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

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.

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

<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>