Occurrences Report

Context, Background, and Motivation

• Occurrences refer to the number of observations in a cell of a Probability Table or a Conditional Probability Table.

• The number of cells in a Conditional Probability Table is a function of the following parameters:

  • The number of Parent Nodes.

  • The number of Node States of the Parent Nodes.

  • The number of Node States of the Child Nodes.

• The following example with one Parent Node (Age, measured in years) and one Child Node (BMI, i.e., Body Mass Index, measured in $\frac{{kg}}{{{m^2}}}$) illustrates this with numbers:
• Here, Age is discretized into 4 states and BMI into 6 for a total of 48 cells in the table associated with BMI.

• The numbers in each cell are counts of observations or Occurrences. In our case, each Occurrence represents one person from the sample of 200 individuals.

• For instance, the Occurrence table associated with BMI states that Count(BMI≤20 | Age≤30)=2. So, we have only two Occurrences of that particular condition, i.e., only two individuals who are 30 years old or younger have a BMI of 20 or lower.

• To create a Bayesian network, BayesiaLab needs to translate the Occurrences in each cell into probabilities.

• However, with a small number of Occurrences, that can become an issue.

• We have repeatedly referenced a rule of thumb, which says that we should have a minimum of 5 Occurrences per cell to estimate a Probability Table or Conditional Probability Table reliably.

• In our example, several cells fall below the recommended minimum.

• Such deficiencies are easy to recognize in a small example, but in more complex networks, it can be difficult to spot such weaknesses.

• That is the motivation for the Occurrence Report. It displays all tables in a network and visually highlights potentially problematic cells with low Occurrences.

Usage

• Select the nodes you want to include in the Occurrences Report. I none are selected, the analysis will be performed on all nodes.

• Select Main Menu > Network > Reports > Reports> Occurrences to create the Occurrences Report.

• The Occurrence Report opens up and shows all Probability Tables and Conditional Probability Tables.

• The fields in the report are color-coded to highlight potential issues:

  • Cells with 0 Occurrences are marked in red.

  • Cells with 5 Occurrences are marked in yellow. This is generally considered the minimum number of Occurrences.

  • Cells with 40 or more Occurrences are marked in green.

• Furthermore, the Occurrence Report calculates the mean number of Occurrences for each row in all Probability Tables and Conditional Probability Tables.

• If the mean value of any row in any of the nodes drops below the threshold of 5, the corresponding nodes are called out at the top of the report.

• The affected nodes in the Graph Panel are also marked with the information icon .