## Modeling unreliable observations in Bayesian networks by credal networks

**Authors: **Alessandro Antonucci and Alberto Piatti

**Abstract:** Bayesian networks are probabilistic graphical models widely employed
in AI for the implementation of knowledge-based systems. Standard
inference algorithms can update the beliefs about a variable of interest
in the network after the observation of some other variables. This
is usually achieved under the assumption that the observations could
reveal the actual states of the variables in a fully reliable way.
We propose a procedure for a more general modeling of the observations,
which allows for updating beliefs in different situations, including
various cases of unreliable, incomplete, uncertain and also missing
observations. This is achieved by augmenting the original Bayesian
network with a number of auxiliary variables corresponding to the
observations. For a flexible modeling of the observational process,
the quantification of the relations between these auxiliary variables
and those of the original Bayesian network is done by credal sets,
i.e., convex sets of probability mass functions. Without any lack
of generality, we show how this can be done by simply estimating
the bounds for the likelihoods of the observations. Overall, the
Bayesian network is transformed into a credal network, for which
a standard updating problem has to be solved. Finally, a number of
transformations that might simplify the updating of the resulting
credal network is provided.

**Year:** 2009.

**Details:** In Godo, L. and Pugliese, A. (Eds.), *Scalable Uncertainty Management, Third International Conference,
SUM 2009, Washington, DC, USA, September 28-30, 2009. Proceedings*. Springer, pp. 28-39.

A version similar to the published paper can be downloaded.