Confidence Intervals Analysis

Context

The Confidence Intervals Analysis helps interpret a wide range of metrics relating to nodes in a Bayesian network.
In many of BayesiaLab’s reports, such as the Target Analysis Report, quantities are displayed as single-point estimates, for instance, the mean value of a node, or the Mutual Information between two nodes.
When comparing such values between several nodes, single-point estimates are not enough to judge as to which node is higher in value or more important.
Importantly, we need to take into account the uncertainty associated with any estimates, regardless of whether the uncertainty comes from assessments or from a small sample size.
Before we explain the workflow for the Confidence Intervals Analysis, we need to take a step back to recapitulate the Confidence Intervals Report.

To start the Confidence Intervals Analysis, go to Menu > Analysis > Visual > Sensitivity > Confidence Intervals.
The Confidence Intervals Analysis constructs the Confidence Intervals exactly the same way the Confidence Intervals Report described above.
This process is conceptualized in the following diagram. It shows the probability densities of the parameter estimates.

Next, BayesiaLab performs a Monte Carlo Simulation by sampling probabilities from the constructed Confidence Intervals and creating a Bayesian network for each sample.
In this context, you need to specify the number of samples BayesiaLab draws from the parameter distributions for generating the corresponding Bayesian networks.
Setting a value of 10,000 means that BayesiaLab will generate 10,000 Bayesian networks with parameters sampled from the Confidence Intervals.
Then, these 10,000 networks are evaluated in terms of how the sampled parameters affect the Joint Probability Distribution.
The Confidence Intervals Analysis Report calculates the following items:
- States’ Probabilities
- Mean
- The screenshot shows the distributions of the State Probabilities of the node Age.
Furthermore, if the network contains a Target Node, and you set the Compute Metrics on Target option, BayesiaLab also computes the following metrics for each node with regard to the Target Node.
- Mutual Information
- Normalized Mutual Information
- Relative Mutual Information
- The following screenshot shows the distribution of Relative Mutual Information of the node Typical Chest Pain with regard to the Target Node Condition. —>

To demonstrate this workflow, we use the Coronary Artery Disease network, which you can download here:

CoronaryArteryDisease.xbl
In this example, we run the Confidence Intervals Analysis on all nodes.
Next, we select Relative Mutual Information as the metric of interest and sort the tabs accordingly.
Each tab at the top of the window represents one node in the network.
As we click through the tabs from left to right, we observe that the Relative Mutual Information decreases.
This is in sync with what we would obtain from a Target Analysis Report Menu > Analysis > Report > Target > Relationship with the Target Node.
We show the corresponding report here just for reference:
We may now be tempted to read this report as a hierarchy in terms of importance.
However, we need to be careful about such conclusions. The following animation highlights the issue:
By overlaying the distributions of the Relative Mutual Information values, we can only find that Typical Chest Pain is clearly distinct from the remaining nodes.
The Relative Mutual Information distributions of the remaining nodes seem to blend into each other, which implies that the hierarchy the Target Analysis Report above suggests isn’t nearly as clear.
As a result, we need to be careful with any claims regarding a rank order of the nodes unless the Confidence Interval Analysis demonstrates clearly separated distributions.