Related papers: A full Bayesian approach for inverse problems
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…
Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…
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…
We can perform inference in Bayesian belief networks by enumerating instantiations with high probability thus approximating the marginals. In this paper, we present a method for determining the fraction of instantiations that has to be…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
Most methods in explainable AI (XAI) focus on providing reasons for the prediction of a given set of features. However, we solve an inverse explanation problem, i.e., given the deviation of a label, find the reasons of this deviation. We…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…
We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
The Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solutions, the classical estimators such as the maximum a…
We consider the problem of estimating a parameter associated to a Bayesian inverse problem. Treating the unknown initial condition as a nuisance parameter, typically one must resort to a numerical approximation of gradient of the…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…