Probabilistic analysis using Bayesian networks
To carry out the probabilistic analysis using Bayesian networks, it is necessary to identify both the parent nodes and the child nodes. The first ones are characterized by their probabilities totals, while the seconds are determined by the conditioned probabilities in the presence of parents. Therefore, from a mathematical point of view, they are used total probabilities as well as conditioned probabilities (of occurrence of A given B) with the formula P (A | B) = P (A ∩ B) / P (B), which represents the probability that an event will occur if another event has occurred previously.
In our case, we will consider as parent nodes those that contain the demographic variables, since we think that they are variables that can have a direct relationship on cognitive impairment; On the other hand, the central node will represent the symptoms depressive, and from this five new child nodes will be derived. Therefore, before calculating the conditioned probabilities, the total probability of
the parent nodes of the central variable, named for this analysis (Depression).
The total probabilities are calculated for nodes that do not have parents. The data reflected reveal that, of the total sample, 69.7% were women, 63.6% of all subjects they were 75 years old or older and 37.9% were married. A second step involves the evaluation of the probabilities of presence of (Depression) conditioned to the presence / absence of their respective parents (gender, age, couple), conclude with the calculation of the conditioned probabilities of your five child nodes to the presence / absence of (Depression). To finish with the data analysis, we present the graphs that reflect the probabilities total and conditioned obtained through the bayes software. Once obtained the total and conditioned probabilities that characterize our sample, inferences are made probabilistic using the aforementioned software and obtaining different results. The program throws a series of graphs. First of all we have the graph that represents the nodes with each of its arcs, that is, the relationships that each node has, figure 1.
 |
| Figure 1. Representation of nodes and arcs using the Bayes software tool |
In the graph that appears in figure 2 the probabilities of occurrence of the different variables are shown, if the depressive symptoms will always be present in the sample, that is, if we only take into account the subsample of depressives
 |
| Figure 2. Representation of nodes indicating each of their probabilities. |