Related papers: Iterative Posterior Inference for Bayesian Kriging
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
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…
Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
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…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
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…
We propose and evaluate an iterative localization mechanism employing Bayesian inference to estimate the position of a target using received signal strength measurements. The probability density functions of the target's coordinates are…
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…
Noninformative priors constructed for estimation purposes are usually not appropriate for model selection and testing. The methodology of integral priors was developed to get prior distributions for Bayesian model selection when comparing…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…