Bayes linear kinematics in the analysis of failure rates and failure time distributions

Collections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times

Suburban watershed nitrogen retention : estimating the effectiveness of stormwater management structures

Excess nitrogen (N) is a primary driver of freshwater and coastal eutrophication globally, and urban stormwater is a rapidly growing source of N pollution. Stormwater best management practices (BMPs) are used widely to remove excess N from runoff in urban and suburban areas, and are expected to perform under a wide variety of environmental conditions. Yet the capacity of BMPs to retain excess N varies; and both the variation and the drivers thereof are largely unknown, hindering the ability of water resource managers to meet water quality targets in a cost-effective way. Here, we use structured expert judgment (SEJ), a performance-weighted method of expert elicitation, to quantify the uncertainty in BMP performance under a range of site-specific environmental conditions and to estimate the extent to which key environmental factors influence variation in BMP performance. We hypothesized that rain event frequency and magnitude, BMP type and size, and physiographic province would significantly influence the experts’ estimates of N retention by BMPs common to suburban Piedmont and Coastal Plain watersheds of the Chesapeake Bay region. Expert knowledge indicated wide uncertainty in BMP performance, with N removal efficiencies ranging from 40%. Experts believed that the amount of rain was the primary identifiable source of variability in BMP efficiency, which is relevant given climate projections of more frequent heavy rain events in the mid-Atlantic. To assess the extent to which those projected changes might alter N export from suburban BMPs and watersheds, we combined downscaled estimates of rainfall with distributions of N loads for different-sized rain events derived from our elicitation. The model predicted higher and more variable N loads under a projected future climate regime, suggesting that current BMP regulations for reducing nutrients may be inadequate in the future