 In this section, we will discuss causal models that incorporate probability in some way. Probability may be used to represent our uncertainty about the value of unobserved variables in a particular case, or the distribution of variable values in a population. Often we are interested in when some feature of the causal structure of a system can be identified from the probability distribution over values of variables, perhaps in conjunction with background assumptions and other observations. For example, we may know the probability distribution over a set of variables \(\bV\), and want to know which causal structures over the variables in \(\bV\) are compatible with the distribution. In realistic scientific cases, we never directly observe the true probability distribution P over a set of variables. Rather, we observe finite data that approximate the true probability when sample sizes are large enough and observation protocols are well-designed. We will not address these important practical concerns here. Rather, our focus will be on what it is possible to infer from probabilities, in principle if not in practice. We will also consider the application of probabilistic causal models to decision theory and counterfactuals.