DAG representing one unit of observation being meant as replicate for all available observations.
  • MCMC methods can be applied to learn the distribution of the quantitative parameters in the model.
  • BNs may also support personalised medical decisions on several drug options, taking into account of a possibly large set of patient characteristics through simulations.
  • It can summarise the balance between risk and benefits in one single measure.
  • Influence diagrams extend BNs to incorporate decision nodes and utility nodes in order to avoid the need to iterate a simulation for each decision option.
  • Variables representing risk and benefits have to be linked to utility nodes after having been preventively defined on the same quantitative scale.[4]

2.3 Visualisation
  • Some expertise may be needed in the interpretation of arrows, as their direction represents how the joint probability distribution is marginalised over the variables, not necessarily information about causal relations.

2.4 Assessability and accessibility
  • Conditional independence among variables may be assessed by means of statistical tests applied on data, e.g. using log-linear regression analysis.
  • Conditional independencies could be also anticipated from knowledge on how the variables are causally related, e.g. from experimental study designs or from information about the temporal order of event.

3. References

[1] Pearl J. Probabilistic reasoning in intelligent systems: networks of plausible inference. San Francisco, CA: Morgan Kaufmann Publishers, Inc.; 1988.
[2] Darwiche A. Bayesian Networks. http://reasoning.cs.ucla.edu/. 2009.
[3] Jensen FV. An introduction to Bayesian Networks. 1 ed. Secaucus, NJ: Springer-Verlag New York, Inc.; 1996.