Related papers: Bayes' Theorem under Conditional Independence

The estimation of causal effects using quasiexperiments often relies on the use of unusual or serendipitous sources of exogenous variation. When the goal is estimating the same causal effects across many different settings, the same unusual…

We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…

Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…

Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able…

We demonstrate how to test for conditional independence of two variables with categorical data using Poisson log-linear models. The size of the conditioning set of variables can vary from 0 (simple independence) up to many variables. We…

We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the…

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…

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 and nonlinear measures of statistical dependence between pairs of random variables are important tools in modern data analysis. In particular the emergence of large data sets can now support the relaxation of linearity…

In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models…

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for…

Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…

This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…

It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…

We describe Bayesian inference for the parameters of Gaussian models of bounded data protected by differential privacy. Using this setting, we demonstrate that analysts can and should take constraints imposed by the bounds into account when…

The very expressiveness of Bayesian networks can introduce fresh challenges due to the large number of relationships they often model. In many domains, it is thus often essential to supplement any available data with elicited expert…