Bayesian inference and uncertainty quantification for source reconstruction of 137Cs released during the Fukushima accident

2021 ◽  
Author(s):  
Joffrey Dumont Le Brazidec ◽  
Marc Bocquet ◽  
Olivier Saunier ◽  
Yelva Roustan
Keyword(s):  
Bayesian Inference ◽  
Source Term ◽  
Temporal Evolution ◽  
Complete Characterization ◽  
Reversible Jump ◽  
Observation Error ◽  
Reversible Jump Mcmc ◽  
Fukushima Accident ◽  
Inference Problem ◽  
Nuclear Disaster

<p><span>In March 2011, large amount of radionuclides were released into the atmosphere throughout the Fukushima Daiichi nuclear disaster. This massive and very complex release, characterized by several peaks and wide temporal variability, lasted for more than three weeks and is subject to large uncertainties. The assessment of the radiological consequences </span><span>due to the exposure during the emergency phase </span><span>is highly dependent on </span><span>the challenging estimate of the source term.</span><span><br><br>Inverse modelling techniques have proven to be efficient in assessing the source term of radionuclides. Through Bayesian inverse methods, distributions of the variables describing the release such as the duration and the magnitude as well as the observation error can be drawn in order to get a complete characterization of the source.</span></p><p><span><br>For complex situations involving releases from several reactors, the temporal evolution of the release may be as difficult to reconstruct as its magnitude. The source term or function of the release is described in the inverse problem as a vector of release rates. Thus, the temporal evolution of the release appears in the definition of the time steps where the release rate is considered constant. The search for the release variability therefore corresponds to the search for the number and length of these successive time steps.</span></p><p><span>In this study, we propose to tackle the Bayesian inference problem through sampling Monte Carlo Markov Chains methods (MCMC), and more precisely the Reversible-Jump MCMC algorithm.<br>The Reversible-Jump MCMC method is a transdimensional algorithm which allows to reconstruct the time evolution of the release and its magnitude in the same procedure.<br></span></p><p><span>Furthermore, to better quantify uncertainty </span><span>linked to the reconstructed source term</span><span>, different approaches are proposed and applied. First, we discuss how to choose the likelihood and propose several distributions. Then, different approaches to model the likelihood covariance matrix are defined.</span></p><p><span><br>These different methods are applied to characterize the </span><sup><span>137</span></sup><span>Cs Fukushima source term. We present </span><span><em>a posteriori</em></span><span> distributions enable to assess the source term and the temporal evolution of the release, to quantify the uncertainties associated to the observations and the modelling of the problem.</span></p>

Bayesian inference and uncertainty quantification for source reconstruction of radionuclides release: application to recent European radionuclide detection events

2020 ◽  
Author(s):  
Joffrey Dumont Le Brazidec ◽  
Marc Bocquet ◽  
Olivier Saunier ◽  
Yelva Roustan
Keyword(s):  
Bayesian Inference ◽  
Source Term ◽  
Dispersion Model ◽  
Optimal Solution ◽  
Unknown Origin ◽  
Inverse Methods ◽  
Model Parameters ◽  
Radiological Protection ◽  
Fukushima Accident ◽  
Inference Problem

<p><span>In case of an accidental radioactive release, the </span><span>Institute for Radiological Protection and Nuclear Safety</span><span> (IRSN) uses atmospheric dispersion models to assess radiological consequences for human health and environment. The accuracy of the models’ results is highly dependent on the meteorological fields and </span>the source term, including the location, the duration, the magnitude and the isotopic composition of t<span>he release. </span></p><p><span>Inverse model</span><span>l</span><span>ing methods have proven to be efficient in assessing </span><span>the </span><span>source term. </span><span>Variational deterministic inverse methods have been used on the Fukushima accident and are suitable in operational use since they are able of quickly providing an optimal solution. </span><span><br>However the quantification of the uncertainties of the source term assessed is usually not easily accessible. In </span><span>contrast</span><span>, Bayesian inverse methods are developed in order to efficiently sample the distributions of the </span><span>variables</span><span> of the source, thus allowing to get a complete characteri</span><span>s</span><span>ation of the source. </span></p><p>In this study, we propose to tackle the Bayesian inference problem through two types of sampling methods: Monte Carlo Markov Chains methods (MCMC) with the parallel tempering algorithm and Stein variational gradient descent. The distributions of the control variables associated to the source and the observations errors are presented. To better quantify observations errors, different approaches based on the definition of the likelihood, the reduction of the number of observations and the perturbation of the meteorological fields and dispersion model parameters are implemented.<br><br>These different methods are applied on two case studies: the detection of Ruthenium 106 of unknown origin in Europe in autumn 2017 and the accidental release of Selenium 75 from a nuclear facility in Mol (Belgium) in May 2019. For both of these events, we present a posteriori distributions enable to identify the origin of the release, to assess the source term and to quantify the uncertainties associated to the observations, the dispersion model and meteorological fields. Finally, we show that the Bayesian method is suitable for operational use.</p>

Bayesian inference by reversible jump MCMC for clustering based on finite generalized inverted Dirichlet mixtures

2018 ◽  
Vol 23 (14) ◽  
pp. 5799-5813 ◽  
Author(s):  
Sami Bourouis ◽  
Faisal R. Al-Osaimi ◽  
Nizar Bouguila ◽  
Hassen Sallay ◽  
Fahd Aldosari ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Reversible Jump ◽  
Reversible Jump Mcmc ◽  
Dirichlet Mixtures ◽  
Inverted Dirichlet

Adaptive Proposal Construction for Reversible Jump MCMC

2008 ◽  
Vol 35 (4) ◽  
pp. 677-690 ◽  
Author(s):  
RICARDO S. EHLERS ◽  
STEPHEN P. BROOKS
Keyword(s):  
Reversible Jump ◽  
Reversible Jump Mcmc

Automating and evaluating reversible jump MCMC proposal distributions

2008 ◽  
Vol 19 (4) ◽  
pp. 409-421 ◽  
Author(s):  
Y. Fan ◽  
G. W. Peters ◽  
S. A. Sisson
Keyword(s):  
Reversible Jump ◽  
Reversible Jump Mcmc

scholarly journals Forecasting Software Using Laplacian AR Model based on Bootstrap-Reversible Jump MCMC: Application on Stock Price Data

Webology ◽  
2021 ◽  
Vol 18 (Special Issue 04) ◽  
pp. 1045-1055
Author(s):  
Sup arman ◽  
Yahya Hairun ◽  
Idrus Alhaddad ◽  
Tedy Machmud ◽  
Hery Suharna ◽  
...  
Keyword(s):  
Stock Price ◽  
Complex Structure ◽  
Arma Model ◽  
Bayesian Estimator ◽  
Ar Model ◽  
Reversible Jump ◽  
Mcmc Algorithm ◽  
Reversible Jump Mcmc ◽  
Variable Dimension ◽  
Fixed Dimension

The application of the Bootstrap-Metropolis-Hastings algorithm is limited to fixed dimension models. In various fields, data often has a variable dimension model. The Laplacian autoregressive (AR) model includes a variable dimension model so that the Bootstrap-Metropolis-Hasting algorithm cannot be applied. This article aims to develop a Bootstrap reversible jump Markov Chain Monte Carlo (MCMC) algorithm to estimate the Laplacian AR model. The parameters of the Laplacian AR model were estimated using a Bayesian approach. The posterior distribution has a complex structure so that the Bayesian estimator cannot be calculated analytically. The Bootstrap-reversible jump MCMC algorithm was applied to calculate the Bayes estimator. This study provides a procedure for estimating the parameters of the Laplacian AR model. Algorithm performance was tested using simulation studies. Furthermore, the algorithm is applied to the finance sector to predict stock price on the stock market. In general, this study can be useful for decision makers in predicting future events. The novelty of this study is the triangulation between the bootstrap algorithm and the reversible jump MCMC algorithm. The Bootstrap-reversible jump MCMC algorithm is useful especially when the data is large and the data has a variable dimension model. The study can be extended to the Laplacian Autoregressive Moving Average (ARMA) model.

Robust Full Bayesian Learning for Radial Basis Networks

2001 ◽  
Vol 13 (10) ◽  
pp. 2359-2407 ◽  
Author(s):  
Christophe Andrieu ◽  
Nando de Freitas ◽  
Arnaud Doucet
Keyword(s):  
Simulated Annealing ◽  
Convergence Theorem ◽  
Bayesian Learning ◽  
Simulated Annealing Algorithm ◽  
Minimum Description Length ◽  
Information Criterion ◽  
Model Parameters ◽  
Reversible Jump ◽  
Reversible Jump Mcmc ◽  
Radial Basis

We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible-jump MCMC simulated annealing algorithm to optimize neural networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima to a large extent. We show that by calibrating the full hierarchical Bayesian prior, we can obtain the classical Akaike information criterion, Bayesian information criterion, and minimum description length model selection criteria within a penalized likelihood framework. Finally, we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible-jump MCMC simulated annealing method.

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