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One of the major problems in adaptive filtering is the problem of system identification. It has been studied extensively due to its immense practical importance in a variety of fields. The underlying goal is to identify the impulse response…
Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target…
This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a sampling algorithm that seeks to adapt proposals to the local geometry of the posterior distribution. The specific form of the Hamiltonian used in RMHMC necessitates {\it…
Over decades, Markov chain Monte Carlo (MCMC) methods have been widely studied, with a typical application being the quantification of posterior uncertainties in Bayesian system identification of structural dynamic models. To address the…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
Informed Markov chain Monte Carlo (MCMC) methods have been proposed as scalable solutions to Bayesian posterior computation on high-dimensional discrete state spaces, but theoretical results about their convergence behavior in general…
Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for…
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…
Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…
Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. This paper presents the…
Markov Chain Monte Carlo (MCMC) excels at sampling complex posteriors but traditionally lags behind nested sampling in accurate evidence estimation, which is crucial for model comparison in astrophysical problems. We introduce reddemcee, an…
Quantile regression has received increased attention in the statistics community in recent years. This article adapts an auxiliary variable method, commonly used in Bayesian variable selection for mean regression models, to the fitting of…