Approximate Bayesian Computation for Estimating Parameters of Data-Consistent Forbush Decrease Model

Abstract

Realistic modeling of complex physical phenomena is always quite a challenging task. The main problem usually concerns the uncertainties surrounding model input parameters, especially when not all information about a modeled phenomenon is known. In such cases, Approximate Bayesian Computation (ABC) methodology may be helpful. The ABC is based on a comparison of the model output data with the experimental data, to estimate the best set of input parameters of the particular model. In this paper, we present a framework applying the ABC methodology to estimate the parameters of the model of Forbush decrease (Fd) of the galactic cosmic ray intensity. The Fd is modeled by the numerical solution of the Fokker–Planck equation in five-dimensional space (three spatial variables, the time and particles energy). The most problematic in Fd modeling is the lack of detailed knowledge about the spatial and temporal profiles of the parameters responsible for the creation of the Fd. Among these parameters, the diffusion coefficient plays a central role. We employ the ABC Sequential Monte Carlo algorithm, scanning the space of the diffusion coefficient parameters within the region of the heliosphere where the Fd is created. Assessment of the correctness of the proposed parameters is done by comparing the model output data with the experimental data of the galactic cosmic ray intensity. The particular attention is put on the rigidity dependence of the rigidity spectrum exponent. The proposed framework is adopted to create the model of the Fd observed by the neutron monitors and ground muon telescope in November 2004.

Parameter Estimation for RANS Models Using Approximate Bayesian Computation

“…The ABC method was introduced, and first widely applied, in population genetics [20][21][22], and was subsequently implemented in a wide range of other scientific areas [23][24][25][26][27][28] (detailed reviews are provided by Csilléry et al [29], Marin et al [30], Lintusaari et al [31], Sisson et al [32], and Beaumont [33]). More recently, ABC has been employed in engineering contexts for the estimation of rate coefficients in chemical kinetic models [34], for the estimation of boundary conditions in complex thermal-fluid flows [35], and for determining unknown model parameters in autonomic [36] and nonlinear [37] subgrid-scale closure models for LES.…”

A method for analyzing complex structured data with elements of machine learning

“…Однако дальнейшие разработки [11] показали, что алгоритм не является достаточно эффективным и может давать недостоверный результат -применение алгоритма за 3 года не позволило идентифицировать более 50 % солнечных протонных событий. Другими учеными [12] предлагается применение методологии приближенных байесовских вычислений для оценки параметров модели Форбуш-понижения интенсивности галактических космических лучей. Но данный подход не получил четкой формализации ввиду отсутствия длинных рядов данных, охватывающих длительность Форбуш-понижения, а также отсутствия данных нескольких детекторов с различимой жесткостью откликов [12].…”

“…Другими учеными [12] предлагается применение методологии приближенных байесовских вычислений для оценки параметров модели Форбуш-понижения интенсивности галактических космических лучей. Но данный подход не получил четкой формализации ввиду отсутствия длинных рядов данных, охватывающих длительность Форбуш-понижения, а также отсутствия данных нескольких детекторов с различимой жесткостью откликов [12].…”

Parameter Estimation for Subgrid-Scale Models Using Markov Chain Monte Carlo Approximate Bayesian Computation

“…The ABC method was introduced and first widely applied in population genetics [20][21][22] and molecular genetics [23]. It has subsequently been used in other scientific areas such as astrophysics [24,25], chemistry [26], epidemiology [27,28] and ecology [29]. More detailed recent reviews of the ABC approach are provided by Csilléry et al [30], Marin et al [31], Lintusaari et al [32], Sisson et al [33] and, most recently, Beaumont [34].…”