• BAYESIAN DECISION ANALYSIS OF A STATISTICAL RAINFALL/RUNOFF RELATION

      Gray, Howard Axtell; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-10)
      The first purpose of this thesis is to provide a framework for the inclusion of data from a secondary source in Bayesian decision analysis as an aid in decision making under uncertainty. A second purpose is to show that the Bayesian procedures can be implemented on a computer to obtain accurate results at little expense in computing time. The state variables of a bridge design example problem are the unknown parameters of the probability distribution of the primary data. The primary source is the annual peak flow data for the stream being spanned. Information pertinent to the choice of bridge design is contained in rainfall data from gauges on the watershed but the distribution of this secondary data cannot be directly expressed in terms of the state variables. This study shows that a linear regression equation relating the primary and secondary data provides a means of using secondary data for finding the Bayes risk and expected opportunity loss associated with any particular bridge design and single new rainfall observation. The numerical results for the example problem indicate that the information gained from the rainfall data reduces the Bayes risk and expected opportunity loss and allows for a more economical structural design. Furthermore, the careful choice of the numerical methods employed reduces the computation time for these quantities to a level acceptable to any budget.