Related papers: Valid and efficient imprecise-probabilistic infere…
Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…
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…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
The inferential model (IM) framework offers an alternative to the classical probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. A key distinction is that classical uncertainty quantification…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human…
Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…
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…
Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…
In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…