Related papers: Weakly informative priors and prior-data conflict …
Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
This paper introduces a framework for incorporating prior information into the design of sequential experiments. These sources may include past experiments, expert opinions, or the experimenter's intuition. We model the problem using a…
Historical data from previous clinical trials, observational studies and health records may be utilized in analysis of clinical trials data to strengthen inference. Under the Bayesian framework incorporation of information obtained from any…
PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution $\rho$ to its empirical risk and to its Kullback-Leibler divergence with…
Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…
Given the joint chances of a pair of random variables one can compute quantities of interest, like the mutual information. The Bayesian treatment of unknown chances involves computing, from a second order prior distribution and the data…
Improper priors are not allowed for the computation of the Bayesian evidence $Z=p({\bf y})$ (a.k.a., marginal likelihood), since in this case $Z$ is not completely specified due to an arbitrary constant involved in the computation. However,…
Updating $\textit{a priori}$ information given some observed data is the core tenet of Bayesian inference. Bayesian transfer learning extends this idea by incorporating information from a related dataset to improve the inference on the…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been…
We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a…
Including prior information about model parameters is a fundamental step of any Bayesian statistical analysis. It is viewed positively by some as it allows, among others, to quantitatively incorporate expert opinion about model parameters.…
This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…
Bayesian model comparison relies upon the model evidence, yet for many models of interest the model evidence is unavailable in closed form and must be approximated. Many of the estimators for evidence that have been proposed in the Monte…
Comparison of appropriate models to describe observational data is a fundamental task of science. The Bayesian model evidence, or marginal likelihood, is a computationally challenging, yet crucial, quantity to estimate to perform Bayesian…
Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…
Model uncertainty is pervasive in real world analysis situations and is an often-neglected issue in applied statistics. However, standard approaches to the research process do not address the inherent uncertainty in model building and,…