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Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the…
Using the framework of weak Poincar\'{e} inequalities, we analyze the convergence properties of deterministic-scan Metropolis-within-Gibbs samplers, an important class of Markov chain Monte Carlo algorithms. Our analysis applies to…
I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression…
Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
Kelly (2007, hereafter K07) described an efficient algorithm, using Gibbs sampling, for performing linear regression in the fairly general case where non-zero measurement errors exist for both the covariates and response variables, where…
We present a modified Gibbs sampler for general state spaces. We establish that this modification can lead to substantial gains in statistical efficiency while maintaining the overall quality of convergence. We illustrate our results in two…
In Smyl et al. [Local and global trend Bayesian exponential smoothing models. International Journal of Forecasting, 2024.], a generalised exponential smoothing model was proposed that is able to capture strong trends and volatility in time…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…
Dependent generalized extreme value (dGEV) models have attracted much attention due to the dependency structure that often appears in real datasets. To construct a dGEV model, a natural approach is to assume that some parameters in the…
Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
Variational Inference (VI) provides a scalable framework for Bayesian inference by optimizing the Evidence Lower Bound (ELBO), but convergence analysis remains challenging due to the objective's non-convexity and non-smoothness in Euclidean…
We incorporate heteroskedasticity into Bayesian Additive Regression Trees (BART) by modeling the log of the error variance parameter as a linear function of prespecified covariates. Under this scheme, the Gibbs sampling procedure for the…
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct…
Gaussian Boson Sampling (GBS) have shown advantages over classical methods for performing some specific sampling tasks. To fully harness the computational power of GBS, there has been great interest in identifying their practical…
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…
This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…