Review
Multidisciplinary Sciences
Arnaud Doucet, Eric Moulines, Achille Thin
Summary: Latent variable models are popular and have been combined with neural networks to create deep latent variable models. However, the intractability of their likelihood function requires approximations for inference. The article reviews recent strategies such as importance sampling, Markov chain Monte Carlo, and sequential Monte Carlo to improve the bounds of the evidence lower bound (ELBO) for these models.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Engineering, Mechanical
P. L. Green, L. J. Devlin, R. E. Moore, R. J. Jackson, J. Li, S. Maskell
Summary: This paper discusses the optimization of the 'L-kernel' in Sequential Monte Carlo samplers to improve performance, resulting in reduced variance of estimates and fewer resampling requirements.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Hillary R. Fairbanks, Umberto Villa, Panayot S. Vassilevski
Summary: This work introduces a new hierarchical multilevel method for generating Gaussian random field realizations in a scalable manner, which is tested in a multilevel MCMC algorithm to explore its feasibility.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Automation & Control Systems
Karl Berntorp
Summary: This paper discusses the recursive joint inference and learning problem for nonlinear systems using a Gaussian-process state-space model and a reduced-rank GP-SSM formulation for efficient online learning. The unknown dynamical system is expressed using basis-function expansion with priors systematically assigned to weights. Results show competitive performance compared to offline Bayesian learning methods and successful application in estimating tire friction with automotive-grade sensors in online settings.
Article
Statistics & Probability
Xiaotian Zheng, Athanasios Kottas, Bruno Sanso
Summary: The study introduces a framework for constructing stationary MTD models that extend beyond linear, Gaussian dynamics. Conditions for first-order strict stationarity are explored, with inference and prediction developed under the Bayesian framework with structured priors for mixture weights. Model properties are investigated analytically and via synthetic data examples, with real data applications illustrating Poisson and Lomax examples.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Kuhwan Jeong, Minwoo Chae, Yongdai Kim
Summary: The Dirichlet process (DP) mixture model is commonly used for clustering and density estimation. Despite the development of Markov chain Monte Carlo algorithms, the computational costs of DP mixture models make them impractical for analyzing large data. To address this, we propose a novel mini-batch online learning algorithm based on assumed density filtering, which improves performance relative to existing online algorithms based on variational inference by leveraging available computing resources.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Engineering, Electrical & Electronic
Hugo T. de Carvalho, Flavio R. Avila, Luiz W. P. Biscainho
Summary: This paper introduces a novel Bayesian approach for joint estimation of pulse location, interpolation of underlying signal, and estimation of long pulse tail in old vinyl and gramophone recordings. Controlled experiments show that the proposed method achieves perceptual results similar to previous approaches with significantly less user intervention, performing well with naturally degraded signals.
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
(2021)
Article
Statistics & Probability
Lewis J. Rendell, Adam M. Johansen, Anthony Lee, Nick Whiteley
Summary: In order to conduct Bayesian inference with large datasets, it is beneficial to distribute the data across multiple machines. By introducing an instrumental hierarchical model and using an SMC sampler with a sequence of association strengths, approximations of posterior expectations can be improved and the association strength can be adjusted accordingly.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2021)
Article
Geosciences, Multidisciplinary
Jonathan R. Bradley, Shijie Zhou, Xu Liu
Summary: Discrepancy error covariance refers to the cross-covariance between the signal and the noise terms in an additive model. A model has recently been proposed that allows for discrepancy error covariances and avoids confounding issues by introducing a telescoping sum. This model, known as the deep hierarchical generalized transformation (DHGT) model, can be efficiently implemented and allows for exact Bayesian implementation without the need for MCMC.
SPATIAL STATISTICS
(2023)
Article
Engineering, Mechanical
Adolphus Lye, Alice Cicirello, Edoardo Patelli
Summary: This tutorial paper reviews the use of advanced Monte Carlo sampling methods in Bayesian model updating for engineering applications, introducing different methods and comparing their performance. Three case studies demonstrate the advantages and limitations of these sampling techniques in parameter identification, posterior distribution sampling, and stochastic identification of model parameters.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Interdisciplinary Applications
Riko Kelter
Summary: This paper introduces a R package that performs Bayesian inference in ANOVA, focusing on effect size estimation instead of hypothesis testing with full posterior inference implemented via MCMC.
Article
Engineering, Environmental
Marco Bacci, Jonas Sukys, Peter Reichert, Simone Ulzega, Carlo Albert
Summary: Due to limited knowledge about complex environmental systems, predicting their behavior under different scenarios or decision alternatives is uncertain. Considering, quantifying, and communicating this uncertainty is important for societal decisions. Stochastic models are often necessary to adequately describe uncertainty, but calibrating these models presents methodological and numerical challenges. To address this, we compare three numerical approaches and find that their performance is comparable for analyzing a stochastic hydrological model with hydrological data, suggesting that generality and practical considerations can guide technique choice for specific applications.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2023)
Article
Ecology
Tsikai S. Chinembiri, Onisimo Mutanga, Timothy Dube
Summary: We propose a novel Bayesian hierarchical geostatistical model using multispectral Landsat-8 and Sentinel-2 remotely sensed data to predict plantation forest carbon stock in the eastern highlands of Zimbabwe. Our hierarchical modelling framework evaluates the influence of two covariate information sources in C stock prediction and aims to build sustainable capacity on carbon reporting and monitoring. The Sentinel-2 based C stock predictive model outperforms its Landsat-8 based counterpart, indicating the potential of improved remote sensing data in enhancing carbon reporting and monitoring.
ECOLOGICAL INFORMATICS
(2023)
Review
Engineering, Civil
Aditya Pandey, Ashmeet Singh, Paolo Gardoni
Summary: This paper reviews the diagrammatic perturbation theory, a technique in Information Field Theory, for analytically estimating moments of perturbative non-Gaussian distributions. When dealing with physical phenomena, which often exhibit non-Gaussian features, approximation of the underlying distribution and inference of its parameter form are commonly used. More rigorous analysis methods such as Markov Chain Monte Carlo can also be employed, but are computationally expensive.
Review
Statistics & Probability
Christopher Nemeth, Paul Fearnhead
Summary: MCMC algorithms are considered the gold standard technique for Bayesian inference, but the computational cost can be prohibitive for large datasets, leading to the development of scalable Monte Carlo algorithms. One type of these algorithms is SGMCMC, which reduces per-iteration cost by utilizing data subsampling techniques.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Blair Robertson, Chris Price
Summary: Spatial sampling designs are crucial for accurate estimation of population parameters. This study proposes a new design method that generates samples with good spatial spread and performs favorably compared to existing designs.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Hiroya Yamazoe, Kanta Naito
Summary: This paper focuses on the simultaneous confidence region of a one-dimensional curve embedded in multi-dimensional space. An estimator of the curve is obtained through local linear regression on each variable in multi-dimensional data. A method to construct a simultaneous confidence region based on this estimator is proposed, and theoretical results for the estimator and the region are developed. The effectiveness of the region is demonstrated through simulation studies and applications to artificial and real datasets.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Cheng Peng, Drew P. Kouri, Stan Uryasev
Summary: This paper introduces a novel optimal experimental design method for quantifying the distribution tails of uncertain system responses. The method minimizes the variance or conditional value-at-risk of the upper bound of the predicted quantile, and estimates the data uncertainty using quantile regression. The optimal design problems are solved as linear programming problems, making the proposed methods efficient even for large datasets.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiaofei Wu, Hao Ming, Zhimin Zhang, Zhenyu Cui
Summary: This paper proposes a model that combines quantile regression and fused LASSO penalty, and introduces an iterative algorithm based on ADMM to solve high-dimensional datasets. The paper proves the global convergence and comparable convergence rates of the algorithm, and analyzes the theoretical properties of the model. Numerical experimental results support the superior performance of the model.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xin He, Xiaojun Mao, Zhonglei Wang
Summary: This paper proposes a nonparametric imputation method with sparsity to estimate the finite population mean, using an efficient kernel method and sparse learning for estimation. An augmented inverse probability weighting framework is adopted to achieve a central limit theorem for the proposed estimator under regularity conditions.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Christian H. Weiss, Fukang Zhu
Summary: This study introduces a multiplicative error model (CMEMs) for discrete-valued count time series, which is closely related to the integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models. It derives the stochastic properties and estimation approaches of different types of INGARCH-CMEMs, and demonstrates their performance and application through simulations and real-world data examples.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Ming-Hung Kao, Ping-Han Huang
Summary: Optimal designs for sparse functional data under the functional empirical component (FEC) settings are investigated. New computational methods and theoretical results are developed to efficiently obtain optimal exact and approximate designs. A hybrid exact-approximate design approach is proposed and demonstrated to be efficient through simulation studies and a real example.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Mateus Maia, Keefe Murphy, Andrew C. Parnell
Summary: The Bayesian additive regression trees (BART) model is a powerful ensemble method for regression tasks, but its lack of smoothness and explicit covariance structure can limit its performance. The Gaussian processes Bayesian additive regression trees (GP-BART) model addresses this limitation by incorporating Gaussian process priors, resulting in superior performance in various scenarios.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xichen Mou, Dewei Wang
Summary: Human biomonitoring is a method of monitoring human health by measuring the accumulation of harmful chemicals in the body. To reduce the high cost of chemical analysis, researchers have adopted a cost-effective approach that combines specimens and analyzes the concentration of toxic substances in the pooled samples. To effectively interpret these aggregated measurements, a new regression framework is proposed by extending the additive partially linear model (APLM). The APLM is versatile in capturing the complex association between outcomes and covariates, making it valuable in assessing the complex interplay between chemical bioaccumulation and potential risk factors.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lili Yu, Yichuan Zhao
Summary: The classical accelerated failure time model is a linear model commonly used for right censored survival data, but it cannot handle heteroscedastic survival data. This paper proposes a Laplace approximated quasi-likelihood method with a continuous estimating equation to address this issue, and provides estimation bias and confidence interval estimation formulas.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Shaobo Jin, Youngjo Lee
Summary: Hierarchical generalized linear models are widely used for fitting random effects models, but the standard error estimators receive less attention. Current standard error estimation methods are not necessarily accurate, and a sandwich estimator is proposed to improve the accuracy of standard error estimation.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Rebeca Pelaez, Ingrid Van Keilegom, Ricardo Cao, Juan M. Vilar
Summary: This article proposes an estimator for the probability of default (PD) in credit risk, derived from a nonparametric conditional survival function estimator based on cure models. The asymptotic expressions for bias, variance, and normality of the estimator are presented. Through simulation and empirical studies, the performance and practical behavior of the nonparametric estimator are compared with other methods.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
L. M. Andre, J. L. Wadsworth, A. O'Hagan
Summary: This paper proposes a dependence model that captures the entire data range in multi-variable cases. By blending two copulas with different characteristics and using a dynamic weighting function for smooth transition, the model is able to flexibly capture various dependence structures.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Niwen Zhou, Xu Guo, Lixing Zhu
Summary: The paper investigates hypothesis testing regarding the potential additional contributions of other covariates to the structural function, given the known covariates. The proposed distance-based test, based on Neyman's orthogonality condition, effectively detects local alternatives and is robust to the influence of nuisance functions. Numerical studies and real data analysis demonstrate the importance of this test in exploring covariates associated with AIDS treatment effects.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)
Article
Computer Science, Interdisciplinary Applications
Blake Moya, Stephen G. Walker
Summary: A full posterior analysis method for nonparametric mixture models using Gibbs-type prior distributions, including the well known Dirichlet process mixture (DPM) model, is presented. The method removes the random mixing distribution and enables a simple-to-implement Markov chain Monte Carlo (MCMC) algorithm. The removal procedure reduces some of the posterior uncertainty and introduces a novel replacement approach. The method only requires the probabilities of a new or an old value associated with the corresponding Gibbs-type exchangeable sequence, without the need for explicit representations of the prior or posterior distributions. This allows the implementation of mixture models with full posterior uncertainty, including one introduced by Gnedin. The paper also provides numerous illustrations and introduces an R-package called CopRe that implements the methodology.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2024)