Related papers: Asymptotic Properties of Approximate Bayesian Comp…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

Approximate Bayesian computation (ABC) performs statistical inference for otherwise intractable probability models by accepting parameter proposals when corresponding simulated datasets are sufficiently close to the observations. Producing…

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Regression models for continuous outcomes often require a transformation of the outcome, which the user either specify {\it a priori} or estimate from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the…