Sometimes it is not quite obvious in which direction a link should point. One should be careful when modeling the causal dependences in a BN. When there is a causal dependence from a node A to another node B, we expect that when A is in a certain state this has an impact on the state of B. The BN in Figure 1 models the causal dependence from Sick to Loses and from Dry to Loses. The nodes Dry and Loses tell us in the same way if the tree is dry and if the tree is losing its leaves, respectively.įigure 1: BN representing the domain of the Apple Jack problem. The node Sick tells us that the apple tree is sick by being in state “sick”. The BN consists of three nodes: Sick, Dry, and Loses which can all be in one of two states: Sick can be either “sick” or “not” - Dry can be either “dry” or “not” - and Loses can be either “yes” or “no”. The situation can be modeled by the BN in Figure 1. On the other hand the losing of leaves can be an indication of a disease. He knows that if the tree is dry (caused by a drought) there is no mystery - it is very common for trees to lose their leaves during a drought. Now, he wants to know why this is happening. One day Apple Jack discovers that his finest apple tree is losing its leaves. The problem domain of this example is a small orchard belonging to Jack Fletcher (let’s call him Apple Jack). The following example tries to make all this more concrete. If the node is continuous, the CPT contains a mean and a variance parameter for each configuration of the states of its discrete parents (one if there are no discrete parents) and a regression coefficient for each continuous parent for each configuration of the states of the discrete parents. Thus, the number of cells in a CPT for a discrete node equals the product of the number of possible states for the node and the product of the number of possible states for the parent nodes. If the node is discrete, each cell in the CPT (or, in more general terms, the conditional probability function (CPF)) of a node contains a conditional probability for the node being in a specific state given a specific configuration of the states of its parents. If a node do have parents (i.e., one or more links pointing towards it), the node contains a conditional probability table (CPT). If the node is continuous, it contains a Gaussian density function (given through mean and variance parameters) for the random variable it represents. If the node is discrete, it contains a probability distribution over the states of the variable that it represents. If a node doesn’t have any parents (i.e., no links pointing towards it), the node will contain a marginal probability table. The links between the nodes represent (causal) relationships between the nodes. Throughout this document, the terms “variable” and “node” are used interchangeably. The network (or graph) of a BN is a directed acyclic graph (DAG), i.e., there is no directed path starting and ending at the same node.Ī node represents either a discrete random variable with a finite number of states or a continuous (Gaussian distributed) random variable. A BN is a network of nodes connected by directed links with a probability function attached to each node.
Previously, the term causal probabilistic networks has also been used. This uncertainty can be due to imperfect understanding of the domain, incomplete knowledge of the state of the domain at the time where a given task is to be performed, randomness in the mechanisms governing the behavior of the domain, or a combination of these.īayesian networks are also called belief networks and Bayesian belief networks. A Bayesian network (BN) is used to model a domain containing uncertainty in some manner.
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