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We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the…

Computational Finance · Quantitative Finance 2009-07-14 Tetsuya Takaishi

Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…

Instrumentation and Methods for Astrophysics · Physics 2026-04-09 Bo Liang , Chang Liu , Hanlin Song , Tianyu Zhao , Minghui Du , He Wang , Haohao Gu , Sensen He , Yuxiang Xu , Wei-Liang Qian , Li-e Qiang , Peng Xu , Ziren Luo , Mingming Sun

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…

Methodology · Statistics 2021-11-19 Yuling Yao , Aki Vehtari , Andrew Gelman

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability…

Numerical Analysis · Mathematics 2021-03-17 Yating Wang , Wei Deng , Guang Lin

In large-scale genomic applications vast numbers of molecular features are scanned in order to find a small number of candidates which are linked to a particular disease or phenotype. This is a variable selection problem in the "large p,…

Computation · Statistics 2014-02-13 Manuela Zucknick , Sylvia Richardson

In the quest for scalable Bayesian computational algorithms we need to exploit the full potential of existing methodologies. In this note we point out that message passing algorithms, which are very well developed for inference in graphical…

Computation · Statistics 2017-09-05 Omiros Papaspiliopoulos , Giacomo Zanella

This paper presents a study using the Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors in the…

Applications · Statistics 2017-12-07 David S. Dias , Ricardo S. Ehlers

We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the…

Computational Finance · Quantitative Finance 2014-08-06 Ting Ting Chen , Tetsuya Takaishi

We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the…

Statistics Theory · Mathematics 2019-09-04 Jimmy Olsson , Tetyana Pavlenko , Felix L. Rios

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…

Applications · Statistics 2017-03-22 Hélène Ruffieux , Anthony C. Davison , Jörg Hager , Irina Irincheeva

This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…

Methodology · Statistics 2018-06-01 Florian Maire , Nial Friel , Pierre Alquier

The increasing size of data sets has lead to variable selection in regression becoming increasingly important. Bayesian approaches are attractive since they allow uncertainty about the choice of variables to be formally included in the…

Computation · Statistics 2014-12-30 Jim Griffin , Krzysztof Latuszynski , Mark Steel

For modeling multivariate financial time series we propose a single factor copula model together with stochastic volatility margins. This model generalizes single factor models relying on the multivariate normal distribution and allows for…

Computation · Statistics 2019-07-22 Alexander Kreuzer , Claudia Czado

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…

Machine Learning · Statistics 2014-03-31 Elaine Angelino , Eddie Kohler , Amos Waterland , Margo Seltzer , Ryan P. Adams

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

Statistics Theory · Mathematics 2016-05-04 Julyan Arbel , Antonio Lijoi , Bernardo Nipoti

Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an…

Computation · Statistics 2023-08-02 Antonios Kamariotis , Luca Sardi , Iason Papaioannou , Eleni Chatzi , Daniel Straub

We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…

Machine Learning · Statistics 2014-11-04 Tom Gunter , Michael A. Osborne , Roman Garnett , Philipp Hennig , Stephen J. Roberts

Bayesian variable selection requires sampling from a posterior distribution that combines discrete model indicators with continuously varying parameters, a challenge often addressed through reversible jump Markov chain Monte Carlo (RJMCMC).…

Methodology · Statistics 2026-05-01 Don van den Bergh , Merlise A. Clyde , Adrian E. Raftery , Maarten Marsman

Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic…

Machine Learning · Statistics 2018-12-05 Ed Wagstaff , Saad Hamid , Michael Osborne

We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in…

Computation · Statistics 2026-05-18 Augusto Fasano , Giovanni Rebaudo
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