相关论文: Akaike's Bayesian information criterion (ABIC) or …

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The…

This paper considers the problem of approximating a density when it can be evaluated up to a normalizing constant at a limited number of points. We call this problem the Boltzmann approximation (BA) problem. The BA problem is ubiquitous in…

We consider a model selection problem for structural equation modeling (SEM) with latent variables for diffusion processes based on high-frequency data. First, we propose the quasi-Akaike information criterion of the SEM and study the…

Evaluation of the marginal likelihood plays an important role in model selection problems. The widely applicable Bayesian information criterion (WBIC) and singular Bayesian information criterion (sBIC) give approximations to the log…

Variable selection is essential for improving inference and interpretation in multivariate linear regression. Although a number of alternative regressor selection criteria have been suggested, the most prominent and widely used are the…

Statistical uncertainties are rarely incorporated in machine learning algorithms, especially for anomaly detection. Here we present the Bayesian Anomaly Detection And Classification (BADAC) formalism, which provides a unified statistical…

One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground…

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…

The upper bound earthquake magnitude (maximum possible magnitude) of a truncated Gutenberg-Richter relation is the right truncation point (right end-point) of a truncated exponential distribution and is important in the probabilistic…

Methods for combining predictions from different models in a supervised learning setting must somehow estimate/predict the quality of a model's predictions at unknown future inputs. Many of these methods (often implicitly) make the…

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the…

We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…

Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…

To determine the exact shape of the luminosity function (LF) of galaxies is one of the central problems in galactic astronomy and observational cosmology. The most popular method to estimate the LF is maximum likelihood, which is clearly…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…