Related papers: Conditional fiducial models
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
Constraint-based causal discovery methods leverage conditional independence tests to infer causal relationships in a wide variety of applications. Just as the majority of machine learning methods, existing work focuses on studying…
An established and growing literature on generalized fiducial inference and related fiducial ideas points to the adoption of fiducial inference as a mainstream perspective among modern statisticians. Like Bayesian posteriors, generalized…
Bounded-confidence models in social dynamics describe multi-agent systems, where each individual interacts only locally with others. Several models are written as systems of ordinary differential equations with discontinuous right-hand…
Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both…
We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects…
What is the difference of a prediction that is made with a causal model and a non-causal model? Suppose we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
This paper explores the challenges of constructing suitable inferential models in scenarios where the parameter of interest is determined in light of the data, such as regression after variable selection. Two compelling arguments for…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model…
Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such…
We consider the problem of estimating a particular type of linear non-Gaussian model. Without resorting to the overcomplete Independent Component Analysis (ICA), we show that under some mild assumptions, the model is uniquely identified by…
Fiducial Inference, introduced by Fisher in the 1930s, has a long history, which at times aroused passionate disagreements. However, its application has been largely confined to relatively simple parametric problems. In this paper, we…
This is the guest editors' general introduction to a Special Issue of the Journal of Statistical Planning and Inference, dedicated to confidence distributions and related themes. Confidence distributions (CDs) are distributions for…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to…
Algorithms for constraint-based causal discovery select graphical causal models among a space of possible candidates (e.g., all directed acyclic graphs) by executing a sequence of conditional independence tests. These may be used to inform…