Developing Complete Conditional Probability Tables from Fractional Data for Bayesian Belief Networks

Abstract

Bayesian belief network (BBN) can be a powerful tool in decision making processes. Development of a BBN requires data or expert knowledge to assist in determining the structure and probabilistic parameters in the model. As data are seldom available in the engineering decision making domain, a major barrier in using domain experts is that they are often required to supply a huge and intractable number of probabilities. Techniques for using fractional data to develop complete conditional probability tables were examined. The results showed good predictability of the missing data in a linear domain by the piecewise representation method. By using piecewise representation, the number of probabilities to be elicited for a binary child node with k binary parent nodes is now 2k rather than 2 k .

Methodology for Bayesian Belief Network Development to Facilitate Compliance with Water Quality Regulations

“…The number of conditional probabilities required to define a node increases exponentially as the number of parent nodes increases (Tang 2005). Therefore, during the development of the model structure, the maximum number of parent nodes for any variable was limited to three by determining which phenomena were most important to represent.…”

“…A possible bias introduced by the probability scale is the use of 1% to describe all low probabilities, since it was the lowest value on the scale and associated with the descriptor "impossible." The probability scale, adapted from Tang and McCabe (2007), is shown in Table 2. Elicitation took place in February 2007 in the City of Saskatoon, Saskatchewan, Canada.…”

“…The latter includes averaging, weighting, and linear and logarithmic opinion pools (Tang 2005). A Bayesian updating technique was selected for this methodology because it addressed two important considerations: benefiting from the heterogeneity of expert knowledge and managing the quality of expert judgements especially from small groups in which overconfidence, in particular, could have a significant impact (Clemen and Winkler 1999).…”

“…The influence of a parent node on the child is quantified by conditional probabilities (Coupé and Van der Gaag 2002). The number of probabilities required to complete a node's probability table is expressed by Equation 1 (Tang 2005):…”

Bayesian Model for Cost Estimation of Construction Projects

“…Kim and Reinschmidt [14] focused on the probabilistic schedule forecasting of ongoing projects. Tang and McCabe [15] approached the development of a method for incomplete data to estimate the whole domain in engineering management decision making. Haas and Einstein [16] applied bayesian techniques to their developed too, decision aids for tunneling.…”