Related papers: Bayesian, classical and hybrid methods of inferenc…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…
Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…
Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural…
Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently…
In Bayesian meta-analysis, the specification of prior probabilities for the between-study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…
Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…
Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…
We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance…
A common strategy for inference in complex models is the relaxation of a simple model into the more complex target model, for example the prior into the posterior in Bayesian inference. Existing approaches that attempt to generate such…