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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…

Difference-in-differences (DiD) is the most popular observational causal inference method in health policy, employed to evaluate the real-world impact of policies and programs. To estimate treatment effects, DiD relies on the "parallel…

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…

Representing uncertainty in causal discovery is a crucial component for experimental design, and more broadly, for safe and reliable causal decision making. Bayesian Causal Discovery (BCD) offers a principled approach to encapsulating this…

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

Complex simulators have become a ubiquitous tool in many scientific disciplines, providing high-fidelity, implicit probabilistic models of natural and social phenomena. Unfortunately, they typically lack the tractability required for…

Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin…

High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…

This work proposes $\mu$GUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or MRI signal representation, with exemplar demonstration in…

Unmeasured confounding is a key threat to reliable causal inference based on observational studies. Motivated from two powerful natural experiment devices, the instrumental variables and difference-in-differences, we propose a new method…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

A novel method is proposed for the exact posterior mean and covariance of the random effects given the response in a generalized linear mixed model (GLMM) when the response does not follow normal. The research solves a long-standing problem…

In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…

Real-world problems, often couched as machine learning applications, involve quantities of interest that have real-world meaning, independent of any statistical model. To avoid potential model misspecification bias or over-complicating the…

Causal inference is a critical research area with multi-disciplinary origins and applications, ranging from statistics, computer science, economics, psychology to public health. In many scientific research, randomized experiments provide a…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty.…

The Bayesian posterior minimizes the "inferential risk" which itself bounds the "predictive risk". This bound is tight when the likelihood and prior are well-specified. However since misspecification induces a gap, the Bayesian posterior…