This example originates from the seminal paper of Lauritzen & Spiegelhalter (1988).
Shortness-of-breath (dyspnoea) may be due to tuberculosis, lung cancer, bronchitis, more than one of these diseases or none of them. A recent visit to Asia increases the risk of tuberculosis, while smoking is known to be a risk factor for both lung cancer and bronchitis. The results of a single chest X-ray do not discriminate between lung cancer and tuberculosis, as neither does the presence or absence of dyspnoea.
If we learn the fact that a patient is a smoker, we will adjust our beliefs (increased risks) regarding lung cancer and bronchitis. However, our beliefs regarding tuberculosis are unchanged (i.e., tuberculosis is conditionally independent of "smoking" given the empty set of variables). Now, suppose we get a positive X-ray result for the patient. This will affect our beliefs regarding tuberculosis and lung cancer, but not our beliefs regarding bronchitis (i.e., bronchitis is conditionally independent of X-ray given smoking). However, had we also known that the patient suffers from shortness-of-breath, the X-ray result would also have affected our beliefs regarding bronchitis (i.e., "bronchitis" is not conditionally independent of "X-ray" given "smoking" and "dyspnoea").
A Bayesian network for the knowledge described above can look like this:
This network has been installed on your computer with the Hugin software. Open the network in the Hugin Graphical User Interface (Note: not all browsers can open Hugin directly). You can find the network in the directory where you installed Hugin (e.g., C:\Program Files\Hugin\Hugin Lite\Samples).
You can also find the samples at the Hugin download area.