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PROBABILITIES AND MATH STATISTICS (113 journals)                     

Showing 1 - 85 of 85 Journals sorted alphabetically
Advances in Statistics     Open Access   (Followers: 10)
Afrika Statistika     Open Access   (Followers: 1)
American Journal of Applied Mathematics and Statistics     Open Access   (Followers: 13)
American Journal of Mathematics and Statistics     Open Access   (Followers: 9)
Annals of Data Science     Hybrid Journal   (Followers: 15)
Applied Medical Informatics     Open Access   (Followers: 12)
Asian Journal of Mathematics & Statistics     Open Access   (Followers: 7)
Asian Journal of Probability and Statistics     Open Access  
Austrian Journal of Statistics     Open Access   (Followers: 4)
Biostatistics & Epidemiology     Hybrid Journal   (Followers: 6)
Calcutta Statistical Association Bulletin     Hybrid Journal  
Communications in Mathematics and Statistics     Hybrid Journal   (Followers: 3)
Communications in Statistics - Simulation and Computation     Hybrid Journal   (Followers: 9)
Communications in Statistics: Case Studies, Data Analysis and Applications     Hybrid Journal  
Comunicaciones en Estadística     Open Access  
Econometrics and Statistics     Hybrid Journal   (Followers: 2)
Forecasting     Open Access   (Followers: 1)
Foundations and Trends® in Optimization     Full-text available via subscription   (Followers: 2)
Geoinformatics & Geostatistics     Hybrid Journal   (Followers: 10)
Geomatics, Natural Hazards and Risk     Open Access   (Followers: 14)
Indonesian Journal of Applied Statistics     Open Access  
International Game Theory Review     Hybrid Journal  
International Journal of Advanced Statistics and IT&C for Economics and Life Sciences     Open Access  
International Journal of Advanced Statistics and Probability     Open Access   (Followers: 7)
International Journal of Applied Mathematics and Statistics     Full-text available via subscription   (Followers: 4)
International Journal of Ecological Economics and Statistics     Full-text available via subscription   (Followers: 4)
International Journal of Game Theory     Hybrid Journal   (Followers: 3)
International Journal of Mathematics and Statistics     Full-text available via subscription   (Followers: 2)
International Journal of Multivariate Data Analysis     Hybrid Journal  
International Journal of Probability and Statistics     Open Access   (Followers: 3)
International Journal of Statistics & Economics     Full-text available via subscription   (Followers: 6)
International Journal of Statistics and Applications     Open Access   (Followers: 2)
International Journal of Statistics and Probability     Open Access   (Followers: 3)
International Journal of Statistics in Medical Research     Hybrid Journal   (Followers: 2)
International Journal of Testing     Hybrid Journal   (Followers: 1)
Iraqi Journal of Statistical Sciences     Open Access  
Japanese Journal of Statistics and Data Science     Hybrid Journal  
Journal of Biometrics & Biostatistics     Open Access   (Followers: 4)
Journal of Cost Analysis and Parametrics     Hybrid Journal   (Followers: 5)
Journal of Environmental Statistics     Open Access   (Followers: 4)
Journal of Game Theory     Open Access   (Followers: 1)
Journal of Mathematical Economics and Finance     Full-text available via subscription  
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Modern Applied Statistical Methods     Open Access   (Followers: 1)
Journal of Official Statistics     Open Access   (Followers: 2)
Journal of Quantitative Economics     Hybrid Journal  
Journal of Social and Economic Statistics     Open Access   (Followers: 4)
Journal of Statistical Theory and Practice     Hybrid Journal   (Followers: 2)
Journal of Statistics and Data Science Education     Open Access   (Followers: 2)
Journal of Survey Statistics and Methodology     Hybrid Journal   (Followers: 6)
Journal of the Indian Society for Probability and Statistics     Full-text available via subscription  
Jurnal Biometrika dan Kependudukan     Open Access   (Followers: 1)
Lietuvos Statistikos Darbai     Open Access   (Followers: 1)
Mathematics and Statistics     Open Access   (Followers: 2)
Methods, Data, Analyses     Open Access   (Followers: 1)
METRON     Hybrid Journal   (Followers: 2)
Nepalese Journal of Statistics     Open Access   (Followers: 1)
North American Actuarial Journal     Hybrid Journal   (Followers: 2)
Open Journal of Statistics     Open Access   (Followers: 3)
Open Mathematics, Statistics and Probability Journal     Open Access  
Pakistan Journal of Statistics and Operation Research     Open Access   (Followers: 1)
Physica A: Statistical Mechanics and its Applications     Hybrid Journal   (Followers: 7)
Probability, Uncertainty and Quantitative Risk     Open Access   (Followers: 2)
Research & Reviews : Journal of Statistics     Open Access   (Followers: 4)
Revista Brasileira de Biometria     Open Access  
Revista Colombiana de Estadística     Open Access  
RMS : Research in Mathematics & Statistics     Open Access   (Followers: 1)
Sankhya B - Applied and Interdisciplinary Statistics     Hybrid Journal  
SIAM Journal on Mathematics of Data Science     Hybrid Journal   (Followers: 6)
SIAM/ASA Journal on Uncertainty Quantification     Hybrid Journal   (Followers: 3)
Spatial Statistics     Hybrid Journal   (Followers: 2)
Stat     Hybrid Journal   (Followers: 1)
Stata Journal     Full-text available via subscription   (Followers: 10)
Statistica     Open Access   (Followers: 6)
Statistical Analysis and Data Mining     Hybrid Journal   (Followers: 23)
Statistical Theory and Related Fields     Hybrid Journal  
Statistics and Public Policy     Open Access   (Followers: 3)
Statistics in Transition New Series : An International Journal of the Polish Statistical Association     Open Access  
Statistics Research Letters     Open Access   (Followers: 1)
Statistics, Optimization & Information Computing     Open Access   (Followers: 5)
Stats     Open Access  
Theory of Probability and its Applications     Hybrid Journal   (Followers: 2)
Theory of Probability and Mathematical Statistics     Full-text available via subscription   (Followers: 2)
Turkish Journal of Forecasting     Open Access   (Followers: 1)
Zeitschrift für die gesamte Versicherungswissenschaft     Hybrid Journal  

           

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SIAM/ASA Journal on Uncertainty Quantification
Journal Prestige (SJR): 0.543
Citation Impact (citeScore): 1
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2166-2525
Published by Society for Industrial and Applied Mathematics Homepage  [17 journals]
  • Subsampling of Parametric Models with Bifidelity Boosting

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      Authors: Nuojin Cheng, Osman Asif Malik, Yiming Xu, Stephen Becker, Alireza Doostan, Akil Narayan
      Pages: 213 - 241
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 213-241, June 2024.
      Abstract.Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are generated using an experimental design process (e.g., a quadrature grid) involving computationally expensive models, or when the data size is large, sketching techniques have shown promise at reducing the cost of the construction of the regression model while ensuring accuracy comparable to that of the full data. However, random sketching strategies, such as those based on leverage scores, lead to regression errors that are random and may exhibit large variability. To mitigate this issue, we present a novel boosting approach that leverages cheaper, lower-fidelity data of the problem at hand to identify the best sketch among a set of candidate sketches. This in turn specifies the sketch of the intended high-fidelity model and the associated data. We provide theoretical analyses of this bifidelity boosting (BFB) approach and discuss the conditions the low- and high-fidelity data must satisfy for a successful boosting. In doing so, we derive a bound on the residual norm of the BFB sketched solution relating it to its ideal, but computationally expensive, high-fidelity boosted counterpart. Empirical results on both manufactured and PDE data corroborate the theoretical analyses and illustrate the efficacy of the BFB solution in reducing the regression error, as compared to the nonboosted solution.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-04-04T07:00:00Z
      DOI: 10.1137/22M1524989
      Issue No: Vol. 12, No. 2 (2024)
       
  • Calculation of Epidemic First Passage and Peak Time Probability
           Distributions

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      Authors: Jacob Curran-Sebastian, Lorenzo Pellis, Ian Hall, Thomas House
      Pages: 242 - 261
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 242-261, June 2024.
      Abstract. Understanding the timing of the peak of a disease outbreak forms an important part of epidemic forecasting. In many cases, such information is essential for planning increased hospital bed demand and for designing of public health interventions. The time taken for an outbreak to become large is inherently stochastic and, therefore, uncertain, but after a sufficient number of infections has been reached the subsequent dynamics can be modeled accurately using ordinary differential equations. Here, we present analytical and numerical methods for approximating the time at which a stochastic model of a disease outbreak reaches a large number of cases and for quantifying the uncertainty arising from demographic stochasticity around that time. We then project this uncertainty forwards in time using an ordinary differential equation model in order to obtain a distribution for the peak timing of the epidemic that agrees closely with large simulations but that, for error tolerances relevant to most realistic applications, requires a fraction of the computational cost of full Monte Carlo approaches.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-04-04T07:00:00Z
      DOI: 10.1137/23M1548049
      Issue No: Vol. 12, No. 2 (2024)
       
  • A Method of Moments Estimator for Interacting Particle Systems and their
           Mean Field Limit

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      Authors: Grigorios A. Pavliotis, Andrea Zanoni
      Pages: 262 - 288
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 262-288, June 2024.
      Abstract.We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear system which is constructed by imposing appropriate conditions on the moments of the invariant distribution of the mean field limit and on the quadratic variation of the process. Our approach is easy to implement as it only requires the approximation of the moments via the ergodic theorem and the solution of a low-dimensional linear system. Moreover, we prove that our estimator is asymptotically unbiased in the limits of infinite data and infinite number of particles (mean field limit). In addition, we present several numerical experiments that validate the theoretical analysis and show the effectiveness of our methodology to accurately infer parameters in systems of interacting particles.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-04-04T07:00:00Z
      DOI: 10.1137/22M153848X
      Issue No: Vol. 12, No. 2 (2024)
       
  • Computing Statistical Moments Via Tensorization of Polynomial Chaos
           Expansions

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      Authors: Rafael Ballester-Ripoll
      Pages: 289 - 308
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 289-308, June 2024.
      Abstract. We present an algorithm for estimating higher-order statistical moments of multidimensional functions expressed as polynomial chaos expansions (PCE). The algorithm starts by decomposing the PCE into a low-rank tensor network using a combination of tensor-train and Tucker decompositions. It then efficiently calculates the desired moments in the compressed tensor domain, leveraging the highly linear structure of the network. Using three benchmark engineering functions, we demonstrate that our approach offers substantial speed improvements over alternative algorithms while maintaining a minimal and adjustable approximation error. Additionally, our method can calculate moments even when the input variable distribution is altered, incurring only a small additional computational cost and without requiring retraining of the regressor.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-04-15T07:00:00Z
      DOI: 10.1137/23M155428X
      Issue No: Vol. 12, No. 2 (2024)
       
  • Nonasymptotic Bounds for Suboptimal Importance Sampling

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      Authors: Carsten Hartmann, Lorenz Richter
      Pages: 309 - 346
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 309-346, June 2024.
      Abstract. Importance sampling is a popular variance reduction method for Monte Carlo estimation, where an evident question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. Previous analysis on importance sampling has often focused on asymptotic arguments that work well in a large deviations regime. In this article, we provide lower and upper bounds on the relative error in a nonasymptotic setting. They depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We particularly focus on path sampling problems for diffusion processes with nonvanishing noise, for which generating good proposals comes with additional technical challenges. We provide numerous numerical examples that support our findings and demonstrate the applicability of the derived bounds.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-04-15T07:00:00Z
      DOI: 10.1137/21M1427760
      Issue No: Vol. 12, No. 2 (2024)
       
  • Wavelet-Based Density Estimation for Persistent Homology

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      Authors: Konstantin Häberle, Barbara Bravi, Anthea Monod
      Pages: 347 - 376
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 347-376, June 2024.
      Abstract. Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram—a multiset of points supported on the upper half-plane—that is often used as a statistical summary of the topological features of data. In this paper, we study the random nature of persistent homology and estimate the density of expected persistence diagrams from observations using wavelets; we show that our wavelet-based estimator is optimal. Furthermore, we propose an estimator that offers a sparse representation of the expected persistence diagram that achieves near-optimality. We demonstrate the utility of our contributions in a machine learning task in the context of dynamical systems.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-04-18T07:00:00Z
      DOI: 10.1137/23M1573811
      Issue No: Vol. 12, No. 2 (2024)
       
  • Nonparametric Estimation for Independent and Identically Distributed
           Stochastic Differential Equations with Space-Time Dependent Coefficients

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      Authors: Fabienne Comte, Valentine Genon-Catalot
      Pages: 377 - 410
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 377-410, June 2024.
      Abstract. We consider [math] independent and identically distributed one-dimensional inhomogeneous diffusion processes [math] with drift [math] and diffusion coefficient [math], where [math] and the functions [math] and [math] are known. Our concern is the nonparametric estimation of the [math]-dimensional unknown function [math] from the continuous observation of the sample paths [math] throughout a fixed time interval [math]. A collection of projection estimators belonging to a product of finite-dimensional subspaces of [math] is built. The [math]-risk is defined by the expectation of either an empirical norm or a deterministic norm fitted to the problem. Rates of convergence for large [math] are discussed. A data-driven choice of the dimensions of the projection spaces is proposed. The theoretical results are illustrated by numerical experiments on simulated data.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-05-21T07:00:00Z
      DOI: 10.1137/23M1581662
      Issue No: Vol. 12, No. 2 (2024)
       
  • Ensemble Kalman Filters with Resampling

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      Authors: Omar Al-Ghattas, Jiajun Bao, Daniel Sanz-Alonso
      Pages: 411 - 441
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 411-441, June 2024.
      Abstract.Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice. These algorithms rely on an ensemble of interacting particles to sequentially estimate the state as new observations become available. Despite the practical success of ensemble Kalman filters, theoretical understanding is hindered by the intricate dependence structure of the interacting particles. This paper investigates ensemble Kalman filters that incorporate an additional resampling step to break the dependency between particles. The new algorithm is amenable to a theoretical analysis that extends and improves upon those available for filters without resampling, while also performing well in numerical examples.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-05-23T07:00:00Z
      DOI: 10.1137/23M1594935
      Issue No: Vol. 12, No. 2 (2024)
       
  • Leveraging Joint Sparsity in Hierarchical Bayesian Learning

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      Authors: Jan Glaubitz, Anne Gelb
      Pages: 442 - 472
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 442-472, June 2024.
      Abstract.We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyperparameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multicoil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-05-24T07:00:00Z
      DOI: 10.1137/23M156255X
      Issue No: Vol. 12, No. 2 (2024)
       
  • Conglomerate Multi-fidelity Gaussian Process Modeling, with Application to
           Heavy-Ion Collisions

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      Authors: Yi Ji, Henry Shaowu Yuchi, Derek Soeder, J.-F. Paquet, Steffen A. Bass, V. Roshan Joseph, C. F. Jeff Wu, Simon Mak
      Pages: 473 - 502
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 473-502, June 2024.
      Abstract.In an era where scientific experimentation is often costly, multi-fidelity emulation provides a powerful tool for predictive scientific computing. While there has been notable work on multi-fidelity modeling, existing models do not incorporate an important “conglomerate” property of multi-fidelity simulators, where the accuracies of different simulator components are controlled by different fidelity parameters. Such conglomerate simulators are widely encountered in complex nuclear physics and astrophysics applications. We thus propose a new CONglomerate multi-FIdelity Gaussian process (CONFIG) model, which embeds this conglomerate structure within a novel non-stationary covariance function. We show that the proposed CONFIG model can capture prior knowledge on the numerical convergence of conglomerate simulators, which allows for cost-efficient emulation of multi-fidelity systems. We demonstrate the improved predictive performance of CONFIG over state-of-the-art models in a suite of numerical experiments and two applications, the first for emulation of cantilever beam deflection and the second for emulating the evolution of the quark-gluon plasma, which was theorized to have filled the universe shortly after the Big Bang.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-05-30T07:00:00Z
      DOI: 10.1137/22M1525004
      Issue No: Vol. 12, No. 2 (2024)
       
  • Quantifying Domain Uncertainty in Linear Elasticity

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      Authors: Helmut Harbrecht, Viacheslav Karnaev, Marc Schmidlin
      Pages: 503 - 523
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 503-523, June 2024.
      Abstract.The present article considers the quantification of uncertainty for the equations of linear elasticity on random domains. To this end, we model the random domains as the images of some given fixed, nominal domain under random domain mappings, which are defined by a Karhunen–Loève expansion. We then prove the analytic regularity of the random solution with respect to the countable random input parameters which enter the problem through the Karhunen–Loève expansion of the random domain mappings. In particular, we provide appropriate bounds on arbitrary derivatives of the random solution with respect to those input parameters. These enable the use of state-of-the-art quadrature methods to compute deterministic statistics of quantities of interest, such as the mean and the variance of the random solution itself or the random von Mises stress, as integrals over the countable random input parameters in a dimensionally robust way. Numerical examples qualify and quantify the theoretical findings.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-05-30T07:00:00Z
      DOI: 10.1137/23M1578589
      Issue No: Vol. 12, No. 2 (2024)
       
  • Computationally Efficient Sampling Methods for Sparsity Promoting
           Hierarchical Bayesian Models

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      Authors: D. Calvetti, E. Somersalo
      Pages: 524 - 548
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 524-548, June 2024.
      Abstract.Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by a hyperprior model for the variances. A widely used choice for the hyperprior is a member of the family of generalized gamma distributions. Most of the work in the literature has concentrated on numerical approximation of the maximum a posteriori estimates, and less attention has been paid on sampling methods or other means for uncertainty quantification. Sampling from the hierarchical models is challenging mainly for two reasons: The hierarchical models are typically high dimensional, thus suffering from the curse of dimensionality, and the strong correlation between the unknown of interest and its variance can make sampling rather inefficient. This work addresses mainly the first one of these obstacles. By using a novel reparametrization, it is shown how the posterior distribution can be transformed into one dominated by a Gaussian white noise, allowing sampling by using the preconditioned Crank–Nicholson (pCN) scheme that has been shown to be efficient for sampling from distributions dominated by a Gaussian component. Furthermore, a novel idea for speeding up the pCN in a special case is developed, and the question of how strongly the hierarchical models are concentrated on sparse solutions is addressed in light of a computed example.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-07T07:00:00Z
      DOI: 10.1137/23M1564043
      Issue No: Vol. 12, No. 2 (2024)
       
  • Differential Equation–Constrained Optimization with Stochasticity

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      Authors: Qin Li, Li Wang, Yunan Yang
      Pages: 549 - 578
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 549-578, June 2024.
      Abstract.Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured data. The formulation is powerful and widely used in many science and engineering fields. However, one crucial assumption is that the unknown parameter must be deterministic. In reality, however, many problems are stochastic in nature, and the unknown parameter is random. The challenge then becomes recovering the full distribution of this unknown random parameter. It is a much more complex task. In this paper, we examine this problem in a general setting. In particular, we conceptualize the PDE solver as a push-forward map that pushes the parameter distribution to the generated data distribution. In this way, the SDE-constrained optimization translates to minimizing the distance between the generated distribution and the measurement distribution. We then formulate a gradient flow equation to seek the ground-truth parameter probability distribution. This opens up a new paradigm for extending many techniques in PDE-constrained optimization to optimization for systems with stochasticity.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-07T07:00:00Z
      DOI: 10.1137/23M1571162
      Issue No: Vol. 12, No. 2 (2024)
       
  • Quantifying the Effect of Random Dispersion for Logarithmic
           Schrödinger Equation

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      Authors: Jianbo Cui, Liying Sun
      Pages: 579 - 613
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 579-613, June 2024.
      Abstract.This paper is concerned with the random effect of the noise dispersion for the stochastic logarithmic Schrödinger equation emerged from the optical fibre with dispersion management. The well-posedness of the logarithmic Schrödinger equation with white noise dispersion is established via the regularization energy approximation and a spatial scaling property. For the small noise case, the effect of the noise dispersion is quantified by the proven large deviation principle under additional regularity assumptions on the initial datum. As an application, we show that for the regularized model, the exit from a neighborhood of the attractor of deterministic equation occurs on a sufficiently large time scale. Furthermore, the exit time and exit point in the small noise case, as well as the effect of large noise dispersion, is also discussed for the stochastic logarithmic Schrödinger equation.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-07T07:00:00Z
      DOI: 10.1137/23M1578619
      Issue No: Vol. 12, No. 2 (2024)
       
  • One-Shot Learning of Surrogates in PDE-Constrained Optimization under
           Uncertainty

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      Authors: Philipp A. Guth, Claudia Schillings, Simon Weissmann
      Pages: 614 - 645
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 614-645, June 2024.
      Abstract.We propose a general framework for machine learning based optimization under uncertainty. Our approach replaces the complex forward model by a surrogate, which is learned simultaneously in a one-shot sense when solving the optimal control problem. Our approach relies on a reformulation of the problem as a penalized empirical risk minimization problem for which we provide a consistency analysis in terms of large data and increasing penalty parameter. To solve the resulting problem, we suggest a stochastic gradient method with adaptive control of the penalty parameter and prove convergence under suitable assumptions on the surrogate model. Numerical experiments illustrate the results for linear and nonlinear surrogate models.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-12T07:00:00Z
      DOI: 10.1137/23M1553170
      Issue No: Vol. 12, No. 2 (2024)
       
  • Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation

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      Authors: Kellin N. Rumsey, Devin Francom, Andy Shen
      Pages: 646 - 666
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 646-666, June 2024.
      Abstract. The multivariate adaptive regression spline (MARS) approach of Friedman [J. H. Friedman, Ann. Statist., 19 (1991), pp. 1–67] and its Bayesian counterpart [D. Francom et al., Statist. Sinica, 28 (2018), pp. 791–816] are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. We propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-20T07:00:00Z
      DOI: 10.1137/23M1577122
      Issue No: Vol. 12, No. 2 (2024)
       
  • Proportional Marginal Effects for Global Sensitivity Analysis

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      Authors: Margot Herin, Marouane Il Idrissi, Vincent Chabridon, Bertrand Iooss
      Pages: 667 - 692
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 667-692, June 2024.
      Abstract.Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts, leading to meaningful sensitivity indices suitable with dependent inputs. The “Shapley effects,” i.e., the Shapley values transposed to variance-based GSA problems, are an example of such indices. However, these indices exhibit a particular behavior that can be undesirable: an exogenous input (i.e., which is not explicitly included in the structural equations of the model) can be associated with a strictly positive index when it is correlated to endogenous inputs. This paper investigates using a different allocation, called the “proportional values” for GSA purposes. First, an extension of this allocation is proposed to make it suitable for variance-based GSA. A novel GSA index is then defined: the proportional marginal effect (PME). The notion of exogeneity is formally defined in the context of variance-based GSA. It is shown that the PMEs are more discriminant than the Shapley values and allow the distinction of exogenous variables, even when they are correlated to endogenous inputs. Moreover, their behavior is compared to the Shapley effects on analytical toy cases and more realistic use cases.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-26T07:00:00Z
      DOI: 10.1137/22M153032X
      Issue No: Vol. 12, No. 2 (2024)
       
  • A Combination Technique for Optimal Control Problems Constrained by Random
           PDEs

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      Authors: Fabio Nobile, Tommaso Vanzan
      Pages: 693 - 721
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 693-721, June 2024.
      Abstract.We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equations. The method requires to solve the OCP for several low-fidelity spatial grids and quadrature formulae for the objective functional. All the computed solutions are then linearly combined to get a final approximation which, under suitable regularity assumptions, preserves the same accuracy of fine tensor product approximations, while drastically reducing the computational cost. The combination technique involves only tensor product quadrature formulae, and thus the discretized OCPs preserve the (possible) convexity of the continuous OCP. Hence, the combination technique avoids the inconveniences of multilevel Monte Carlo and/or sparse grids approaches but remains suitable for high-dimensional problems. The manuscript presents an a priori procedure to choose the most important mixed differences and an analysis stating that the asymptotic complexity is exclusively determined by the spatial solver. Numerical experiments validate the results.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-06-26T07:00:00Z
      DOI: 10.1137/22M1532263
      Issue No: Vol. 12, No. 2 (2024)
       
  • Error Estimate of a Quasi-Monte Carlo Time-Splitting Pseudospectral Method
           for Nonlinear Schrödinger Equation with Random Potentials

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      Authors: Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao
      Pages: 1 - 29
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 1-29, March 2024.
      Abstract. In this paper, we consider the numerical solution of a nonlinear Schrödinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combined with the time-splitting pseudospectral discretization is applied and analyzed. The nonlinearity in the equation induces difficulties in estimating the regularity of the solution in random space. By the technique of weighted Sobolev space, we identify the possible weights and show the existence of QMC that converges optimally at the almost-linear rate without dependence on dimensions. The full error estimate of the scheme is established. We present numerical results to verify the accuracy and investigate the wave propagation.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-01-30T08:00:00Z
      DOI: 10.1137/22M1525181
      Issue No: Vol. 12, No. 1 (2024)
       
  • Analysis of a Computational Framework for Bayesian Inverse Problems:
           Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

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      Authors: Daniel Sanz-Alonso, Nathan Waniorek
      Pages: 30 - 68
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 30-68, March 2024.
      Abstract. This paper analyzes a popular computational framework for solving infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory for characterizing the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and maximum a posteriori (MAP) estimators for nonlinear inverse problems. Our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-02-02T08:00:00Z
      DOI: 10.1137/23M1567035
      Issue No: Vol. 12, No. 1 (2024)
       
  • Projective Integral Updates for High-Dimensional Variational Inference

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      Authors: Jed A. Duersch
      Pages: 69 - 100
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 69-100, March 2024.
      Abstract. Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. This integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-02-08T08:00:00Z
      DOI: 10.1137/22M1529919
      Issue No: Vol. 12, No. 1 (2024)
       
  • Multifidelity Bayesian Experimental Design to Quantify Rare-Event
           Statistics

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      Authors: Xianliang Gong, Yulin Pan
      Pages: 101 - 127
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 101-127, March 2024.
      Abstract. In this work, we develop a multifidelity Bayesian experimental design framework to efficiently quantify the rare-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. The key idea here is to leverage low-fidelity samples whose responses can be computed with a cost of a certain fraction of that for high-fidelity samples, in an optimized configuration to reduce the total computational cost. To accomplish this goal, we employ a multifidelity Gaussian process as the surrogate model of the ItR function and develop a new acquisition based on which the optimized next sample can be selected in terms of its location in the sample space and the fidelity level. In addition, we develop an inexpensive analytical evaluation of the acquisition and its derivative, avoiding numerical integrations that are prohibitive for high-dimensional problems. The new method is mainly tested in a bifidelity context for a series of synthetic problems with varying dimensions, low-fidelity model accuracy, and computational costs. Compared with the single-fidelity method and the bifidelity method with a predefined fidelity hierarchy, our method consistently shows the best (or among the best) performance for all the test cases. Finally, we demonstrate the superiority of our method in solving an engineering problem of estimating rare-event statistics of ship motion in irregular waves, using computational fluid dynamics with two different grid resolutions as the high- and low-fidelity models.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-02-29T08:00:00Z
      DOI: 10.1137/22M1503956
      Issue No: Vol. 12, No. 1 (2024)
       
  • Adaptive Importance Sampling Based on Fault Tree Analysis for Piecewise
           Deterministic Markov Process

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      Authors: Guillaume Chennetier, Hassane Chraibi, Anne Dutfoy, Josselin Garnier
      Pages: 128 - 156
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 128-156, March 2024.
      Abstract. Piecewise deterministic Markov processes (PDMPs) can be used to model complex dynamical industrial systems. The counterpart of this modeling capability is their simulation cost, which makes reliability assessment untractable with standard Monte Carlo methods. A significant variance reduction can be obtained with an adaptive importance sampling method based on a cross-entropy procedure. The success of this method relies on the selection of a good family of approximations of the committor function of the PDMP. In this paper original families are proposed. Their forms are based on reliability concepts related to fault tree analysis: minimal path sets and minimal cut sets. They are well adapted to high-dimensional industrial systems. The proposed method is discussed in detail and applied to academic systems and to a realistic system from the nuclear industry.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-03-07T08:00:00Z
      DOI: 10.1137/22M1522838
      Issue No: Vol. 12, No. 1 (2024)
       
  • Stacking Designs: Designing Multifidelity Computer Experiments with Target
           Predictive Accuracy

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      Authors: Chih-Li Sung, Yi (Irene) Ji, Simon Mak, Wenjia Wang, Tao Tang
      Pages: 157 - 181
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 157-181, March 2024.
      Abstract. In an era where scientific experiments can be very costly, multifidelity emulators provide a useful tool for cost-efficient predictive scientific computing. For scientific applications, the experimenter is often limited by a tight computational budget, and thus wishes to (i) maximize predictive power of the multifidelity emulator via a careful design of experiments, and (ii) ensure this model achieves a desired error tolerance with some notion of confidence. Existing design methods, however, do not jointly tackle objectives (i) and (ii). We propose a novel stacking design approach that addresses both goals. A multilevel reproducing kernel Hilbert space (RKHS) interpolator is first introduced to build the emulator, under which our stacking design provides a sequential approach for designing multifidelity runs such that a desired prediction error of [math] is met under regularity assumptions. We then prove a novel cost complexity theorem that, under this multilevel interpolator, establishes a bound on the computation cost (for training data simulation) needed to achieve a prediction bound of [math]. This result provides novel insights on conditions under which the proposed multifidelity approach improves upon a conventional RKHS interpolator which relies on a single fidelity level. Finally, we demonstrate the effectiveness of stacking designs in a suite of simulation experiments and an application to finite element analysis.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-03-11T07:00:00Z
      DOI: 10.1137/22M1532007
      Issue No: Vol. 12, No. 1 (2024)
       
  • Perron–Frobenius Operator Filter for Stochastic Dynamical Systems

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      Authors: Ningxin Liu, Lijian Jiang
      Pages: 182 - 211
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 182-211, March 2024.
      Abstract.Filtering problems are derived from a sequential minimization of a quadratic function representing a compromise between the model and data. In this paper, we use the Perron–Frobenius operator in a stochastic process to develop a Perron–Frobenius operator filter. The proposed method belongs to Bayesian filtering and works for non-Gaussian distributions for nonlinear stochastic dynamical systems. The recursion of the filtering can be characterized by the composition of the Perron–Frobenius operator and likelihood operator. This gives a significant connection between the Perron–Frobenius operator and Bayesian filtering. We numerically fulfill the recursion by approximating the Perron–Frobenius operator by Ulam’s method. In this way, the posterior measure is represented by a convex combination of the indicator functions in Ulam’s method. To get a low-rank approximation for the Perron–Frobenius operator filter, we take a spectral decomposition for the posterior measure by using the eigenfunctions of the discretized Perron–Frobenius operator. The Perron–Frobenius operator filter employs data instead of flow equations to model the evolution of underlying stochastic dynamical systems. In contrast, standard particle filters require explicit equations or transition probability density for sampling. A few numerical examples are presented to illustrate the advantage of the Perron–Frobenius operator filter over the particle filter and extended Kalman filter.
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-03-15T07:00:00Z
      DOI: 10.1137/23M1547391
      Issue No: Vol. 12, No. 1 (2024)
       
  • Corrigendum: Quasi–Monte Carlo Finite Element Analysis for Wave
           Propagation in Heterogeneous Random Media

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      Authors: M. Ganesh, Frances Y. Kuo, Ian H. Sloan
      Pages: 212 - 212
      Abstract: SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 212-212, March 2024.
      Abstract.  
      Citation: SIAM/ASA Journal on Uncertainty Quantification
      PubDate: 2024-03-29T07:00:00Z
      DOI: 10.1137/23M1624609
      Issue No: Vol. 12, No. 1 (2024)
       
 
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Advances in Statistics     Open Access   (Followers: 10)
Afrika Statistika     Open Access   (Followers: 1)
American Journal of Applied Mathematics and Statistics     Open Access   (Followers: 13)
American Journal of Mathematics and Statistics     Open Access   (Followers: 9)
Annals of Data Science     Hybrid Journal   (Followers: 15)
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Asian Journal of Mathematics & Statistics     Open Access   (Followers: 7)
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Austrian Journal of Statistics     Open Access   (Followers: 4)
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Calcutta Statistical Association Bulletin     Hybrid Journal  
Communications in Mathematics and Statistics     Hybrid Journal   (Followers: 3)
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Foundations and Trends® in Optimization     Full-text available via subscription   (Followers: 2)
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Geomatics, Natural Hazards and Risk     Open Access   (Followers: 14)
Indonesian Journal of Applied Statistics     Open Access  
International Game Theory Review     Hybrid Journal  
International Journal of Advanced Statistics and IT&C for Economics and Life Sciences     Open Access  
International Journal of Advanced Statistics and Probability     Open Access   (Followers: 7)
International Journal of Applied Mathematics and Statistics     Full-text available via subscription   (Followers: 4)
International Journal of Ecological Economics and Statistics     Full-text available via subscription   (Followers: 4)
International Journal of Game Theory     Hybrid Journal   (Followers: 3)
International Journal of Mathematics and Statistics     Full-text available via subscription   (Followers: 2)
International Journal of Multivariate Data Analysis     Hybrid Journal  
International Journal of Probability and Statistics     Open Access   (Followers: 3)
International Journal of Statistics & Economics     Full-text available via subscription   (Followers: 6)
International Journal of Statistics and Applications     Open Access   (Followers: 2)
International Journal of Statistics and Probability     Open Access   (Followers: 3)
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International Journal of Testing     Hybrid Journal   (Followers: 1)
Iraqi Journal of Statistical Sciences     Open Access  
Japanese Journal of Statistics and Data Science     Hybrid Journal  
Journal of Biometrics & Biostatistics     Open Access   (Followers: 4)
Journal of Cost Analysis and Parametrics     Hybrid Journal   (Followers: 5)
Journal of Environmental Statistics     Open Access   (Followers: 4)
Journal of Game Theory     Open Access   (Followers: 1)
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Journal of Modern Applied Statistical Methods     Open Access   (Followers: 1)
Journal of Official Statistics     Open Access   (Followers: 2)
Journal of Quantitative Economics     Hybrid Journal  
Journal of Social and Economic Statistics     Open Access   (Followers: 4)
Journal of Statistical Theory and Practice     Hybrid Journal   (Followers: 2)
Journal of Statistics and Data Science Education     Open Access   (Followers: 2)
Journal of Survey Statistics and Methodology     Hybrid Journal   (Followers: 6)
Journal of the Indian Society for Probability and Statistics     Full-text available via subscription  
Jurnal Biometrika dan Kependudukan     Open Access   (Followers: 1)
Lietuvos Statistikos Darbai     Open Access   (Followers: 1)
Mathematics and Statistics     Open Access   (Followers: 2)
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METRON     Hybrid Journal   (Followers: 2)
Nepalese Journal of Statistics     Open Access   (Followers: 1)
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Open Journal of Statistics     Open Access   (Followers: 3)
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Physica A: Statistical Mechanics and its Applications     Hybrid Journal   (Followers: 7)
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RMS : Research in Mathematics & Statistics     Open Access   (Followers: 1)
Sankhya B - Applied and Interdisciplinary Statistics     Hybrid Journal  
SIAM Journal on Mathematics of Data Science     Hybrid Journal   (Followers: 6)
SIAM/ASA Journal on Uncertainty Quantification     Hybrid Journal   (Followers: 3)
Spatial Statistics     Hybrid Journal   (Followers: 2)
Stat     Hybrid Journal   (Followers: 1)
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Statistics in Transition New Series : An International Journal of the Polish Statistical Association     Open Access  
Statistics Research Letters     Open Access   (Followers: 1)
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Stats     Open Access  
Theory of Probability and its Applications     Hybrid Journal   (Followers: 2)
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