Related papers: On the Probability of Immunity
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
This paper examines a commonly used measure of persuasion whose precise interpretation has been obscure in the literature. By using the potential outcome framework, we define the causal persuasion rate by a proper conditional probability of…
We consider $N$ events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Nonignorable missingness and noncompliance can occur even in well-designed randomized experiments making the intervention effect that the experiment was designed to estimate nonidentifiable. Nonparametric causal bounds provide a way to…
Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…
In this chapter, we review the class of causal effects based on incremental propensity scores interventions proposed by Kennedy [2019]. The aim of incremental propensity score interventions is to estimate the effect of increasing or…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
Turing's estimator allows one to estimate the probabilities of outcomes that either do not appear or only rarely appear in a given random sample. We perform a simulation study to understand the finite sample performance of several related…
An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…
In situations with non-manipulable exposures, interventions can be targeted to shift the distribution of intermediate variables between exposure groups to define interventional disparity indirect effects. In this work, we present a…
We show that if the exposure and the outcome affect the selection indicator in the same direction and have non-positive interaction on the risk difference, risk ratio or odds ratio scale, the exposure-outcome odds ratio in the selected…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
Inferring the causal effect of a non-randomly assigned exposure on an outcome requires adjusting for common causes of the exposure and outcome to avoid biased conclusions. Notwithstanding the efforts investigators routinely make to measure…
In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…
We propose a novel definition of selection bias in analytic epidemiology using potential outcomes. This definition captures selection bias under both the structural approach (where conditioning on selection into the study opens a noncausal…
In this work, we propose an approach for assessing sensitivity to unobserved confounding in studies with multiple outcomes. We demonstrate how prior knowledge unique to the multi-outcome setting can be leveraged to strengthen causal…