Networks for Bayesian Statistical Inference

Abstract

We first spell out how a credal network can be related to a statistical model, i.e. a set of statistical hypotheses. Recall that a credal network is associated with a credal set, a set of probability functions over some designated set of variables. Hence a credal set may be viewed as a statistical model: each element of the credal set is a probability function over the set of variables, and this probability may be read as a likelihood of some hypothesis for observations of valuations of the network. Conversely, any statistical model concerns inter-related trials of some specific set of variables, so that we can identify any statistical model with a credal network containing these variables. Here we deal with non-causal statistical hypotheses; (Leuridan, 2008, Chapter 4) argues that credal nets can also be used to represent causal hypotheses. An detailed illustration of many ideas in this section can be found in (Romeijn et al., 2009).