Sets of Priors Reflecting Prior-Data Conflict and Agreement

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the advantage that prior-data conflict sensitivity can be modelled: Ranges of posterior inferences should be larger when prior and data are in conflict. We propose a new method for generating prior sets which, in addition to prior-data conflict sensitivity, allows to reflect strong prior-data agreement by decreased posterior imprecision.Comment: 12 pages, 6 figures, In: Paulo Joao Carvalho et al. (eds.), IPMU 2016: Proceedings of the 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Eindhoven, The Netherland

Lower Willamette River Model: Boundary Conditions and Model Setup

Water Environment Services of Clackamas County is in the process of planning upgrades on several of its sewage treatment plants which discharge into the Lower Willamette River. The goals of the modeling effort are to: • Gather data to construct a computer simulation model of the Lower Willamette River system including part of the Lower Columbia River and the Willamette River above the Oregon City Falls; Because of the tidal influence in the Lower Willamette River, portions of the Columbia River that might affect the Lower Willamette River water quality were also modeled. Also, a section of the Willamette River above the head of tide, the Oregon City Falls, was modeled because of the lack of good boundary condition data at the Falls. • Ensure that the model accurately represents the system physics and chemistry (flow, temperature, dissolved oxygen and nutrient dynamics); • Use the model to evaluate how to meet various future discharge scenarios for the sewage district. A hydrodynamic and water quality model, CE-QUAL-W2 Version 3 (Wells, 1997), is being applied to model the Willamette-Columbia system. CE-QUAL-W2 is a two dimensional (longitudinal-vertical), laterally averaged, hydrodynamic and water quality model that has been under development by the Corps of Engineers Waterways Experiments Station (Cole and Wells, 2000). In order to model the system, the following data were required: • Willamette and Columbia River flow, water level and water quality data • Tributary inflows and water quality • Meteorological conditions • Bathymetry of the Columbia and Willamette Rivers and several side channels • Point source inflows and water quality characteristics Many local, state and federal agencies have been collecting data in the Lower Willamette and Columbia Rivers. This report summarizes data used in the modeling effort

Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. When the variance term is null we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation and the methodology is illustrated using real and simulated data sets.Comment: 8 graphs 35 page