This paper presents a probabilistic model for rea soning about the state of a system as it changes over time, both due to exogenous and endoge nous influences. Our target domain is a class of medical prediction problems that are neither so urgent as to preclude careful diagnosis nor progress so slowly as to allow arbitrary testing and treatment options. In these domains there is typically enough time to gather information about the patient's state and consider alterna tive diagnoses and treatments, but the temporal interaction between the timing of tests, treat ments, and the course of the disease must also be considered. Our approach is to elicit a qualitative structural model of the patient from a human expert-the model identifies important attributes, the way in which exogenous changes affect attribute val ues, and the way in which the patient's condition changes endogenously. We then elicit probabilis tic information to capture the expert's uncer tainty about the effects of tests and treatments and the nature and timing of endogenous state changes. This paper describes the model in the context of a problem in treating vehicle accident trauma, and suggests a method for solving the model based on the technique of sequential im putation. A complementary goal of this work is to un derstand and synthesize a disparate collection of research efforts all using the name "proba bilistic temporal reasoning." This paper ana lyzes related work and points out essential dif ferences between our proposed model and other approaches in the literature. of "temporal decision problems." Temporal decision problems are those in which the physician's options in gathering information about the patient or treat ing a diagnosed problem take roughly as much time as it takes the disease to cause significant changes in the patient's condition if left untreated. Therefore the physician will typically have some time to gather addi tional information, think about alternative diagnoses, or wait for a change in the patient's status. On the other hand, delaying treatment to gather information or to consider alternative diagnoses might lead to sit uations in which the patient's state changes for the worse. We therefore need to model both the exogenous changes to the patient (traumatic events, treatments, tests) and endogenous changes (due to the progression of a disease or injury, for example), and we will con centrate on those problems in which endogenous and exogenous changes tend to occur at the same rate. 1 The fact that our models will be elicited from a human expert requires that the model's structure and param eters be elicitable naturally and concisely. Our experi ence with elicitation leads us to a model in which the expert first provides a structural model of the domain, and then provides probabilistic parameters that quan tify his uncertainty associated with that structure. The paper is organized as follows: first we present a motivating example and describe the model. Next we discuss the inference problem, and describe techniques for incrementally building and solving the model. We finish with a comparison of this work to other research in the area, pointing out an essential difference be tween two disparate lines of work both using the name "probabilistic temporal reasoning." 2 Example The following example will motivate the representa tional needs and choices for the model, and in Sec-1 Exogenous changes are those caused by forces external to the system as opposed to endogenous changes which are generated by forces internal to the system.
The "Network of exogenous events and endogenous changes" REF ) is a probabilistic model for reasoning about the system as it changes over time, both due to exogenous events and endogenous changes.
Probabilistic Temporal Reasoning with Endogenous Change
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Computer Science