Related papers: General sample size analysis for probabilities of …
Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a…
The delta method creates more general inference results when coupled with central limit theorem results for the finite population. This opens up a range of new estimators for which we can find finite population asymptotic properties. We…
We discuss the problem of estimating the number of principal components in Principal Com- ponents Analysis (PCA). Despite of the importance of the problem and the multitude of solutions proposed in the literature, it comes as a surprise…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
This paper investigates the theoretical foundation and develops analytical formulas for sample size and power calculations for causal inference with observational data. By analyzing the variance of an inverse probability weighting estimator…
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…
In this paper, we develop an approach for the exact determination of the minimum sample size for the estimation of a Poisson parameter with prescribed margin of error and confidence level. The exact computation is made possible by reducing…
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
Most clinical trials conducted in drug development contain multiple endpoints in order to collectively assess the intended effects of the drug on various disease characteristics. Focusing on the estimation of the global win probability,…
Probabilities of causation play a crucial role in modern decision-making. This paper addresses the challenge of predicting probabilities of causation for subpopulations with insufficient data using machine learning models. Tian and Pearl…
Let $\theta_0,\theta_1 \in \mathbb{R}^d$ be the population risk minimizers associated to some loss $\ell:\mathbb{R}^d\times \mathcal{Z}\to\mathbb{R}$ and two distributions $\mathbb{P}_0,\mathbb{P}_1$ on $\mathcal{Z}$. The models…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Probabilities of causation play a central role in modern decision making. Tian and Pearl first introduced formal definitions and derived tight bounds for three binary probabilities of causation, such as the probability of necessity and…
This paper deals with the problem of learning the probabilities of causation of subpopulations given finite population data. The tight bounds of three basic probabilities of causation, the probability of necessity and sufficiency (PNS), the…
In prior work we have introduced an asymptotic threshold of sufficient randomness for causal inference from observational data. In this paper we extend that prior work in three main ways. First, we show how to empirically estimate a lower…
This paper deals with the problem of estimating the probabilities of causation when treatment and effect are not binary. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of…
Sample size derivation is a crucial element of the planning phase of any confirmatory trial. A sample size is typically derived based on constraints on the maximal acceptable type I error rate and a minimal desired power. Here, power…