相关论文: Gibbs posterior convergence and the thermodynamic …

Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications and it is not straightforward to sample directly from the…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…

In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of…

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty.…

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…

Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

We consider Gibbs samplers for a normal linear regression model with a global-local shrinkage prior and show that they produce geometrically ergodic Markov chains. First, under the horseshoe local prior and a three-parameter beta global…

In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…

In this paper, we present the Bayesian inference procedures for the parameters of the multivariate random effects model derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…