Related papers: Large Deviation Asymptotics and Bayesian Posterior…

This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on…

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…

In this paper, we consider Bayesian inference on a class of multivariate median and the multivariate quantile functionals of a joint distribution using a Dirichlet process prior. Since, unlike univariate quantiles, the exact posterior…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of…

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…

The sampling efficiency of MCMC methods in Bayesian inference for stochastic volatility (SV) models is known to highly depend on the actual parameter values, and the effectiveness of samplers based on different parameterizations varies…

We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such…

Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical…

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.