Article
Engineering, Chemical
Sarada Ghosh, Guruprasad Samanta, Manuel De la Sen
Summary: Ischemic heart disease is the most common cause of death in various countries, and statistical models are crucial for evaluating risk factors. A new flexible class of zero inflated models and Bayesian estimation method have shown better performance in analyzing the data related to heart disease.
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
Computer Science, Interdisciplinary Applications
DanHua ShangGuan
Summary: The Monte Carlo method is a powerful tool in many research fields, but the increasing complexity of physical models and mathematical models requires efficient algorithms to overcome the computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Theory & Methods
Minas Karamanis, Florian Beutler
Summary: Slice sampling is a powerful Markov Chain Monte Carlo algorithm, but sensitive to user-specified parameters and struggles with strongly correlated distributions. Ensemble Slice Sampling introduces a new class of algorithms that adaptively tune parameters and utilize parallel walkers to efficiently handle strong correlations, significantly improving sampling efficiency.
STATISTICS AND COMPUTING
(2021)
Article
Physics, Multidisciplinary
Yuliya Shapovalova
Summary: This study empirically illustrates the performance of different classes of Bayesian inference methods in estimating stochastic volatility models, comparing their adaptability to various model specifications and dimensions. The research emphasizes the importance of considering various data-generating processes for a fair assessment of the methods used in comparing models.
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
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
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)
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
Mathematics, Applied
Tony Lelievre, Gabriel Stoltz, Wei Zhang
Summary: This study proposes a new MCMC algorithm for sampling probability distributions on submanifolds. Unlike previous methods, this algorithm uses set-valued maps in the proposal step and ensures the correctness of the sampling results through carefully enforced reversibility property.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Computer Science, Theory & Methods
Andrew D. Davis, Youssef Marzouk, Aaron Smith, Natesh Pillai
Summary: Many Bayesian inference problems involve computationally expensive target density functions. By using a small number of carefully chosen density evaluations for local approximation, the computational cost of Markov chain Monte Carlo (MCMC) sampling can be significantly reduced, while asymptotically exact sampling can still be guaranteed. We propose a new strategy for balancing the decay rate of the approximation bias with that of the MCMC variance, and prove that the resulting local approximation MCMC (LA-MCMC) algorithm decays at an expected rate of 1/root T. We also introduce an algorithmic parameter that guarantees convergence with weak tail bounds, strengthening previous convergence results. Finally, we apply LA-MCMC to a computationally intensive Bayesian inverse problem in groundwater hydrology.
STATISTICS AND COMPUTING
(2022)
Article
Physics, Multidisciplinary
Hanqing Zhao, Marija Vucelja
Summary: We introduce an efficient nonreversible Markov chain Monte Carlo algorithm for generating self-avoiding walks with a variable endpoint, and compare its performance with existing algorithms in two and three dimensions.
FRONTIERS IN PHYSICS
(2022)
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
Automation & Control Systems
Jakob Robnik, G. Bruno De Luca, Eva Silverstein, Uros Seljak
Summary: In this paper, we develop two models, Microcanonical Hamiltonian Monte Carlo (MCHMC) and Microcanonical Langevin Monte Carlo (MCLMC), which achieve sampling from the target distribution on a fixed energy surface by tuning the Hamiltonian function. These two methods exhibit favorable scalings with condition number and dimensionality.
JOURNAL OF MACHINE LEARNING RESEARCH
(2023)
Article
Mathematics
Samuel Livingstone
Summary: This study investigates the impact of proposal distributions on the ergodicity of the Metropolis-Hastings method, showing that suitable choices can alter the ergodic properties of the algorithm. It is found that allowing the proposal variance to grow unboundedly in the tails of heavy-tailed distributions can establish geometric ergodicity, but the growth rate needs to be carefully controlled to avoid high rejection rates. Furthermore, a judicious choice of proposal distribution can lead to geometric ergodicity in scenarios where probability concentrates on narrower tails, which is not the case for the Random Walk Metropolis.
