Related papers: General sample size analysis for probabilities of …
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i =…
We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be…
Bayesian predictive probabilities of success (PPoS) use interim trial data to calculate the probability of trial success. These quantities can be used to optimize trial size or to stop for futility. In this paper, we describe a…
Principal stratification (PS) is a commonly used approach for understanding the mechanisms through which a treatment affects an outcome. The goal of this work is to extend the PS framework to studies with continuous treatments, which…
We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify…
In many settings, robust data analysis involves computational methods for uncertainty quantification and statistical inference. To design frequentist studies that leverage robust analysis methods, suitable sample sizes to achieve desired…
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
When evaluating the performance of a model for individualised risk prediction, the sample size needs to be large enough to precisely estimate the performance measures of interest. Current sample size guidance is based on precisely…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
In recent years, research unveiled more and more evidence for the so-called Bayesian Brain Paradigm, i.e. the human brain is interpreted as a probabilistic inference machine and Bayesian modelling approaches are hence used successfully. One…
In systematic reviews and meta-analysis, researchers often pool the results of the sample mean and standard deviation from a set of similar clinical trials. A number of the trials, however, reported the study using the median, the minimum…
In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal…
We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…
Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to…
Decisions about health interventions are often made using limited evidence. Mathematical models used to inform such decisions often include uncertainty analysis to account for the effect of uncertainty in the current evidence base on…
We study the convergence of probability measures in terms of moments by applying operators to their Bessel generating functions. We consider a general setting of applying operators such as the Dunkl operator to formal power series that are…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…