Related papers: The How and Why of Bayesian Nonparametric Causal I…

Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…

Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of…

Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian…

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks,…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number…

Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…

Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…