Logical Probability and Risk Assessment

Publisher Website
Google Scholar
Abstract
A risk assessment is intended to provide a statement of current knowledge which is intended to inform a decision-maker of the current state of knowledge in response to a particular concern. Because answering the concerns of decision-makers often requires inferences to be drawn, doubt often arises over how the inference is to be drawn. In quantitative risk assessment, where a mathematical equation or model is used to draw the inference, this uncertainty is referred to as model uncertainty. A two-step process, which is referred to as logical probability, is proposed as a technique for representing model uncertainty in a risk assessment. The first step involves assigning model weights in which the degree of evidential support for each of the alternative models is considered. The second step involves assigning a unique interval in the range of 0 to 1 for each model which reflects the models' weight, to form a probability distribution. While the second step is straightforward, the first step is not. Assigning model weights requires consideration of any line of evidence that may reasonably impact the validity of the assertion of a model. While the development of a procedure for doing so may be expected to be a process which reflects the subjective preferences of whomever is involved in creating it, there are some historical precedents on which to build. Foremost among these are (1) the use of a correlation coefficient or other goodness-of-fit criteria to measure the degree of correspondence between a given model and a set of observations which are used as evidence to support it, and (2) preference given to models which are simpler, which may be ascertained as the number of adjustable parameters the model contains. Additional principles, which have little or no tradition to stand on, must be used to reflect the impact of other empirically supported beliefs on model preference. The procedure proposed is comparable to the procedure known as decision analysis, in which probabilities are assigned to alternative models based on expert or subjective input. The principal difference in the present case is that it is suggested that principles which transcend the decision at hand should be sought and articulated in order to generate a consistent measure of uncertainty arising from interpretation.