Related papers: Post-Inference Prior Swapping
We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on…
Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Modern predictive systems encode beliefs that can act as useful prior information for statistical inference in data-limited settings. Using them for prior construction introduces a tradeoff: an informative prior built from a predictive…
Inference is an integral part of probabilistic topic models, but is often non-trivial to derive an efficient algorithm for a specific model. It is even much more challenging when we want to find a fast inference algorithm which always…
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…
We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…
There has been much recent interest in modifying Bayesian inference for misspecified models so that it is useful for specific purposes. One popular modified Bayesian inference method is "cutting feedback" which can be used when the model…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
A partially identified model, where the parameters can not be uniquely identified, often arises during statistical analysis. While researchers frequently use Bayesian inference to analyze the models, when Bayesian inference with an…
The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its…
The authors derive likelihood-based exact inference methods for the multivariate regression model, for singly imputed synthetic data generated via Posterior Predictive Sampling (PPS) and for multiply imputed synthetic data generated via a…
Bayesian inference can often be sensitive to the choice of hyperparameters of the prior or likelihood, yet defining and quantifying this sensitivity in a principled and computationally feasible way remains challenging in practice.…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
We propose a surrogate function for efficient yet principled use of score-based priors in Bayesian imaging. We consider ill-posed inverse imaging problems in which one aims for a clean image posterior given incomplete or noisy measurements.…
It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides…
We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional…