Related papers: Posterior Adaptation With New Priors

In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by…

How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators.…

We present a new model and methods for the posterior drift problem where the regression function in the target domain is modeled as a linear adjustment (on an appropriate scale) of that in the source domain, an idea that inherits the…

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…

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments…

Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…

An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…

We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…

We propose a score-based generative algorithm for sampling from power-scaled priors and likelihoods within the Bayesian inference framework. Our algorithm enables flexible control over prior-likelihood influence without requiring retraining…

We obtain rates of contraction of posterior distributions in inverse problems defined by scales of smoothness classes. We derive abstract results for general priors, with contraction rates determined by Galerkin approximation. The rate…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…