# Probabilistic Modelling as Decision Making

*by*Mircea Grigoriu, Research Assoc.; Dept. of Civ. Engrg., McGill Univ., Montreal, Canada,

C. Allin Cornell, (M.ASCE), Prof. of Civ. Engrg.; Massachusetts Inst. of Tech., Cambridge, Mass.,

Daniele Veneziano, (A.M.ASCE), Assoc. Prof. of Civ. Engrg.; Massachusetts Inst. of Tech., Cambridge, Mass.,

**Serial Information**: Issue 4, Pg. 585-596

**Document Type:**Journal Paper

**Abstract:**

One of the factors that limits application of probabilistic reliability to engineering design is the arbitrariness with which probability distribution may be chosen. The problem is particularly severe when high reliability is demanded and information is scarce, e.g., in selecting tail probability laws for load and resistance variables. At the origin of this arbitrariness is the attempt to select models through inference procedures, i.e., solely on the basis of physical and statistical information. The problem is, by its very nature, one of decision making and should be resolved through methods of decision theory. If this is done, then a number of interesting facts emerge: (1)The optimal distribution is also defined under conditions of extreme uncertainty; (2)the optimal distribution is less sensitive to statistical sample variations than the distribution obtained by inference procedures; and (3)with limited statistical information, optimal distributions tend to err on the side of conservative design, with a degree of conservatism that decreases as the amount of information increases.

**Subject Headings:**Probability | Probability distribution | Statistics | Arbitration | Load and resistance factor design | Physical models | Decision making | Uncertainty principles

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