Our approach to temporal reasoning for the HDP raises several issues: Why temporal constraints? What does a hypothesis represent? What hypotheses belong in a differential? What do the probabilities represent?
One possible alternative to temporal constraints is to use probability density functions (PDFs). Probability statements such as that for high LAP causing PC with different probabilities for times less than an hour, one to six hours, and greater than six hours are essentially approximations of PDFs. There are two problems with using PDFs. The obvious one is the increased computational burden imposed on an already computation intensive task. The second problem is how to break up a structure consisting of PDFs into hypotheses. The explicit time bounds provide a natural way to generate and compare different hypotheses. Finally, it is difficult to estimate the time bounds and probabilities for this model and the task of estimating PDFs for each causal relation in a 200 node model would be nearly impossible.
Given a hypothesis consisting of a network of causally linked nodes with temporal intervals, what does it represent? If one thinks in terms of possible scenarios producing the observed findings, the hypothesis is a finite region in the space of possible scenarios. That is, it is all scenarios meeting the constraints on the hypothesis nodes. The bounds of the region are defined by the clinically significant distinctions that determine the time bounds in the model. Thus, each region defined by a hypothesis network should differ from every other region in some detail of potential clinical significance. The question then is what differences might have clinical significance. The most extreme position would be to use each region defined by a distinction in the model as an indication of clinical significance. In the analysis of the example, we took a less restrictive position and once the temporal constraints of the data was accounted for no other distinctions were enforced unless they involved nodes being included in the hypothesis. A third possible position would be to only enforce the temporal distinctions of the data and leave nodes for which there is no evidence other than a possible cause as unknown. The appropriate strategy depends on the purpose of the diagnosis, since diagnosis is a tool for patient management and not an end in itself.
What hypotheses belong in the differential again depends to some extent on the purpose of the differential. If the user is interested in the overall diagnosis of the patient, only hypotheses that differ in nodes of diagnostic significance should be included. In the example, the distinction of with and without pneumonia is significant but the distinction of continuing or ended low LV function may be too small a detail. However, if the user is considering what changes to make in the therapy for the patient, the fact that the low LV function may have ended and therefore the nitroglycerin may no longer be necessary is a useful consideration. So far, the principle use of the HDP has been to explain the overall diagnosis, so the program only presents hypotheses with diagnostic distinctions.
If the hypothesis represents all possible combinations of times of causation and persistence that are consistent with the pattern of nodes in the hypothesis within the time constraints on the nodes, then the probability should be the sum of the probabilities of all of the mutually exclusive allowable combinations of times through the hypothesis - essentially a multiple integration of the possible probabilities over time. Because of the computational difficulties associated with this strategy, we have chosen a heuristic for estimating the probability. The probability for each time interval is determined locally from the constraints on the causes. Thus, in the `corrected high LAP' hypothesis, there was no need to decide how long the low LVF continued and no reason to decide how long the high LAP continued in the `normalized LVF' hypothesis. It would be possible to make a model in which there were situations where unlikely hypotheses would be attributed significant probabilities, but in practice the relative probabilities for the hypotheses produced are consistent with our expectations.