Dynamic spatial Bayesian models for radioactivity deposition

Abstract

Dynamic spatial Bayesian (DSB) models are proposed for the analytical modelling of radioactivity deposition after a nuclear accident. The proposed models are extensions of the multi-variate time-series dynamic linear models of West and Harrison (1997) to Markov random field processes. They combine the outputs from a long-range atmospheric dispersal model with measured data (and prior information) to provide improved deposition prediction in space and time. Two versions of a Gaussian DSB model were applied to the radioactivity deposition in Bavaria over a 15 days period during the Chernobyl nuclear accident. One version had fixed functional forms for its spatial variances and covariances while the other allowed those to adapt and 'learn' from data in the conjugate Bayesian paradigm. There were two main sources of information for radioactivity deposition in our application: radioactivity measurements at a sparse set of 13 monitoring stations, and the numerical deposition evaluation of the atmospheric dispersal K-model for the points of a 64 · 64 regular grid. We have analysed the temporal predictions (one-step-ahead forecasting) of those DSB models to show that the dispersal K-model tended in general to underestimate the deposition levels at all times while the DSB models corrected for that although with different degrees of adjustment.

Bayesian decision support for complex systems with many distributed experts

“…-We relate the lines of the pseudo-code of Algorithm 3.1 to the equations (3)-(6) of Theorem 1 and their variations which include optimization steps in equations (7) and (8); -We then show that each panel and the SB have sufficient information to perform the steps of the algorithm they are responsible for; -We conclude by showing that the optimization steps, which in the algorithm correspond to lines (8) and (15), are able to identify optimal decisions using only combinations of quantities individual panels are able to calculate.…”

“…Since the SB : u * t,i −→ G i , each panel is able to computeū * t,i (lines 10-11) following equation (8). As noted before, if i is not the root of the DAG,ū * t,i is sent to the appropriate panel, whilst if i = 1, as specified…”

“…Each panel has enough information to do this, since line (10) guarantees that the scores are communicated to the panels overseeing father vertices and line (14) denotes the fact that the SB transmitsû t,i to the appropriate panels. The functionsũ t,i are then sent to the SB, who performs an optimization step in line (8) and communicates the result back to the panel. We address the validity of this step below.…”

“…For nuclear emergency management the first such probabilistic DSSs tended to focus on the initial consequences of the accident (French et al, 1995;Smith and Papamichail, 1999). Since then more sophisticated probabilistic modules modelling both early and later stages of the accident have been introduced (De and Faria, 2011;Richter et al, 2002;Zheng et al, 2009). …”

Using graphical models and multi-attribute utility theory for probabilistic uncertainty handling in large systems, with application to the nuclear emergency management

“…However in [3] it was recognized that the development of methodologies for uncertainty handling for use in nuclear DSSs that are both formal and practical were still in their infancy. During the intervening years technologies applying Bayesian techniques to this area ( [4], [5]) have advanced sufficiently to ensure that if fully formal methods are developed then it will be possible to actually implement those. So it is now timely to revisit this problem.…”