Related papers: Misspecification in infinite-dimensional Bayesian …
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that "all models are wrong", but little formal guidance exists on how to…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…
The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise.…
We investigate Bayes posterior distributions in high-dimensional generalized linear models (GLMs) under the proportional asymptotics regime, where the number of features and samples diverge at a comparable rate. Specifically, we…
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…
We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior…
The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…
In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured,…
In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution,…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate representation employing its…
Model misspecification constitutes a major obstacle to reliable inference in many inverse problems. Inverse problems in seismology, for example, are particularly affected by misspecification of wave propagation velocities. In this paper, we…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
We study Bayesian posterior consistency in parametric density models with proper priors, challenging the perception that the problem is settled. Classical results established consistency via MLE convergence under regularity and…