Related papers: Reference prior for Bayesian estimation of seismic…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
These notes introduce the theory of susceptibilities as developed in [arXiv:2504.18274, arXiv:2601.12703] for interpreting neural networks. The susceptibility of an observable $\phi$ to a data perturbation is defined as a derivative of a…
When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…
Full waveform inversion (FWI) is an advanced seismic inversion technique for quantitatively estimating subsurface properties. However, with FWI, it is hard to converge to a geologically-realistic subsurface model. Thus, we propose a…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Regression models with fat-tailed error terms are an increasingly popular choice to obtain more robust inference to the presence of outlying observations. This article focuses on Bayesian inference for the Student-$t$ linear regression…
Rapid and accurate estimation of post-earthquake ground failures and building damage is critical for effective post-disaster responses. Progression in remote sensing technologies has paved the way for rapid acquisition of detailed,…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…
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…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…
Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…
Expected-posterior priors (EPP) have been proved to be extremely useful for testing hypothesis on the regression coefficients of normal linear models. One of the advantages of using EPPs is that impropriety of baseline priors causes no…
Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…
Informative Bayesian priors are often difficult to elicit, and when this is the case, modelers usually turn to noninformative or objective priors. However, objective priors such as the Jeffreys and reference priors are not tractable to…
Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a…
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…