Abstract: Advances in Markov chain Monte Carlo in the past 30 years have made Bayesian analysis a routine practice. However, there is virtually no practice of performing Monte Carlo integration from the Bayesian perspective; indeed,this problem has earned the “paradox” label in the context of computing normalizing constants (Wasserman, 2013). We first use the modeling-what-we-ignore idea of Kong et al. (2003) to explain that the crux of the paradox is not with the likelihood theory, which is essentially the same…

Abstract:   In the last two decades, ambient levels of air pollution have declined substantially. Yet, as mandated by the Clean Air Act, we must continue to address the following question: is exposure to levels of air pollution that are well below the National Ambient Air Quality Standards (NAAQS) harmful to human health? Furthermore, the highly contentious nature surrounding environmental regulations necessitates casting this question within a causal inference framework. Several parametric and semi-parametric regression modeling approaches have been used to…

Abstract: In many applications, there are natural statistical models with interpretable parameters that provide insight into questions of interest. While useful, these models are almost always wrong in the sense that they only approximate the true data generating process. In some cases, it is important to account for this model error when quantifying uncertainty in the parameters. We propose to model the distribution of the observed data as a perturbation of an idealized model of interest by using a nonparametric…

Abstract: The finite element method (FEM) is one of the great triumphs of modern day applied mathematics, numerical analysis and software development. Every area of the sciences and engineering has been positively impacted by the ability to model and study complex physical and natural systems described by systems of partial differential equations (PDE) via the FEM . In parallel the recent developments in sensor, measurement, and signalling technologies enables the phenomenological study of systems as diverse as protein signalling in the…