In this study, decomposition is used as a tool for the assessment of continuous probability distributions. The goal of using decomposition is to obtain better calibrated probability distributions by expressing a variable as a known function of several component variables. Three target quantities were used in the study. Each was assessed holistically and using two different decompositions. Thus, each subject provided three distributions for each of the three target quantities. The recomposed assessments were compared to holistic assessments. The distributions obtained using decomposition were found to be much better calibrated than those obtained holistically. Two methods of aggregating distributions from multiple subjects were also examined. One involves aggregating (averaging) distributions before recomposing while the second method involves recomposing and then averaging distributions for the target variable. The second method was found to be slightly better, although both showed better calibration than was found in the individual assessments.When formal methods are employed to quantify the judgments of subjects, decomposition may be used to reduce the complexity of the task, make the rationales behind the judgments transparent, and improve the quality of the elicited distributions. While there are a number of studies evaluating the usefulness of decomposition in establishing point estimates, there is little empirical evidence regarding the ability of this method to produce better probability assessments than holistic methods. This is the primary research question of interest in this study.When individuals in a group are required to make judgments of component events, the method of combining their judgments has not been resolved in the literature. This is a secondary item of interest and will be examined in an exploratory manner in the present study.
DECOMPOSITION AND PROBABILITY ASSESSMENTDecomposition of the target quantity into several constituent quantities may be accomplished using simple mathematical models of known relations. The target quantity is expressed through a mathematical function such as T =AX, Y,Z). This form of decomposition is called algorithmic decomposition
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