For snow avalanches, passive defense structures are generally designed by considering high return period events. However, defining a return period turns out to be tricky as soon as different variables are simultaneously considered. This problem can be overcome by maximizing the expected economic benefit of the defense structure, but purely stochastic approaches are not possible for paths with a complex geometry in the runout zone. Therefore, in this paper, we include a multivariate numerical avalanche propagation model within a Bayesian decisional framework. The influence of a vertical dam on an avalanche flow is quantified in terms of local energy dissipation with a simple semi-empirical relation. Costs corresponding to dam construction and the damage to a building situated in the runout zone are roughly evaluated for each dam height-hazard value pair, with damage intensity depending on avalanche velocity. Special attention is given to the poor local information to be taken into account for the decision. Using a case study from the French avalanche database, the Bayesian optimal dam height is shown to be more pessimistic than the classical optimal height because of the increasing effect of parameter uncertainty. It also appears that the lack of local information is especially critical for a building exposed to the most extreme events only. The residual hazard after dam construction is analyzed and the sensitivity to the different modelling assumptions is evaluated. Finally, possible further developments of the approach are discussed.